//chapter3 section 3 group 1 graph_linear_equations_inequalities_two_variables //
var mc_graph_linear_equations_inequalities_two_variables_max_count = 4;
var mc_graph_linear_equations_inequalities_two_variables_1 = 'Which of the following are linear equations?';
var choice1_mc_graph_linear_equations_inequalities_two_variables_1 = '3x + 4y = 12';
var answer_choice1_mc_graph_linear_equations_inequalities_two_variables_1 = 'true';
var right_answer_choice1_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice1_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice2_mc_graph_linear_equations_inequalities_two_variables_1 = '7x - 2 = 0';
var answer_choice2_mc_graph_linear_equations_inequalities_two_variables_1 = 'true';
var right_answer_choice2_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice2_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice3_mc_graph_linear_equations_inequalities_two_variables_1 = '5x<sup>2</sup> - 2x + 9 = 0';
var answer_choice3_mc_graph_linear_equations_inequalities_two_variables_1 = 'false';
var right_answer_choice3_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice3_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice4_mc_graph_linear_equations_inequalities_two_variables_1 = '2x + 7y = 2y - 8x + 4';
var answer_choice4_mc_graph_linear_equations_inequalities_two_variables_1 = 'true';
var right_answer_choice4_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice4_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice5_mc_graph_linear_equations_inequalities_two_variables_1 = '|3x + 5| = 9';
var answer_choice5_mc_graph_linear_equations_inequalities_two_variables_1 = 'false';
var right_answer_choice5_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice5_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice6_mc_graph_linear_equations_inequalities_two_variables_1 = '7xy - 2 = 0';
var answer_choice6_mc_graph_linear_equations_inequalities_two_variables_1 = 'false';
var right_answer_choice6_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice6_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice7_mc_graph_linear_equations_inequalities_two_variables_1 = '7x + 5 < 2';
var answer_choice7_mc_graph_linear_equations_inequalities_two_variables_1 = 'false';
var right_answer_choice7_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice7_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice8_mc_graph_linear_equations_inequalities_two_variables_1 = 'x - y = 4y + 2x';
var answer_choice8_mc_graph_linear_equations_inequalities_two_variables_1 = 'true';
var right_answer_choice8_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice8_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice9_mc_graph_linear_equations_inequalities_two_variables_1 = '<img src="../../image/equation1_small.gif">';
var answer_choice9_mc_graph_linear_equations_inequalities_two_variables_1 = 'false';
var right_answer_choice9_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice9_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice10_mc_graph_linear_equations_inequalities_two_variables_1 = '<img src="../../image/equation2_small.gif">';
var answer_choice10_mc_graph_linear_equations_inequalities_two_variables_1 = 'true';
var right_answer_choice10_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice10_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice11_mc_graph_linear_equations_inequalities_two_variables_1 = '<img src="../../image/equation3_small.gif">';
var answer_choice11_mc_graph_linear_equations_inequalities_two_variables_1 = 'false';
var right_answer_choice11_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice11_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice12_mc_graph_linear_equations_inequalities_two_variables_1 = '<img src="../../image/equation4_small.gif">';
var answer_choice12_mc_graph_linear_equations_inequalities_two_variables_1 = 'false';
var right_answer_choice12_mc_graph_linear_equations_inequalities_two_variables_1 = 'Correct: ';
var wrong_answer_choice12_mc_graph_linear_equations_inequalities_two_variables_1 = 'Incorrect:  ';

var choice_count_mc_graph_linear_equations_inequalities_two_variables_1 = 12;

var mc_graph_linear_equations_inequalities_two_variables_2 = 'Which of the following are linear equations in one variable?';
var choice1_mc_graph_linear_equations_inequalities_two_variables_2 = '3x + 4y = 12';
var answer_choice1_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice1_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice1_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice2_mc_graph_linear_equations_inequalities_two_variables_2 = '7x - 2 = 0';
var answer_choice2_mc_graph_linear_equations_inequalities_two_variables_2 = 'true';
var right_answer_choice2_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice2_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice3_mc_graph_linear_equations_inequalities_two_variables_2 = '5x<sup>2</sup> - 2x + 9 = 0';
var answer_choice3_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice3_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice3_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice4_mc_graph_linear_equations_inequalities_two_variables_2 = '2x + 7y = 2y - 8x + 4';
var answer_choice4_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice4_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice4_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice5_mc_graph_linear_equations_inequalities_two_variables_2 = '|3x + 5| = 9';
var answer_choice5_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice5_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice5_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice6_mc_graph_linear_equations_inequalities_two_variables_2 = '7xy - 2 = 0';
var answer_choice6_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice6_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice6_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice7_mc_graph_linear_equations_inequalities_two_variables_2 = '7x + 5 < 2';
var answer_choice7_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice7_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice7_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice8_mc_graph_linear_equations_inequalities_two_variables_2 = 'x - y = 4y + 2x';
var answer_choice8_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice8_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice8_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice9_mc_graph_linear_equations_inequalities_two_variables_2 = '<img src="../../image/equation1_small.gif">';
var answer_choice9_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice9_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice9_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice10_mc_graph_linear_equations_inequalities_two_variables_2 = '<img src="../../image/equation2_small.gif">';
var answer_choice10_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice10_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice10_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice11_mc_graph_linear_equations_inequalities_two_variables_2 = '<img src="../../image/equation3_small.gif">';
var answer_choice11_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice11_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice11_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice12_mc_graph_linear_equations_inequalities_two_variables_2 = '<img src="../../image/equation4_small.gif">';
var answer_choice12_mc_graph_linear_equations_inequalities_two_variables_2 = 'false';
var right_answer_choice12_mc_graph_linear_equations_inequalities_two_variables_2 = 'Correct: ';
var wrong_answer_choice12_mc_graph_linear_equations_inequalities_two_variables_2 = 'Incorrect:  ';

var choice_count_mc_graph_linear_equations_inequalities_two_variables_2 = 12;

var mc_graph_linear_equations_inequalities_two_variables_3 = 'Which of the following are linear equations in two variables?';
var choice1_mc_graph_linear_equations_inequalities_two_variables_3 = '3x + 4y = 12';
var answer_choice1_mc_graph_linear_equations_inequalities_two_variables_3 = 'true';
var right_answer_choice1_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice1_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice2_mc_graph_linear_equations_inequalities_two_variables_3 = '7x - 2 = 0';
var answer_choice2_mc_graph_linear_equations_inequalities_two_variables_3 = 'false';
var right_answer_choice2_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice2_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice3_mc_graph_linear_equations_inequalities_two_variables_3 = '5x<sup>2</sup> - 2x + 9 = 0';
var answer_choice3_mc_graph_linear_equations_inequalities_two_variables_3 = 'false';
var right_answer_choice3_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice3_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice4_mc_graph_linear_equations_inequalities_two_variables_3 = '2x + 7y = 2y - 8x + 4';
var answer_choice4_mc_graph_linear_equations_inequalities_two_variables_3 = 'true';
var right_answer_choice4_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice4_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice5_mc_graph_linear_equations_inequalities_two_variables_3 = '|3x + 5| = 9';
var answer_choice5_mc_graph_linear_equations_inequalities_two_variables_3 = 'false';
var right_answer_choice5_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice5_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice6_mc_graph_linear_equations_inequalities_two_variables_3 = '7xy - 2 = 0';
var answer_choice6_mc_graph_linear_equations_inequalities_two_variables_3 = 'false';
var right_answer_choice6_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice6_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice7_mc_graph_linear_equations_inequalities_two_variables_3 = '7x + 5 < 2';
var answer_choice7_mc_graph_linear_equations_inequalities_two_variables_3 = 'false';
var right_answer_choice7_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice7_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice8_mc_graph_linear_equations_inequalities_two_variables_3 = 'x - y = 4y + 2x';
var answer_choice8_mc_graph_linear_equations_inequalities_two_variables_3 = 'true';
var right_answer_choice8_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice8_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice9_mc_graph_linear_equations_inequalities_two_variables_3 = '<img src="../../image/equation1_small.gif">';
var answer_choice9_mc_graph_linear_equations_inequalities_two_variables_3 = 'false';
var right_answer_choice9_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice9_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice10_mc_graph_linear_equations_inequalities_two_variables_3 = '<img src="../../image/equation2_small.gif">';
var answer_choice10_mc_graph_linear_equations_inequalities_two_variables_3 = 'true';
var right_answer_choice10_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice10_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice11_mc_graph_linear_equations_inequalities_two_variables_3 = '<img src="../../image/equation3_small.gif">';
var answer_choice11_mc_graph_linear_equations_inequalities_two_variables_3 = 'false';
var right_answer_choice11_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice11_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice12_mc_graph_linear_equations_inequalities_two_variables_3 = '<img src="../../image/equation4_small.gif">';
var answer_choice12_mc_graph_linear_equations_inequalities_two_variables_3 = 'false';
var right_answer_choice12_mc_graph_linear_equations_inequalities_two_variables_3 = 'Correct: ';
var wrong_answer_choice12_mc_graph_linear_equations_inequalities_two_variables_3 = 'Incorrect:  ';

var choice_count_mc_graph_linear_equations_inequalities_two_variables_3 = 12;

var mc_graph_linear_equations_inequalities_two_variables_4 = 'Which of the following are solutions of 3x + 2y = 6?';
var choice1_mc_graph_linear_equations_inequalities_two_variables_4 = '(3,2)';
var answer_choice1_mc_graph_linear_equations_inequalities_two_variables_4 = 'false';
var right_answer_choice1_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice1_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice2_mc_graph_linear_equations_inequalities_two_variables_4 = '2';
var answer_choice2_mc_graph_linear_equations_inequalities_two_variables_4 = 'false';
var right_answer_choice2_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice2_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice3_mc_graph_linear_equations_inequalities_two_variables_4 = '(0, 3)';
var answer_choice3_mc_graph_linear_equations_inequalities_two_variables_4 = 'true';
var right_answer_choice3_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice3_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice4_mc_graph_linear_equations_inequalities_two_variables_4 = '(-2, 0)';
var answer_choice4_mc_graph_linear_equations_inequalities_two_variables_4 = 'false';
var right_answer_choice4_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice4_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice5_mc_graph_linear_equations_inequalities_two_variables_4 = '(1, <img src="../../image/3over2_small.gif">)';
var answer_choice5_mc_graph_linear_equations_inequalities_two_variables_4 = 'true';
var right_answer_choice5_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice5_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice6_mc_graph_linear_equations_inequalities_two_variables_4 = '(2,0)';
var answer_choice6_mc_graph_linear_equations_inequalities_two_variables_4 = 'true';
var right_answer_choice6_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice6_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice7_mc_graph_linear_equations_inequalities_two_variables_4 = '(-1,<img src="../../image/9over2_small.gif">)';
var answer_choice7_mc_graph_linear_equations_inequalities_two_variables_4 = 'true';
var right_answer_choice7_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice7_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice8_mc_graph_linear_equations_inequalities_two_variables_4 = '(0, 2)';
var answer_choice8_mc_graph_linear_equations_inequalities_two_variables_4 = 'false';
var right_answer_choice8_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice8_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice9_mc_graph_linear_equations_inequalities_two_variables_4 = '(1,1)';
var answer_choice9_mc_graph_linear_equations_inequalities_two_variables_4 = 'false';
var right_answer_choice9_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice9_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice10_mc_graph_linear_equations_inequalities_two_variables_4 = '(<img src="../../image/minus2over3_small.gif">,4)';
var answer_choice10_mc_graph_linear_equations_inequalities_two_variables_4 = 'true';
var right_answer_choice10_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice10_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice11_mc_graph_linear_equations_inequalities_two_variables_4 = '(3, 0)';
var answer_choice11_mc_graph_linear_equations_inequalities_two_variables_4 = 'false';
var right_answer_choice11_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice11_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice12_mc_graph_linear_equations_inequalities_two_variables_4 = '(0,6)';
var answer_choice12_mc_graph_linear_equations_inequalities_two_variables_4 = 'false';
var right_answer_choice12_mc_graph_linear_equations_inequalities_two_variables_4 = 'Correct: ';
var wrong_answer_choice12_mc_graph_linear_equations_inequalities_two_variables_4 = 'Incorrect:  ';

var choice_count_mc_graph_linear_equations_inequalities_two_variables_4 = 12;






//chapter3 section 1 group 1 graph_equations_two_variables //
var mc_graph_equations_two_variables_max_count = 3;
var mc_graph_equations_two_variables_1 = 'Which of the following points are in the first quadrant?';
var choice1_mc_graph_equations_two_variables_1 = '(1, 3)';
var answer_choice1_mc_graph_equations_two_variables_1 = 'true';
var right_answer_choice1_mc_graph_equations_two_variables_1 = 'Correct: ';
var wrong_answer_choice1_mc_graph_equations_two_variables_1 = 'Incorrect:  ';

var choice2_mc_graph_equations_two_variables_1 = '(-3, 5)';
var answer_choice2_mc_graph_equations_two_variables_1 = 'false';
var right_answer_choice2_mc_graph_equations_two_variables_1 = 'Correct: ';
var wrong_answer_choice2_mc_graph_equations_two_variables_1 = 'Incorrect:  ';

var choice3_mc_graph_equations_two_variables_1 = '(-2, -5)';
var answer_choice3_mc_graph_equations_two_variables_1 = 'false';
var right_answer_choice3_mc_graph_equations_two_variables_1 = 'Correct: ';
var wrong_answer_choice3_mc_graph_equations_two_variables_1 = 'Incorrect:  ';

var choice4_mc_graph_equations_two_variables_1 = '(1, 1)';
var answer_choice4_mc_graph_equations_two_variables_1 = 'true';
var right_answer_choice4_mc_graph_equations_two_variables_1 = 'Correct: ';
var wrong_answer_choice4_mc_graph_equations_two_variables_1 = 'Incorrect:  ';

var choice5_mc_graph_equations_two_variables_1 = '(-3, -3)';
var answer_choice5_mc_graph_equations_two_variables_1 = 'false';
var right_answer_choice5_mc_graph_equations_two_variables_1 = 'Correct: ';
var wrong_answer_choice5_mc_graph_equations_two_variables_1 = 'Incorrect:  ';

var choice6_mc_graph_equations_two_variables_1 = '(-k, 4) if k > 0.';
var answer_choice6_mc_graph_equations_two_variables_1 = 'false';
var right_answer_choice6_mc_graph_equations_two_variables_1 = 'Correct: ';
var wrong_answer_choice6_mc_graph_equations_two_variables_1 = 'Incorrect:  ';

var choice7_mc_graph_equations_two_variables_1 = '(-k, 4) if k < 0';
var answer_choice7_mc_graph_equations_two_variables_1 = 'true';
var right_answer_choice7_mc_graph_equations_two_variables_1 = 'Correct: ';
var wrong_answer_choice7_mc_graph_equations_two_variables_1 = 'Incorrect:  ';

var choice8_mc_graph_equations_two_variables_1 = '(-w, -g) if w < 0 and g < 0.';
var answer_choice8_mc_graph_equations_two_variables_1 = 'true';
var right_answer_choice8_mc_graph_equations_two_variables_1 = 'Correct: ';
var wrong_answer_choice8_mc_graph_equations_two_variables_1 = 'Incorrect:  ';

var choice_count_mc_graph_equations_two_variables_1 = 8;

var mc_graph_equations_two_variables_2 = 'Which of the following points are above the x-axis?';
var choice1_mc_graph_equations_two_variables_2 = '(1, 3)';
var answer_choice1_mc_graph_equations_two_variables_2 = 'true';
var right_answer_choice1_mc_graph_equations_two_variables_2 = 'Correct: ';
var wrong_answer_choice1_mc_graph_equations_two_variables_2 = 'Incorrect:  ';

var choice2_mc_graph_equations_two_variables_2 = '(-3, 5)';
var answer_choice2_mc_graph_equations_two_variables_2 = 'true';
var right_answer_choice2_mc_graph_equations_two_variables_2 = 'Correct: ';
var wrong_answer_choice2_mc_graph_equations_two_variables_2 = 'Incorrect:  ';

var choice3_mc_graph_equations_two_variables_2 = '(-2, -5)';
var answer_choice3_mc_graph_equations_two_variables_2 = 'false';
var right_answer_choice3_mc_graph_equations_two_variables_2 = 'Correct: ';
var wrong_answer_choice3_mc_graph_equations_two_variables_2 = 'Incorrect:  ';

var choice4_mc_graph_equations_two_variables_2 = '(1, 1)';
var answer_choice4_mc_graph_equations_two_variables_2 = 'true';
var right_answer_choice4_mc_graph_equations_two_variables_2 = 'Correct: ';
var wrong_answer_choice4_mc_graph_equations_two_variables_2 = 'Incorrect:  ';

var choice5_mc_graph_equations_two_variables_2 = '(-3, -3)';
var answer_choice5_mc_graph_equations_two_variables_2 = 'false';
var right_answer_choice5_mc_graph_equations_two_variables_2 = 'Correct: ';
var wrong_answer_choice5_mc_graph_equations_two_variables_2 = 'Incorrect:  ';

var choice6_mc_graph_equations_two_variables_2 = '(-k, 4) if k > 0.';
var answer_choice6_mc_graph_equations_two_variables_2 = 'true';
var right_answer_choice6_mc_graph_equations_two_variables_2 = 'Correct: ';
var wrong_answer_choice6_mc_graph_equations_two_variables_2 = 'Incorrect:  ';

var choice7_mc_graph_equations_two_variables_2 = '(-k, 4) if k < 0';
var answer_choice7_mc_graph_equations_two_variables_2 = 'true';
var right_answer_choice7_mc_graph_equations_two_variables_2 = 'Correct: ';
var wrong_answer_choice7_mc_graph_equations_two_variables_2 = 'Incorrect:  ';

var choice8_mc_graph_equations_two_variables_2 = '(-w, -g) if w < 0 and g < 0.';
var answer_choice8_mc_graph_equations_two_variables_2 = 'true';
var right_answer_choice8_mc_graph_equations_two_variables_2 = 'Correct: ';
var wrong_answer_choice8_mc_graph_equations_two_variables_2 = 'Incorrect:  ';

var choice_count_mc_graph_equations_two_variables_2 = 8;

var mc_graph_equations_two_variables_3 = 'Which of the following points are below the x-axis?';
var choice1_mc_graph_equations_two_variables_3 = '(1, 3)';
var answer_choice1_mc_graph_equations_two_variables_3 = 'false';
var right_answer_choice1_mc_graph_equations_two_variables_3 = 'Correct: ';
var wrong_answer_choice1_mc_graph_equations_two_variables_3 = 'Incorrect:  ';

var choice2_mc_graph_equations_two_variables_3 = '(-3, 5)';
var answer_choice2_mc_graph_equations_two_variables_3 = 'false';
var right_answer_choice2_mc_graph_equations_two_variables_3 = 'Correct: ';
var wrong_answer_choice2_mc_graph_equations_two_variables_3 = 'Incorrect:  ';

var choice3_mc_graph_equations_two_variables_3 = '(-2, -5)';
var answer_choice3_mc_graph_equations_two_variables_3 = 'true';
var right_answer_choice3_mc_graph_equations_two_variables_3 = 'Correct: ';
var wrong_answer_choice3_mc_graph_equations_two_variables_3 = 'Incorrect:  ';

var choice4_mc_graph_equations_two_variables_3 = '(1, 1)';
var answer_choice4_mc_graph_equations_two_variables_3 = 'false';
var right_answer_choice4_mc_graph_equations_two_variables_3 = 'Correct: ';
var wrong_answer_choice4_mc_graph_equations_two_variables_3 = 'Incorrect:  ';

var choice5_mc_graph_equations_two_variables_3 = '(-3, -3)';
var answer_choice5_mc_graph_equations_two_variables_3 = 'true';
var right_answer_choice5_mc_graph_equations_two_variables_3 = 'Correct: ';
var wrong_answer_choice5_mc_graph_equations_two_variables_3 = 'Incorrect:  ';

var choice6_mc_graph_equations_two_variables_3 = '(-k, 4) if k > 0.';
var answer_choice6_mc_graph_equations_two_variables_3 = 'false';
var right_answer_choice6_mc_graph_equations_two_variables_3 = 'Correct: ';
var wrong_answer_choice6_mc_graph_equations_two_variables_3 = 'Incorrect:  ';

var choice7_mc_graph_equations_two_variables_3 = '(-k, 4) if k < 0';
var answer_choice7_mc_graph_equations_two_variables_3 = 'false';
var right_answer_choice7_mc_graph_equations_two_variables_3 = 'Correct: ';
var wrong_answer_choice7_mc_graph_equations_two_variables_3 = 'Incorrect:  ';

var choice8_mc_graph_equations_two_variables_3 = '(-w, -g) if w < 0 and g < 0.';
var answer_choice8_mc_graph_equations_two_variables_3 = 'true';
var right_answer_choice8_mc_graph_equations_two_variables_3 = 'Correct: ';
var wrong_answer_choice8_mc_graph_equations_two_variables_3 = 'Incorrect:  ';

var choice_count_mc_graph_equations_two_variables_3 = 8;





//chapter3 section 4 group 1 slope_line //
var mc_slope_line_max_count = 1;
var mc_slope_line_1 = 'Which of the following can be written in compact form?';
var choice1_mc_slope_line_1 = 'COMING SOON';
var answer_choice1_mc_slope_line_1 = 'true';
var right_answer_choice1_mc_slope_line_1 = 'Correct: ';
var wrong_answer_choice1_mc_slope_line_1 = 'Incorrect:  ';

var choice2_mc_slope_line_1 = 'COMING sOON';
var answer_choice2_mc_slope_line_1 = 'true';
var right_answer_choice2_mc_slope_line_1 = 'Correct: ';
var wrong_answer_choice2_mc_slope_line_1 = 'Incorrect:  ';
var choice_count_mc_slope_line_1 = 2;

//chapter3 section 5 group 1 equations_of_lines //
var mc_equations_of_lines_max_count = 1;

var mc_equations_of_lines_1 = 'Which of the following can be written in compact form?';
 
var choice1_mc_equations_of_lines_1 = 'COMING SOON';
var answer_choice1_mc_equations_of_lines_1 = 'true';
var right_answer_choice1_mc_equations_of_lines_1 = 'Correct: ';
var wrong_answer_choice1_mc_equations_of_lines_1 = 'Incorrect:  ';

var choice2_mc_equations_of_lines_1 = 'COMING sOON';
var answer_choice2_mc_equations_of_lines_1 = 'true';
var right_answer_choice2_mc_equations_of_lines_1 = 'Correct: ';
var wrong_answer_choice2_mc_equations_of_lines_1 = 'Incorrect:  ';

var choice_count_mc_equations_of_lines_1 = 2;

//chapter2 section 5 group 2 compound _inequalities //
var mc_compound_inequalities_max_count = 3;

var mc_compound_inequalities_1 = 'Which of the following can be written in compact form?';
 
var choice1_mc_compound_inequalities_1 = '3 < x and x < 9';
var answer_choice1_mc_compound_inequalities_1 = 'true';
var right_answer_choice1_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice1_mc_compound_inequalities_1 = 'Incorrect:  ';
 
var choice2_mc_compound_inequalities_1 = 'x > 2 and x < 5';
var answer_choice2_mc_compound_inequalities_1 = 'true';
var right_answer_choice2_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice2_mc_compound_inequalities_1 = 'Incorrect:  '; 
 
var choice3_mc_compound_inequalities_1 = 'x > 2 and x > 5';
var answer_choice3_mc_compound_inequalities_1 = 'false';
var right_answer_choice3_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice3_mc_compound_inequalities_1 = 'Incorrect:  '; 

var choice4_mc_compound_inequalities_1 = '2 < x or x < 5';
var answer_choice4_mc_compound_inequalities_1 = 'false';
var right_answer_choice4_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice4_mc_compound_inequalities_1 = 'Incorrect:  '; 

var choice5_mc_compound_inequalities_1 = '2 < 5x + 9 and 5x + 9 < 5';
var answer_choice5_mc_compound_inequalities_1 = 'true';
var right_answer_choice5_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice5_mc_compound_inequalities_1 = 'Incorrect:  '; 

var choice6_mc_compound_inequalities_1 = '2 < 5x + 9 or 5x + 9 < 5';
var answer_choice6_mc_compound_inequalities_1 = 'false';
var right_answer_choice6_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice6_mc_compound_inequalities_1 = 'Incorrect:  '; 

var choice7_mc_compound_inequalities_1 = '2 < 5x + 9 and 5x + 9 > 5';
var answer_choice7_mc_compound_inequalities_1 = 'false';
var right_answer_choice7_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice7_mc_compound_inequalities_1 = 'Incorrect:  '; 


var choice8_mc_compound_inequalities_1 = '2 < 5x + 9 and 3x - 2 < 5';
var answer_choice8_mc_compound_inequalities_1 = 'false';
var right_answer_choice8_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice8_mc_compound_inequalities_1 = 'Incorrect:  '; 

var choice9_mc_compound_inequalities_1 = '8 < 5x + 9 and 2 < 5x + 9';
var answer_choice9_mc_compound_inequalities_1 = 'false';
var right_answer_choice9_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice9_mc_compound_inequalities_1 = 'Incorrect:  '; 

var choice10_mc_compound_inequalities_1 = '-2 < 5x + 9 and 5x + 9 < -5';
var answer_choice10_mc_compound_inequalities_1 = 'false';
var right_answer_choice10_mc_compound_inequalities_1 = 'Correct: ';
var wrong_answer_choice10_mc_compound_inequalities_1 = 'Incorrect:  '; 

var choice_count_mc_compound_inequalities_1 = 10;
 

var mc_compound_inequalities_2 = 'The solution set for which of the following is the intersection of two solution sets?';
 
var choice1_mc_compound_inequalities_2 = '3 < x and x < 9';
var answer_choice1_mc_compound_inequalities_2 = 'true';
var right_answer_choice1_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice1_mc_compound_inequalities_2 = 'Incorrect:  ';
 
var choice2_mc_compound_inequalities_2 = 'x > 2 and x < 5';
var answer_choice2_mc_compound_inequalities_2 = 'true';
var right_answer_choice2_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice2_mc_compound_inequalities_2 = 'Incorrect:  '; 
 
var choice3_mc_compound_inequalities_2 = 'x > 2 or x > 5';
var answer_choice3_mc_compound_inequalities_2 = 'false';
var right_answer_choice3_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice3_mc_compound_inequalities_2 = 'Incorrect:  '; 

var choice4_mc_compound_inequalities_2 = '2 < x or x < 5';
var answer_choice4_mc_compound_inequalities_2 = 'false';
var right_answer_choice4_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice4_mc_compound_inequalities_2 = 'Incorrect:  '; 

var choice5_mc_compound_inequalities_2 = '2 < 5x + 9 and 5x + 9 < 5';
var answer_choice5_mc_compound_inequalities_2 = 'true';
var right_answer_choice5_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice5_mc_compound_inequalities_2 = 'Incorrect:  '; 

var choice6_mc_compound_inequalities_2 = '2 < 5x + 9 or 5x + 9 < 5';
var answer_choice6_mc_compound_inequalities_2 = 'false';
var right_answer_choice6_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice6_mc_compound_inequalities_2 = 'Incorrect:  '; 

var choice7_mc_compound_inequalities_2 = '2 < 5x + 9 and 5x + 9 > 5';
var answer_choice7_mc_compound_inequalities_2 = 'true';
var right_answer_choice7_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice7_mc_compound_inequalities_2 = 'Incorrect:  '; 


var choice8_mc_compound_inequalities_2 = '2 < 5x + 9 and 3x - 2 < 5';
var answer_choice8_mc_compound_inequalities_2 = 'true';
var right_answer_choice8_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice8_mc_compound_inequalities_2 = 'Incorrect:  '; 

var choice9_mc_compound_inequalities_2 = '8 < 5x + 9 or 2 < 5x + 9';
var answer_choice9_mc_compound_inequalities_2 = 'false';
var right_answer_choice9_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice9_mc_compound_inequalities_2 = 'Incorrect:  '; 

var choice10_mc_compound_inequalities_2 = '-2 < 5x + 9 and 5x + 9 < -5';
var answer_choice10_mc_compound_inequalities_2 = 'true';
var right_answer_choice10_mc_compound_inequalities_2 = 'Correct: ';
var wrong_answer_choice10_mc_compound_inequalities_2 = 'Incorrect:  '; 

var choice_count_mc_compound_inequalities_2 = 10; 

 

var mc_compound_inequalities_3 = 'The solution set for which of the following is the union of two solution sets?';
 
var choice1_mc_compound_inequalities_3 = '3 < x and x < 9';
var answer_choice1_mc_compound_inequalities_3 = 'true';
var right_answer_choice1_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice1_mc_compound_inequalities_3 = 'Incorrect:  ';
 
var choice2_mc_compound_inequalities_3 = 'x > 2 and x < 5';
var answer_choice2_mc_compound_inequalities_3 = 'true';
var right_answer_choice2_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice2_mc_compound_inequalities_3 = 'Incorrect:  '; 
 
var choice3_mc_compound_inequalities_3 = 'x > 2 or x > 5';
var answer_choice3_mc_compound_inequalities_3 = 'false';
var right_answer_choice3_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice3_mc_compound_inequalities_3 = 'Incorrect:  '; 

var choice4_mc_compound_inequalities_3 = '2 < x or x < 5';
var answer_choice4_mc_compound_inequalities_3 = 'false';
var right_answer_choice4_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice4_mc_compound_inequalities_3 = 'Incorrect:  '; 

var choice5_mc_compound_inequalities_3 = '2 < 5x + 9 and 5x + 9 < 5';
var answer_choice5_mc_compound_inequalities_3 = 'true';
var right_answer_choice5_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice5_mc_compound_inequalities_3 = 'Incorrect:  '; 

var choice6_mc_compound_inequalities_3 = '2 < 5x + 9 or 5x + 9 < 5';
var answer_choice6_mc_compound_inequalities_3 = 'false';
var right_answer_choice6_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice6_mc_compound_inequalities_3 = 'Incorrect:  '; 

var choice7_mc_compound_inequalities_3 = '2 < 5x + 9 and 5x + 9 > 5';
var answer_choice7_mc_compound_inequalities_3 = 'true';
var right_answer_choice7_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice7_mc_compound_inequalities_3 = 'Incorrect:  '; 


var choice8_mc_compound_inequalities_3 = '2 < 5x + 9 and 3x - 2 < 5';
var answer_choice8_mc_compound_inequalities_3 = 'true';
var right_answer_choice8_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice8_mc_compound_inequalities_3 = 'Incorrect:  '; 

var choice9_mc_compound_inequalities_3 = '8 < 5x + 9 or 2 < 5x + 9';
var answer_choice9_mc_compound_inequalities_3 = 'false';
var right_answer_choice9_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice9_mc_compound_inequalities_3 = 'Incorrect:  '; 

var choice10_mc_compound_inequalities_3 = '-2 < 5x + 9 and 5x + 9 < -5';
var answer_choice10_mc_compound_inequalities_3 = 'true';
var right_answer_choice10_mc_compound_inequalities_3 = 'Correct: ';
var wrong_answer_choice10_mc_compound_inequalities_3 = 'Incorrect:  '; 

var choice_count_mc_compound_inequalities_3 = 10; 

//chapter2 section 5 group 1 percent //
 var mc_percent_max_count = 1;

 var mc_percent_1 = ' COMING SOON';
 
 var choice1_mc_percent_1 = 'COMING';
 var answer_choice1_mc_percent_1 = 'false';
 var right_answer_choice1_mc_percent_1 = 'Correct: ';
 var wrong_answer_choice1_mc_percent_1 = 'Incorrect:  ';
 
 var choice2_mc_percent_1 = 'SOON';
 var answer_choice2_mc_percent_1 = 'false';
 var right_answer_choice2_mc_percent_1 = 'Correct: ';
 var wrong_answer_choice2_mc_percent_1 = 'Incorrect:  '; 
 
 var choice_count_mc_percent_1 = 2;

//chapter1 section 2 group 3 absolute_value //
 var mc_absolute_value_max_count = 3;

 var mc_absolute_value_1 =
 ' Which of the following are the absolute value of -5?';
 
 var choice1_mc_absolute_value_1 = '-5';
 var answer_choice1_mc_absolute_value_1 = 'false';
 var right_answer_choice1_mc_absolute_value_1 = 'Correct: ';
 var wrong_answer_choice1_mc_absolute_value_1 = 'Incorrect:  ';

 var choice2_mc_absolute_value_1 = '5';
 var answer_choice2_mc_absolute_value_1 = 'true';
 var right_answer_choice2_mc_absolute_value_1 = 'Correct: ';
 var wrong_answer_choice2_mc_absolute_value_1 = 'Incorrect:  ';
 
  var choice3_mc_absolute_value_1 = 'the opposite of -5';
 var answer_choice3_mc_absolute_value_1 = 'true';
 var right_answer_choice3_mc_absolute_value_1 = 'Correct: ';
 var wrong_answer_choice3_mc_absolute_value_1 = 'Incorrect:  ';
 
  var choice4_mc_absolute_value_1 = ' the opposite of 5';
 var answer_choice4_mc_absolute_value_1 = 'false';
 var right_answer_choice4_mc_absolute_value_1 = 'Correct: ';
 var wrong_answer_choice4_mc_absolute_value_1 = 'Incorrect:  ';

 var choice_count_mc_absolute_value_1 = 4;


 var mc_absolute_value_2 =
 ' Which of the following are the absolute value of -<img src="../../image/square_root_of_4_over_7_small.gif" alt="square root of 4 over 7" align="middle">?';
 
 var choice1_mc_absolute_value_2 = '-<img src="../../image/square_root_of_4_over_7_small.gif" alt="square root of 4 over 7">';
 var answer_choice1_mc_absolute_value_2 = 'false';
 var right_answer_choice1_mc_absolute_value_2 = 'Correct: ';
 var wrong_answer_choice1_mc_absolute_value_2 = 'Incorrect:  ';

 var choice2_mc_absolute_value_2 = '<img src="../../image/square_root_of_4_over_7_small.gif" alt="square root of 4 over 7">';
 var answer_choice2_mc_absolute_value_2 = 'true';
 var right_answer_choice2_mc_absolute_value_2 = 'Correct: ';
 var wrong_answer_choice2_mc_absolute_value_2 = 'Incorrect:  ';
 
  var choice3_mc_absolute_value_2 = 'the opposite of -<img src="../../image/square_root_of_4_over_7_small.gif" alt="square root of 4 over 7">';
 var answer_choice3_mc_absolute_value_2 = 'true';
 var right_answer_choice3_mc_absolute_value_2 = 'Correct: ';
 var wrong_answer_choice3_mc_absolute_value_2 = 'Incorrect:  ';
 
  var choice4_mc_absolute_value_2 = ' the opposite of <img src="../../image/square_root_of_4_over_7_small.gif" alt="square root of 4 over 7">';
 var answer_choice4_mc_absolute_value_2 = 'false';
 var right_answer_choice4_mc_absolute_value_2 = 'Correct: ';
 var wrong_answer_choice4_mc_absolute_value_2 = 'Incorrect:  ';

 var choice_count_mc_absolute_value_2 = 4;
 
 
 var mc_absolute_value_3 =
 ' Which of the following are the opposite of the absolute value of -9?';
 
 var choice1_mc_absolute_value_3 = '-9';
 var answer_choice1_mc_absolute_value_3 = 'true';
 var right_answer_choice1_mc_absolute_value_3 = 'Correct: ';
 var wrong_answer_choice1_mc_absolute_value_3 = 'Incorrect:  ';

 var choice2_mc_absolute_value_3 = '9';
 var answer_choice2_mc_absolute_value_3 = 'false';
 var right_answer_choice2_mc_absolute_value_3 = 'Correct: ';
 var wrong_answer_choice2_mc_absolute_value_3 = 'Incorrect:  ';
 
  var choice3_mc_absolute_value_3 = 'the opposite of -9';
 var answer_choice3_mc_absolute_value_3 = 'false';
 var right_answer_choice3_mc_absolute_value_3 = 'Correct: ';
 var wrong_answer_choice3_mc_absolute_value_3 = 'Incorrect:  ';
 
  var choice4_mc_absolute_value_3 = ' the opposite of 9';
 var answer_choice4_mc_absolute_value_3 = 'true';
 var right_answer_choice4_mc_absolute_value_3 = 'Correct: ';
 var wrong_answer_choice4_mc_absolute_value_3 = 'Incorrect:  ';

 var choice_count_mc_absolute_value_3 = 4;
 
 

//chapter1 section 2 group 2 sets_of_numbers //
 var mc_sets_of_numbers_max_count = 13;

 var mc_sets_of_numbers_1 =
 ' Which of the following are rational numbers?';
 
 var choice1_mc_sets_of_numbers_1 = '7';
 var answer_choice1_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice1_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_1 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_1 = '-28';
 var answer_choice2_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice2_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_1 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_1 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_1 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_1 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_1 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_1 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice5_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_1 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_1 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_1 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_1 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_1 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_1 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_1 = '0';
 var answer_choice8_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice8_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_1 = '41';
 var answer_choice9_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice9_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_1 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice10_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_1 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_1 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_1 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_1 = '1';
 var answer_choice12_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice12_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_1 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_1 = '28';
 var answer_choice13_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice13_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_1 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_1 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_1 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_1 = '8';
 var answer_choice15_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice15_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
  var choice16_mc_sets_of_numbers_1 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_1 = 'true';
 var right_answer_choice16_mc_sets_of_numbers_1 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_1 = 'Incorrect:  ';
 
 var choice_count_mc_sets_of_numbers_1 = 16;


 var mc_sets_of_numbers_2 =
 ' Which of the following are natural numbers?';
 
 var choice1_mc_sets_of_numbers_2 = '7';
 var answer_choice1_mc_sets_of_numbers_2 = 'true';
 var right_answer_choice1_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_2 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_2 = '-28';
 var answer_choice2_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice2_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_2 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_2 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_2 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_2 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_2 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_2 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_2 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_2 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_2 = '0';
 var answer_choice8_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_2 = '41';
 var answer_choice9_mc_sets_of_numbers_2 = 'true';
 var right_answer_choice9_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_2 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_2 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_2 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_2 = '1';
 var answer_choice12_mc_sets_of_numbers_2 = 'true';
 var right_answer_choice12_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_2 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_2 = '28';
 var answer_choice13_mc_sets_of_numbers_2 = 'true';
 var right_answer_choice13_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_2 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_2 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_2 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_2 = '8';
 var answer_choice15_mc_sets_of_numbers_2 = 'true';
 var right_answer_choice15_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
  var choice16_mc_sets_of_numbers_2 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_2 = 'true';
 var right_answer_choice16_mc_sets_of_numbers_2 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_2 = 'Incorrect:  ';
 
 var choice_count_mc_sets_of_numbers_2= 16;
 
 
 var mc_sets_of_numbers_3 =
 ' Which of the following are prime numbers?';
 
 var choice1_mc_sets_of_numbers_3 = '7';
 var answer_choice1_mc_sets_of_numbers_3 = 'true';
 var right_answer_choice1_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_3 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_3 = '-28';
 var answer_choice2_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice2_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_3 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_3 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_3 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_3 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_3 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_3 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_3 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_3 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_3 = '0';
 var answer_choice8_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_3 = '41';
 var answer_choice9_mc_sets_of_numbers_3 = 'true';
 var right_answer_choice9_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_3 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_3 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_3 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_3 = '1';
 var answer_choice12_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice12_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_3 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_3 = '28';
 var answer_choice13_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice13_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_3 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_3 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_3 = '8';
 var answer_choice15_mc_sets_of_numbers_3 = 'false';
 var right_answer_choice15_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
  var choice16_mc_sets_of_numbers_3 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_3 = 'true';
 var right_answer_choice16_mc_sets_of_numbers_3 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_3 = 'Incorrect:  ';
 
 var choice_count_mc_sets_of_numbers_3 = 16; 

 var mc_sets_of_numbers_4 =
 ' Which of the following are integers?';
 
 var choice1_mc_sets_of_numbers_4 = '7';
 var answer_choice1_mc_sets_of_numbers_4 = 'true';
 var right_answer_choice1_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_4 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_4 = '-28';
 var answer_choice2_mc_sets_of_numbers_4 = 'true';
 var right_answer_choice2_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_4 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_4 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_4 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_4 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_4 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_4 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_4 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_4 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_4 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_4 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_4 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_4 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_4 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_4 = '0';
 var answer_choice8_mc_sets_of_numbers_4 = 'true';
 var right_answer_choice8_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_4 = '41';
 var answer_choice9_mc_sets_of_numbers_4 = 'true';
 var right_answer_choice9_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_4 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_4 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_4 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_4 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_4 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_4 = '1';
 var answer_choice12_mc_sets_of_numbers_4 = 'true';
 var right_answer_choice12_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_4 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_4 = '28';
 var answer_choice13_mc_sets_of_numbers_4 = 'true';
 var right_answer_choice13_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_4 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_4 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_4 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_4 = '8';
 var answer_choice15_mc_sets_of_numbers_4 = 'true';
 var right_answer_choice15_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice16_mc_sets_of_numbers_4 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_4 = 'true';
 var right_answer_choice16_mc_sets_of_numbers_4 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_4 = 'Incorrect:  ';
 
 var choice_count_mc_sets_of_numbers_4 = 16;


 var mc_sets_of_numbers_5 =
 ' Which of the following are irrational numbers?';
 
 var choice1_mc_sets_of_numbers_5 = '7';
 var answer_choice1_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice1_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_5 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_5 = '-28';
 var answer_choice2_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice2_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_5 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_5 = 'true';
 var right_answer_choice3_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_5 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_5 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_5 = 'true';
 var right_answer_choice4_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_5 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_5 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_5 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_5 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_5 = 'true';
 var right_answer_choice7_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_5 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_5 = '0';
 var answer_choice8_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_5 = '41';
 var answer_choice9_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice9_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_5 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_5 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_5 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_5 = 'true';
 var right_answer_choice11_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_5 = '1';
 var answer_choice12_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice12_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_5 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_5 = '28';
 var answer_choice13_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice13_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_5 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_5 = 'true';
 var right_answer_choice14_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_5 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_5 = '8';
 var answer_choice15_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice15_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
  var choice16_mc_sets_of_numbers_5 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_5 = 'false';
 var right_answer_choice16_mc_sets_of_numbers_5 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_5 = 'Incorrect:  ';
 
 var choice_count_mc_sets_of_numbers_5 = 16;
 
 
 var mc_sets_of_numbers_6 =
 ' Which of the following are composite numbers?';
 
 var choice1_mc_sets_of_numbers_6 = '7';
 var answer_choice1_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice1_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_6 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_6 = '-28';
 var answer_choice2_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice2_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_6 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_6 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_6 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_6 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_6 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_6 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_6 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_6 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_6 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_6 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_6 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_6 = '0';
 var answer_choice8_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_6 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_6 = '41';
 var answer_choice9_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice9_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_6 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_6 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_6 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_6 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_6 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_6 = '1';
 var answer_choice12_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice12_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_6 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_6 = '28';
 var answer_choice13_mc_sets_of_numbers_6 = 'true';
 var right_answer_choice13_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_6 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_6 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_6 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_6 = '8';
 var answer_choice15_mc_sets_of_numbers_6 = 'true';
 var right_answer_choice15_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_6 = 'Incorrect:  ';
 
  var choice16_mc_sets_of_numbers_6 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_6 = 'false';
 var right_answer_choice16_mc_sets_of_numbers_6 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_6 = 'Incorrect:  ';

 var choice_count_mc_sets_of_numbers_6 = 16; 
 
 
 var mc_sets_of_numbers_7 =
 ' Which of the following are natural numbers but are neither prime numbers nor composite numbers?';
 
 var choice1_mc_sets_of_numbers_7 = '7';
 var answer_choice1_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice1_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_7 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_7 = '-28';
 var answer_choice2_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice2_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_7 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_7 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_7 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_7 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_7 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_7 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_7 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_7 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_7 = '0';
 var answer_choice8_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_7 = '41';
 var answer_choice9_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice9_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_7 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_7 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_7 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_7 = '1';
 var answer_choice12_mc_sets_of_numbers_7 = 'true';
 var right_answer_choice12_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_7 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_7 = '28';
 var answer_choice13_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice13_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_7 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_7 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_7 = '8';
 var answer_choice15_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice15_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
  var choice16_mc_sets_of_numbers_7 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_7 = 'false';
 var right_answer_choice16_mc_sets_of_numbers_7 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_7 = 'Incorrect:  ';
 
 var choice_count_mc_sets_of_numbers_7 = 16;


 var mc_sets_of_numbers_8 =
 ' Which of the following are whole numbers?';
 
 var choice1_mc_sets_of_numbers_8 = '7';
 var answer_choice1_mc_sets_of_numbers_8 = 'true';
 var right_answer_choice1_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_8 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_8 = '-28';
 var answer_choice2_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice2_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_8 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_8 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_8 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_8 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_8 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_8 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_8 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_8 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_8 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_8 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_8 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_8 = '0';
 var answer_choice8_mc_sets_of_numbers_8 = 'true';
 var right_answer_choice8_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_8 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_8 = '41';
 var answer_choice9_mc_sets_of_numbers_8 = 'true';
 var right_answer_choice9_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_8 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_8 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_8 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_8 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_8 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_8 = '1';
 var answer_choice12_mc_sets_of_numbers_8 = 'true';
 var right_answer_choice12_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_8 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_8 = '28';
 var answer_choice13_mc_sets_of_numbers_8 = 'true';
 var right_answer_choice13_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_8 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_8 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_8 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_8 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_8 = '8';
 var answer_choice15_mc_sets_of_numbers_8 = 'true';
 var right_answer_choice15_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_8 = 'Incorrect:  ';
 
  var choice16_mc_sets_of_numbers_8 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_8 = 'true';
 var right_answer_choice16_mc_sets_of_numbers_8 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_8 = 'Incorrect:  ';

 
 var choice_count_mc_sets_of_numbers_8 = 16;
 
 
 var mc_sets_of_numbers_9 =
 ' Which of the following are real numbers?';
 
 var choice1_mc_sets_of_numbers_9 = '7';
 var answer_choice1_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice1_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_9 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_9 = '-28';
 var answer_choice2_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice2_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_9 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice3_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_9 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_9 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice4_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_9 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice5_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_9 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_9 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_9 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_9 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice7_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_9 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_9 = '0';
 var answer_choice8_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice8_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_9 = '41';
 var answer_choice9_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice9_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_9 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice10_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_9 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_9 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice11_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_9 = '1';
 var answer_choice12_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice12_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_9 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_9 = '28';
 var answer_choice13_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice13_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_9 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice14_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_9 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_9 = '8';
 var answer_choice15_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice15_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
  var choice16_mc_sets_of_numbers_9 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_9 = 'true';
 var right_answer_choice16_mc_sets_of_numbers_9 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_9 = 'Incorrect:  ';
 
 var choice_count_mc_sets_of_numbers_9 = 16; 
 

 var mc_sets_of_numbers_10 =
 ' Which of the following are negative integers?';
 
 var choice1_mc_sets_of_numbers_10 = '7';
 var answer_choice1_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice1_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_10 = 'Incorrect:  ';

 var choice2_mc_sets_of_numbers_10 = '-28';
 var answer_choice2_mc_sets_of_numbers_10 = 'true';
 var right_answer_choice2_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice3_mc_sets_of_numbers_10 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of 5" align="absmiddle">';
 var answer_choice3_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_10 = 'Incorrect:  ';

 var choice4_mc_sets_of_numbers_10 = '<img src="../../image/cube_root_of 4_small.gif" alt="cube root of four" align="absmiddle">';
 var answer_choice4_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice5_mc_sets_of_numbers_10 = '<img src="../../image/7over8_small.gif" alt="7 over 8" align="absmiddle">';
 var answer_choice5_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_10 = 'Incorrect:  ';

 var choice6_mc_sets_of_numbers_10 = '<img src="../../image/symbol_number_infinity_small.gif" alt="infinity" align="absmiddle">';
 var answer_choice6_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice7_mc_sets_of_numbers_10 = '7<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice7_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_10 = 'Incorrect:  '; 
 
 var choice8_mc_sets_of_numbers_10 = '0';
 var answer_choice8_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice9_mc_sets_of_numbers_10 = '41';
 var answer_choice9_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice9_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice10_mc_sets_of_numbers_10 = '<img src="../../image/13over2_small.gif" alt="13 over 2" align="absmiddle">';
 var answer_choice10_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_10 = 'Incorrect:  ';

 var choice11_mc_sets_of_numbers_10 = '<img src="../../image/number_fraction_seventeen_thirds_small.gif" alt="17 over 3" align="absmiddle"><img src="../../image/square_root_of_5_over_square_root_of_2_small.gif" alt="square root of 5 over square root of 2" align="absmiddle">';
 var answer_choice11_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice12_mc_sets_of_numbers_10 = '1';
 var answer_choice12_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice12_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_10 = 'Incorrect:  ';

 var choice13_mc_sets_of_numbers_10 = '28';
 var answer_choice13_mc_sets_of_numbers_10 = 'true';
 var right_answer_choice13_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice14_mc_sets_of_numbers_10 = '<img src="../../image/pi_small.gif" alt="the number pi" align="absmiddle">';
 var answer_choice14_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_10 = 'Incorrect:  ';

 var choice15_mc_sets_of_numbers_10 = '8';
 var answer_choice15_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice15_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice15_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice16_mc_sets_of_numbers_10 = '<img src="../../image/cube_root_of 8_small.gif" alt="cube root of 8" align="absmiddle">';
 var answer_choice16_mc_sets_of_numbers_10 = 'false';
 var right_answer_choice16_mc_sets_of_numbers_10 = 'Correct: ';
 var wrong_answer_choice16_mc_sets_of_numbers_10 = 'Incorrect:  ';
 
 var choice_count_mc_sets_of_numbers_10 = 16;


 var mc_sets_of_numbers_11 =
 ' Which of the following are correct examples of set builder notation?';
 
 var choice1_mc_sets_of_numbers_11 = '<span class=nobr>(3,7)</span>';
 var answer_choice1_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice1_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_11 = 'Incorrect: (3,7) is a good example of interval notation. ';

 var choice2_mc_sets_of_numbers_11 = '<span class=nobr>{x|4 < x}</span>';
 var answer_choice2_mc_sets_of_numbers_11 = 'true';
 var right_answer_choice2_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_11 = 'Incorrect: <span class=nobr>{x|4 < x}</span> exactly matches the definition of set builder notation.';

 var choice3_mc_sets_of_numbers_11 = '<span class=nobr>{p|p <img src="../../image/symbol_set_isin_small.gif" alt="is an element of" align="absmiddle"> <b>P</b>}';
 var answer_choice3_mc_sets_of_numbers_11 = 'true';
 var right_answer_choice3_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_11 = 'Incorrect: This is a perfect example of set builder notation.';
 
 var choice4_mc_sets_of_numbers_11 = '<span class=nobr>[5,-3)</span>';
 var answer_choice4_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_11 = 'Incorrect: This is a meaningless collection of symbols.  In interval notation the left endpoint must be less than the right endpoint.';

 var choice5_mc_sets_of_numbers_11 = '<span class=nobr>(3,7,2,45,5)</span>';
 var answer_choice5_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_11 = 'Incorrect: About the only thing <span class=nobr>(3,7,2,45,5)</span> could represent is a point in five dimensional space.';
 
 var choice6_mc_sets_of_numbers_11 = '<span class=nobr>(9,&infin;)</span>';
 var answer_choice6_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_11 = 'Incorrect: <span class=nobr>(9,&infin;)</span> is a good example of interval notation to represent a ray.';
 
 var choice7_mc_sets_of_numbers_11 = '<span class=nobr>{3,7,2,45,5}</span>';
 var answer_choice7_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_11 = 'Incorrect: This is a good example of the roster method.';
 
 var choice8_mc_sets_of_numbers_11 = '<span class=nobr>[&infin;, 237]</span>';
 var answer_choice8_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_11 = 'Incorrect: This is meaningless.  -&infin; is not a real number and therefore cannot be included in a ray as indicated by [.'; 
 
 var choice9_mc_sets_of_numbers_11 = '<span class=nobr>(-22,97]</span>';
 var answer_choice9_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice9_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_11 = 'Incorrect: This is a good example of interval notation.'; 
 
  var choice10_mc_sets_of_numbers_11 = '<span class=nobr>{x|8 < x < 10 and x &isin; <b>Q</b></span>}';
 var answer_choice10_mc_sets_of_numbers_11 = 'true';
 var right_answer_choice10_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_11 = 'Incorrect: This matches exactly the definition of set builder notation.';
 
 var choice11_mc_sets_of_numbers_11 = '<span class=nobr>{2,45}</span>';
 var answer_choice11_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_11 = 'Incorrect: <span class=nobr>{2,45}</span> is a perfect example of the roster method.'; 
 
 var choice12_mc_sets_of_numbers_11 = '<span class=nobr>{7 > x > 1}</span>';
 var answer_choice12_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice12_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_11 = 'Incorrect: <span class=nobr>{7 > x > 1}</span> is a meaningless collection of symbols.';
 
 var choice13_mc_sets_of_numbers_11 = '<span class=nobr>{2, 4, 6, 8, &hellip;}</span>';
 var answer_choice13_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice13_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_11 = 'Incorrect: <span class=nobr>{2, 4, 6, 8, &hellip;}</span> is a good example of using ellipsis in the roster method.';

 var choice14_mc_sets_of_numbers_11 = '<span class=nobr>{&hellip;, -3, -1, 1, 3, &hellip;}</span>';
 var answer_choice14_mc_sets_of_numbers_11 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_11 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_11 = 'Incorrect: <span class=nobr>{&hellip;, -3, -1, 1, 3, &hellip;} </span>is a good example of using ellipsis in the roster method.';
 
var choice_count_mc_sets_of_numbers_11 = 14; 


 var mc_sets_of_numbers_12 =
 ' Which of the following are examples of correct interval notation?';
 
 var choice1_mc_sets_of_numbers_12 = '<span class=nobr>(3,7)</span>';
 var answer_choice1_mc_sets_of_numbers_12 = 'true';
 var right_answer_choice1_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_12 = 'Incorrect: (3,7) is interval notation. It exactly matches the definition of interval. ';

 var choice2_mc_sets_of_numbers_12 = '<span class=nobr>{x|4 < x}</span>';
 var answer_choice2_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice2_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_12 = 'Incorrect: This is a good example of set builder notation.';

 var choice3_mc_sets_of_numbers_12 = '<span class=nobr>{p|p <img src="../../image/symbol_set_isin_small.gif" alt="is an element of" align="absmiddle"> <b>P</b>}';
 var answer_choice3_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_12 = 'Incorrect: This is a good example of set builder notation.';
 
 var choice4_mc_sets_of_numbers_12 = '<span class=nobr>[5,-3)</span>';
 var answer_choice4_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_12 = 'Incorrect: This is a meaningless collection of symbols.  In interval notation the left endpoint must be less than the right endpoint.';

 var choice5_mc_sets_of_numbers_12 = '<span class=nobr>(3,7,2,45,5)</span>';
 var answer_choice5_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_12 = 'Incorrect: About the only thing <span class=nobr>(3,7,2,45,5)</span> could represent is a point in five dimensional space.';
 
 var choice6_mc_sets_of_numbers_12 = '<span class=nobr>(9,&infin;)</span>';
 var answer_choice6_mc_sets_of_numbers_12 = 'true';
 var right_answer_choice6_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_12 = 'Incorrect: <span class=nobr>(9,&infin;)</span> is a good example of interval notation to represent a ray.';
 
 var choice7_mc_sets_of_numbers_12 = '<span class=nobr>{3,7,2,45,5}</span>';
 var answer_choice7_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice7_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_12 = 'Incorrect: <span class=nobr>{3,7,2,45,5}</span> is a good example of the roster method.';
 
 var choice8_mc_sets_of_numbers_12 = '<span class=nobr>[-&infin;, 237]</span>';
 var answer_choice8_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_12 = 'Incorrect: This is meaninless.  -&infin; is not a real number and therefore cannot be included in a ray as indicated by [.'; 
 
 var choice9_mc_sets_of_numbers_12 = '<span class=nobr>(-22,97]</span>';
 var answer_choice9_mc_sets_of_numbers_12 = 'true';
 var right_answer_choice9_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_12 = 'Incorrect: <span class=nobr>(-22,97]</span> is a perfect example of interval notation for all real numbers between -22 and 97, including 97 but not -22.'; 
 
  var choice10_mc_sets_of_numbers_12 = '<span class=nobr>{x|8 < x < 10 and x &isin; <b>Q</b></span>}';
 var answer_choice10_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_12 = 'Incorrect: This is a good example of set builder notation.';
 
 var choice11_mc_sets_of_numbers_12 = '<span class=nobr>{2,45}</span>';
 var answer_choice11_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice11_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_12 = 'Incorrect: The only permissible symbols to use for the ends of an interval in interval notation are 9, [, 0, or ].'; 
 
 var choice12_mc_sets_of_numbers_12 = '<span class=nobr>{7 > x > 1}</span>';
 var answer_choice12_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice12_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_12 = 'Incorrect: <span class=nobr>{7 > x > 1}</span> is a meaningless collection of symbols.';
 
 var choice13_mc_sets_of_numbers_12 = '<span class=nobr>{2, 4, 6, 8, &hellip;}</span>';
 var answer_choice13_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice13_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_12 = 'Incorrect: <span class=nobr>{2, 4, 6, 8, &hellip;}</span> is a good example of using ellipsis in the roster method.';

 var choice14_mc_sets_of_numbers_12 = '<span class=nobr>{&hellip;, -3, -1, 1, 3, &hellip;}</span>';
 var answer_choice14_mc_sets_of_numbers_12 = 'false';
 var right_answer_choice14_mc_sets_of_numbers_12 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_12 = 'Incorrect: <span class=nobr>{&hellip;, -3, -1, 1, 3, &hellip;}</span> is a good example of using ellipsis in the roster method.';
 
var choice_count_mc_sets_of_numbers_12 = 14; 

var mc_sets_of_numbers_13 =
 ' Which of the following illustrate correct use of the roster method?';
 
 var choice1_mc_sets_of_numbers_13 = '<span class=nobr>(3,7)</span>';
 var answer_choice1_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice1_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_of_numbers_13 = 'Incorrect: <span class=nobr>(3,7)</span> is interval notation. ';

 var choice2_mc_sets_of_numbers_13 = '<span class=nobr>{x|4 < x}</span>';
 var answer_choice2_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice2_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_of_numbers_13 = 'Incorrect: <span class=nobr>{x|4 < x}</span> is a good example of set builder notation.';

 var choice3_mc_sets_of_numbers_13 = '<span class=nobr>{p|p <img src="../../image/symbol_set_isin_small.gif" alt="is an element of" align="absmiddle"> <b>P</b>}';
 var answer_choice3_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice3_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_of_numbers_13 = 'Incorrect: This is another good example of set builder notation.';
 
 var choice4_mc_sets_of_numbers_13 = '<span class=nobr>[5,-3)</span>';
 var answer_choice4_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice4_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_of_numbers_13 = 'Incorrect: This is a meaningless collection of symbols.  In interval notation the left endpoint must be less than the right endpoint.';

 var choice5_mc_sets_of_numbers_13 = '<span class=nobr>(3,7,2,45,5)</span>';
 var answer_choice5_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice5_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_of_numbers_13 = 'Incorrect: About the only thing <span class=nobr>(3,7,2,45,5)</span> could represent is a point in five dimensional space.';
 
 var choice6_mc_sets_of_numbers_13 = '<span class=nobr>(9,&infin;)</span>';
 var answer_choice6_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice6_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_of_numbers_13 = 'Incorrect: <span class=nobr>(9,&infin;)</span> is a good example of interval notation for a ray.';
 
 var choice7_mc_sets_of_numbers_13 = '<span class=nobr>{3,7,2,45,5}</span>';
 var answer_choice7_mc_sets_of_numbers_13 = 'true';
 var right_answer_choice7_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_of_numbers_13 = 'Incorrect: <span class=nobr>{3,7,2,45,5}</span> exactly matches the definition of the roster method.';
 
 var choice8_mc_sets_of_numbers_13 = '<span class=nobr>[-&infin;, 237]</span>';
 var answer_choice8_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice8_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_of_numbers_13 = 'Incorrect: This is meaninless.  -&infin; is not a real number and therefore cannot be included in a ray as indicated by [.'; 
 
 var choice9_mc_sets_of_numbers_13 = '<span class=nobr>(-22,97]</span>';
 var answer_choice9_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice9_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice9_mc_sets_of_numbers_13 = 'Incorrect: <span class=nobr>(-22,97]</span> is a good example of interval notation.'; 
 
  var choice10_mc_sets_of_numbers_13 = '<span class=nobr>{x|8 < x < 10 and x &isin; <b>Q</b></span>}';
 var answer_choice10_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice10_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice10_mc_sets_of_numbers_13 = 'Incorrect: This is a good example of set builder notation.';
 
 var choice11_mc_sets_of_numbers_13 = '<span class=nobr>{2,45}</span>';
 var answer_choice11_mc_sets_of_numbers_13 = 'true';
 var right_answer_choice11_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice11_mc_sets_of_numbers_13 = 'Incorrect: <span class=nobr>{2,45}</span> exactly matches the definition of the roster method.'; 
 
 var choice12_mc_sets_of_numbers_13 = '<span class=nobr>{7 > x > 1}</span>';
 var answer_choice12_mc_sets_of_numbers_13 = 'false';
 var right_answer_choice12_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice12_mc_sets_of_numbers_13 = 'Incorrect: <span class=nobr>{7 > x > 1}</span> is a meaningless collection of symbols.';
 
 var choice13_mc_sets_of_numbers_13 = '<span class=nobr>{2, 4, 6, 8, &hellip;}</span>';
 var answer_choice13_mc_sets_of_numbers_13 = 'true';
 var right_answer_choice13_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice13_mc_sets_of_numbers_13 = 'Incorrect: Ellipsis are used to extend the basic idea of the roster method.';

 var choice14_mc_sets_of_numbers_13 = '<span class=nobr>{&hellip;, -3, -1, 1, 3, &hellip;}</span>';
 var answer_choice14_mc_sets_of_numbers_13 = 'true';
 var right_answer_choice14_mc_sets_of_numbers_13 = 'Correct: ';
 var wrong_answer_choice14_mc_sets_of_numbers_13 = 'Incorrect: Ellipsis are used to extend the basic idea of the roster method.';
 
var choice_count_mc_sets_of_numbers_13 = 14; 


//chapter1 section1 group2 sets_intro //

 var mc_sets_intro_max_count = 4;

 var mc_sets_intro_1 =
 ' Which of the following are subsets of {a, b, c}?';
 var choice1_mc_sets_intro_1 = 'b';
 var answer_choice1_mc_sets_intro_1 = 'false';
 var right_answer_choice1_mc_sets_intro_1 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_intro_1 = 'Incorrect:  b is an element of the set but not a subset.  Carefully study the definitions.  Ask for clarification.';

 var choice2_mc_sets_intro_1 = '{c, a}';
 var answer_choice2_mc_sets_intro_1 = 'true';
 var right_answer_choice2_mc_sets_intro_1 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_intro_1 = 'Incorrect: The elements of {c, a} are c and a.  Both of them are elements of {a, b, c} and therefore according to the definition of subset {c, a} is a subset of {a, b, c}.';
   
 var choice3_mc_sets_intro_1 = 'b, c';
 var answer_choice3_mc_sets_intro_1 = 'false';
 var right_answer_choice3_mc_sets_intro_1 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_intro_1 = 'Incorrect:  ';
 
 var choice4_mc_sets_intro_1 = '<img src="../../image/symbol_set_null_small.gif" alt="the empty set" border="0" align="absmiddle">';
 var answer_choice4_mc_sets_intro_1 = 'true';
 var right_answer_choice4_mc_sets_intro_1 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_intro_1 = 'Incorrect:  ';
 
 var choice5_mc_sets_intro_1 = '{c, a, b}';
 var answer_choice5_mc_sets_intro_1 = 'true';
 var right_answer_choice5_mc_sets_intro_1 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_intro_1 = 'Incorrect:  ';
 
 var choice6_mc_sets_intro_1 = '{a, b}';
 var answer_choice6_mc_sets_intro_1 = 'true';
 var right_answer_choice6_mc_sets_intro_1 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_intro_1 = 'Incorrect:  ';
 
 var choice7_mc_sets_intro_1 = '{b}';
 var answer_choice7_mc_sets_intro_1 = 'true';
 var right_answer_choice7_mc_sets_intro_1 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_intro_1 = 'Incorrect:  '; 
 
  var choice8_mc_sets_intro_1 = '{1, 2, 3}';
 var answer_choice8_mc_sets_intro_1 = 'false';
 var right_answer_choice8_mc_sets_intro_1 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_intro_1 = 'Incorrect:  '; 
 
 var choice_count_mc_sets_intro_1 = 8;  
 

 var mc_sets_intro_2 =
 ' Which of the following are elements of {a, b, c}?';
 var choice1_mc_sets_intro_2 = 'b';
 var answer_choice1_mc_sets_intro_2 = 'true';
 var right_answer_choice1_mc_sets_intro_2 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_intro_2 = 'Incorrect:  ';

 var choice2_mc_sets_intro_2 = '{b}';
 var answer_choice2_mc_sets_intro_2 = 'false';
 var right_answer_choice2_mc_sets_intro_2 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_intro_2 = 'Incorrect: ';
   
 var choice3_mc_sets_intro_2 = 'b and c';
 var answer_choice3_mc_sets_intro_2 = 'true';
 var right_answer_choice3_mc_sets_intro_2 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_intro_2 = 'Incorrect:  ';
 
 var choice4_mc_sets_intro_2 = '<img src="../../image/symbol_set_null_small.gif" alt="the empty set" border="0" align="absmiddle">';
 var answer_choice4_mc_sets_intro_2 = 'false';
 var right_answer_choice4_mc_sets_intro_2 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_intro_2 = 'Incorrect:  ';
 
 var choice5_mc_sets_intro_2 = '{c, b}';
 var answer_choice5_mc_sets_intro_2 = 'false';
 var right_answer_choice5_mc_sets_intro_2 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_intro_2 = 'Incorrect:  ';
 
 var choice6_mc_sets_intro_2 = 'b and c';
 var answer_choice6_mc_sets_intro_2 = 'true';
 var right_answer_choice6_mc_sets_intro_2 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_intro_2 = 'Incorrect:  ';
 
 var choice7_mc_sets_intro_2 = '{a}';
 var answer_choice7_mc_sets_intro_2 = 'false';
 var right_answer_choice7_mc_sets_intro_2 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_intro_2 = 'Incorrect:  '; 
 
  var choice8_mc_sets_intro_2 = 'a';
 var answer_choice8_mc_sets_intro_2 = 'true';
 var right_answer_choice8_mc_sets_intro_2 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_intro_2 = 'Incorrect:  '; 
 
 var choice_count_mc_sets_intro_2 = 8;  


 var mc_sets_intro_3 =
 ' Which of the following are examples of the roster method?';
 var choice1_mc_sets_intro_3 = '{b}';
 var answer_choice1_mc_sets_intro_3 = 'true';
 var right_answer_choice1_mc_sets_intro_3 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_intro_3 = 'Incorrect:  ';

 var choice2_mc_sets_intro_3 = '{2, 4, 6, 8, &hellip;}';
 var answer_choice2_mc_sets_intro_3 = 'true';
 var right_answer_choice2_mc_sets_intro_3 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_intro_3 = 'Incorrect: ';
   
 var choice3_mc_sets_intro_3 = '{k|k is a number less than 5}';
 var answer_choice3_mc_sets_intro_3 = 'false';
 var right_answer_choice3_mc_sets_intro_3 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_intro_3 = 'Incorrect:  ';
 
 var choice4_mc_sets_intro_3 = '{y|y is a brown dog}';
 var answer_choice4_mc_sets_intro_3 = 'false';
 var right_answer_choice4_mc_sets_intro_3 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_intro_3 = 'Incorrect:  ';
 
 var choice5_mc_sets_intro_3 = '{x|x <img src="../../image/symbol_set_isin_small.gif" alt="is an element of" border="0" align="absmiddle"> <b>Z</b>}';
 var answer_choice5_mc_sets_intro_3 = 'false';
 var right_answer_choice5_mc_sets_intro_3 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_intro_3 = 'Incorrect:  ';
 
 var choice6_mc_sets_intro_3 = '{-9, &delta;, 43, &Delta;, <img src="../../image/7over8_small.gif" alt="7 over 8" border="0" align="absmiddle">}';
 var answer_choice6_mc_sets_intro_3 = 'true';
 var right_answer_choice6_mc_sets_intro_3 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_intro_3 = 'Incorrect:  ';
 
 var choice7_mc_sets_intro_3 = '<b>Q</b> is the set of rational numbers.';
 var answer_choice7_mc_sets_intro_3 = 'false';
 var right_answer_choice7_mc_sets_intro_3 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_intro_3 = 'Incorrect:  '; 
 
  var choice8_mc_sets_intro_3 = '{a, 5, 14,&Sigma;, &clubs;}';
 var answer_choice8_mc_sets_intro_3 = 'true';
 var right_answer_choice8_mc_sets_intro_3 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_intro_3 = 'Incorrect:  '; 
 
 var choice_count_mc_sets_intro_3 = 8; 
  

 var mc_sets_intro_4 =
 ' Which of the following are examples of set builder notation?';
 var choice1_mc_sets_intro_4 = '{b}';
 var answer_choice1_mc_sets_intro_4 = 'false';
 var right_answer_choice1_mc_sets_intro_4 = 'Correct: ';
 var wrong_answer_choice1_mc_sets_intro_4 = 'Incorrect:  ';

 var choice2_mc_sets_intro_4 = '{2, 4, 6, 8, &hellip;}';
 var answer_choice2_mc_sets_intro_4 = 'false';
 var right_answer_choice2_mc_sets_intro_4 = 'Correct: ';
 var wrong_answer_choice2_mc_sets_intro_4 = 'Incorrect: ';
   
 var choice3_mc_sets_intro_4 = '{k|k is a number less than 5}';
 var answer_choice3_mc_sets_intro_4 = 'true';
 var right_answer_choice3_mc_sets_intro_4 = 'Correct: ';
 var wrong_answer_choice3_mc_sets_intro_4 = 'Incorrect:  ';
 
 var choice4_mc_sets_intro_4 = '{y|y is a brown dog}';
 var answer_choice4_mc_sets_intro_4 = 'true';
 var right_answer_choice4_mc_sets_intro_4 = 'Correct: ';
 var wrong_answer_choice4_mc_sets_intro_4 = 'Incorrect:  ';
 
 var choice5_mc_sets_intro_4 = '{x|x <img src="../../image/symbol_set_isin_small.gif" alt="is an element of" border="0" align="absmiddle"> <b>Z</b>}';
 var answer_choice5_mc_sets_intro_4 = 'true';
 var right_answer_choice5_mc_sets_intro_4 = 'Correct: ';
 var wrong_answer_choice5_mc_sets_intro_4 = 'Incorrect:  ';
 
 var choice6_mc_sets_intro_4 = '{-9, &delta;, 43, &Delta;, <img src="../../image/7over8_small.gif" alt="7 over 8" border="0" align="absmiddle">}';
 var answer_choice6_mc_sets_intro_4 = 'false';
 var right_answer_choice6_mc_sets_intro_4 = 'Correct: ';
 var wrong_answer_choice6_mc_sets_intro_4 = 'Incorrect:  ';
 
 var choice7_mc_sets_intro_4 = '<b>Q</b> is the set of rational numbers.';
 var answer_choice7_mc_sets_intro_4 = 'false';
 var right_answer_choice7_mc_sets_intro_4 = 'Correct: ';
 var wrong_answer_choice7_mc_sets_intro_4 = 'Incorrect:  '; 
 
  var choice8_mc_sets_intro_4 = '{a, 5, 14,&Sigma;, &clubs;}';
 var answer_choice8_mc_sets_intro_4 = 'false';
 var right_answer_choice8_mc_sets_intro_4 = 'Correct: ';
 var wrong_answer_choice8_mc_sets_intro_4 = 'Incorrect:  '; 
 
 var choice_count_mc_sets_intro_4 = 8; 


  //chapter1 section 1 group 1 formulas_basic //

 var mc_formulas_basic_max_count = 6;

 var mc_formulas_basic_1 =
 ' Which of the following are formulas?';
 var choice1_mc_formulas_basic_1 = 'A=LW';
 var answer_choice1_mc_formulas_basic_1 = 'true';
 var right_answer_choice1_mc_formulas_basic_1 = 'Correct: ';
 var wrong_answer_choice1_mc_formulas_basic_1 = 'Incorrect:  Review the definition of formula and the list of basic formulas.';

 var choice2_mc_formulas_basic_1 = '<img src="../../image/formula_trapezoid_area_small.gif" alt="formula for the area of a trapezoid" border="0" align="absmiddle">';
 var answer_choice2_mc_formulas_basic_1 = 'true';
 var right_answer_choice2_mc_formulas_basic_1 = 'Correct: ';
 var wrong_answer_choice2_mc_formulas_basic_1 = 'Incorrect: This is the formula for the area of a trapezoid.';
 
 var choice3_mc_formulas_basic_1 = 'LW';
 var answer_choice3_mc_formulas_basic_1 = 'false';
 var right_answer_choice3_mc_formulas_basic_1 = 'Correct: Good Job!';
 var wrong_answer_choice3_mc_formulas_basic_1 = 'Incorrect: A formula must be an equation.';
 
 var choice4_mc_formulas_basic_1 = 'A=x<sup>2</sup>';
 var answer_choice4_mc_formulas_basic_1 = 'true';
 var right_answer_choice4_mc_formulas_basic_1 = 'Correct: ';
 var wrong_answer_choice4_mc_formulas_basic_1 = 'Incorrect:  This is the formula for the area of a square.'; 
 
 var choice5_mc_formulas_basic_1 = '(1/2)(B + b)h';
 var answer_choice5_mc_formulas_basic_1 = 'false';
 var right_answer_choice5_mc_formulas_basic_1 = 'Correct: ';
 var wrong_answer_choice5_mc_formulas_basic_1 = 'Incorrect: A formula must be an equation.'; 
 
 var choice6_mc_formulas_basic_1 = '<img src="../../image/formula_circle_area_small.gif" alt="formula for the area of a circle" border="0" align="absmiddle">';
 var answer_choice6_mc_formulas_basic_1 = 'true';
 var right_answer_choice6_mc_formulas_basic_1 = 'Correct ';
 var wrong_answer_choice6_mc_formulas_basic_1 = 'Incorrect: This is the formula for the area of a circle.';  
 
 var choice7_mc_formulas_basic_1 = 'C = 2<img src="../../image/pi_small.gif" alt="pi" border="0" align="absmiddle">r';
 var answer_choice7_mc_formulas_basic_1 = 'true';
 var right_answer_choice7_mc_formulas_basic_1 = 'Correct: ';
 var wrong_answer_choice7_mc_formulas_basic_1 = 'Incorrect: This is the formula for the circumference of a circle.';  
 
 var choice8_mc_formulas_basic_1 = '(b<sup>2</sup> - 4ac)/2a';
 var answer_choice8_mc_formulas_basic_1 = 'false';
 var right_answer_choice8_mc_formulas_basic_1 = 'Correct: ';
 var wrong_answer_choice8_mc_formulas_basic_1 = 'Incorrect: A formula must be an equation.'; 
 
 var choice9_mc_formulas_basic_1 = '<img src="../../image/formula_triangle_area_small.gif" alt="formula for the area of a triangle" border="0"  align="absmiddle">';
 var answer_choice9_mc_formulas_basic_1 = 'true';
 var right_answer_choice9_mc_formulas_basic_1 = 'Correct: ';
 var wrong_answer_choice9_mc_formulas_basic_1 = 'Incorrect: This is the formula for the area of a triangle.';  

 var choice10_mc_formulas_basic_1 = '(1/2)bh';
 var answer_choice10_mc_formulas_basic_1 = 'false';
 var right_answer_choice10_mc_formulas_basic_1 = 'Correct: ';
 var wrong_answer_choice10_mc_formulas_basic_1 = 'Incorrect: A formula must be an equation.'; 
 
 var choice_count_mc_formulas_basic_1 = 10;

 
 var mc_formulas_basic_2 =
 ' Which of the following could be the area of a geometric figure?';
 var choice1_mc_formulas_basic_2 = '5 sq.in.';
 var answer_choice1_mc_formulas_basic_2 = 'true';
 var right_answer_choice1_mc_formulas_basic_2 = 'Correct: Can you construct five figures whose area is 5 sq.in.?';
 var wrong_answer_choice1_mc_formulas_basic_2 = 'Incorrect: Clearly a rectangle which is 5 inches long and 1 inch wide has an area equal to 5 sq.in. ';

 var choice2_mc_formulas_basic_2 = '7 ft.';
 var answer_choice2_mc_formulas_basic_2 = 'false';
 var right_answer_choice2_mc_formulas_basic_2 = 'Correct: ';
 var wrong_answer_choice2_mc_formulas_basic_2 = 'Incorrect: feet is a linear measure and area is a square measure'; 
 
 var choice3_mc_formulas_basic_2 = '43 acres';
 var answer_choice3_mc_formulas_basic_2 = 'true';
 var right_answer_choice3_mc_formulas_basic_2 = 'Correct: Do you know how many square feet are in 43 acres?';
 var wrong_answer_choice3_mc_formulas_basic_2 = 'Incorrect: Acre is a measure of area.  Usually used in land measurement. 1 acre = 43,560 sq.ft.'; 
 
 var choice4_mc_formulas_basic_2 = '3m<sup>2</sup>';
 var answer_choice4_mc_formulas_basic_2 = 'true';
 var right_answer_choice4_mc_formulas_basic_2 = 'Correct: This is read as three meters squared or three square meters which is clearly a measure of area.';
 var wrong_answer_choice4_mc_formulas_basic_2 = 'Incorrect: This is read as three meters squared or three square meters which is clearly a measure of area.'; 
 
 var choice5_mc_formulas_basic_2 = '13 yards';
 var answer_choice5_mc_formulas_basic_2 = 'false';
 var right_answer_choice5_mc_formulas_basic_2 = 'Correct: Frequently the term yard is misused to mean cubic yard.  As in five yards of concrete.  Do not make that mistake.';
 var wrong_answer_choice5_mc_formulas_basic_2 = 'Incorrect: yard is a linear measure and area is a square measure'; 
 
 var choice6_mc_formulas_basic_2 = '8 cu.ft.';
 var answer_choice6_mc_formulas_basic_2 = 'false';
 var right_answer_choice6_mc_formulas_basic_2 = 'Correct: Do you know how many cubic inches are in 8 cu.ft.? Do you know how many cubic yards are in 8 cu.ft.?';
 var wrong_answer_choice6_mc_formulas_basic_2 = 'Incorrect: cubic feet is a cubic measure and area is a square measure'; 
 
 var choice_count_mc_formulas_basic_2 = 6; 
 
 
 
 var mc_formulas_basic_3 =
 ' Which of the following are polygons?';
 var choice1_mc_formulas_basic_3 = 'quadrilateral';
 var answer_choice1_mc_formulas_basic_3 = 'true';
 var right_answer_choice1_mc_formulas_basic_3 = 'Correct:';
 var wrong_answer_choice1_mc_formulas_basic_3 = 'Incorrect:  You must compare the definition of quadrilateral with the definition of polygon.';
 
 var choice2_mc_formulas_basic_3 = 'square';
 var answer_choice2_mc_formulas_basic_3 = 'true';
 var right_answer_choice2_mc_formulas_basic_3 = 'Correct:';
 var wrong_answer_choice2_mc_formulas_basic_3 = 'Incorrect:  You must compare the definition of square with the definition of polygon.'; 
 
 var choice3_mc_formulas_basic_3 = 'parallelogram';
 var answer_choice3_mc_formulas_basic_3 = 'true';
 var right_answer_choice3_mc_formulas_basic_3 = 'Correct: ';
 var wrong_answer_choice3_mc_formulas_basic_3 = 'Incorrect:   You must compare the definition of parallelogram with the definition of polygon.'; 
 
 var choice4_mc_formulas_basic_3 = 'rectangle';
 var answer_choice4_mc_formulas_basic_3 = 'true';
 var right_answer_choice4_mc_formulas_basic_3 = 'Correct: ';
 var wrong_answer_choice4_mc_formulas_basic_3 = 'Incorrect: You must compare the definition of rectangle with the definition of polygon.'; 
 
 var choice5_mc_formulas_basic_3 = 'triangle';
 var answer_choice5_mc_formulas_basic_3 = 'true';
 var right_answer_choice5_mc_formulas_basic_3 = 'Correct: ';
 var wrong_answer_choice5_mc_formulas_basic_3 = 'Incorrect: You must compare the definition of triangle with the definition of polygon.'; 
 
 var choice6_mc_formulas_basic_3 = 'trapezoid';
 var answer_choice6_mc_formulas_basic_3 = 'true';
 var right_answer_choice6_mc_formulas_basic_3 = 'Correct: ';
 var wrong_answer_choice6_mc_formulas_basic_3 = 'Incorrect: You must compare the definition of trapezoid with the definition of polygon.'; 
 
 var choice7_mc_formulas_basic_3 = 'circle';
 var answer_choice7_mc_formulas_basic_3 = 'false';
 var right_answer_choice7_mc_formulas_basic_3 = 'Correct: ';
 var wrong_answer_choice7_mc_formulas_basic_3 = 'Incorrect: You must compare the definition of circle with the definition of polygon.'; 
 
  var choice8_mc_formulas_basic_3 = 'ellipse';
 var answer_choice8_mc_formulas_basic_3 = 'false';
 var right_answer_choice8_mc_formulas_basic_3 = 'Correct: ';
 var wrong_answer_choice8_mc_formulas_basic_3 = 'Incorrect: You must compare the definition of ellipse with the definition of polygon.'; 
 
  var choice_count_mc_formulas_basic_3 = 8; 
 
 
  var mc_formulas_basic_4 =
 ' Which of the following are variables?';
 var choice1_mc_formulas_basic_4 = 'x';
 var answer_choice1_mc_formulas_basic_4 = 'true';
 var right_answer_choice1_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice1_mc_formulas_basic_4 = 'Incorrect: A variable is a letter or a subscripted letter which represents a number.';
 
 var choice2_mc_formulas_basic_4 = '3x';
 var answer_choice2_mc_formulas_basic_4 = 'false';
 var right_answer_choice2_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice2_mc_formulas_basic_4 = 'Incorrect:  A variable is a letter or a subscripted letter which represents a number.';
 
 var choice3_mc_formulas_basic_4 = 'x + y';
 var answer_choice3_mc_formulas_basic_4 = 'false';
 var right_answer_choice3_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice3_mc_formulas_basic_4 = 'Incorrect:  A variable is a letter or a subscripted letter which represents a number.';
 
 var choice4_mc_formulas_basic_4 = '-x';
 var answer_choice4_mc_formulas_basic_4 = 'false';
 var right_answer_choice4_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice4_mc_formulas_basic_4 = 'Incorrect: This is the product of -1 and x. Products are not permitted in variables.';
 
 var choice5_mc_formulas_basic_4 = '5';
 var answer_choice5_mc_formulas_basic_4 = 'false';
 var right_answer_choice5_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice5_mc_formulas_basic_4 = 'Incorrect:  Numbers are not variables. A variable is a letter or a subscripted letter which represents a number.';
 
 var choice6_mc_formulas_basic_4 = '&theta';
 var answer_choice6_mc_formulas_basic_4 = 'true';
 var right_answer_choice6_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice6_mc_formulas_basic_4 = 'Incorrect:  A variable is a letter or a subscripted letter which represents a number.';
 
 var choice7_mc_formulas_basic_4 = 'x = 8';
 var answer_choice7_mc_formulas_basic_4 = 'false';
 var right_answer_choice7_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice7_mc_formulas_basic_4 = 'Incorrect:  Equations may involve variables but equations are not variables.';
 
 var choice8_mc_formulas_basic_4 = 'M<sub>k</sub>';
 var answer_choice8_mc_formulas_basic_4 = 'true';
 var right_answer_choice8_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice8_mc_formulas_basic_4 = 'Incorrect:  A variable is a letter or a subscripted letter which represents a number.';
 
 var choice9_mc_formulas_basic_4 = 'x<sub>3</sub>';
 var answer_choice9_mc_formulas_basic_4 = 'true';
 var right_answer_choice9_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice9_mc_formulas_basic_4 = 'Incorrect:  A variable is a letter or a subscripted letter which represents a number.';
 
 var choice10_mc_formulas_basic_4 = '4&lambda;<sup>6</sup>';
 var answer_choice10_mc_formulas_basic_4 = 'false';
 var right_answer_choice10_mc_formulas_basic_4 = 'Correct';
 var wrong_answer_choice10_mc_formulas_basic_4 = 'Incorrect:  A variable cannot involve products or powers.  A variable is a letter or a subscripted letter which represents a number.'; 
 
  var choice_count_mc_formulas_basic_4 = 10; 
 
 

  var mc_formulas_basic_5 =
 ' Which of the following are algebraic expressions?';
 var choice1_mc_formulas_basic_5 = 'x';
 var answer_choice1_mc_formulas_basic_5 = 'true';
 var right_answer_choice1_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice1_mc_formulas_basic_5 = 'Incorrect: Variables are algebraic expressions.';
 
 var choice2_mc_formulas_basic_5 = '3x';
 var answer_choice2_mc_formulas_basic_5 = 'true';
 var right_answer_choice2_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice2_mc_formulas_basic_5 = 'Incorrect: Products of variables and numbers are algebraic expressions.';
 
 var choice3_mc_formulas_basic_5 = 'x + y';
 var answer_choice3_mc_formulas_basic_5 = 'false';
 var right_answer_choice3_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice3_mc_formulas_basic_5 = 'Incorrect: Sums of variables are algebraic expressions.';
 
 var choice4_mc_formulas_basic_5 = 'Phred is a jerk.';
 var answer_choice4_mc_formulas_basic_5 = 'false';
 var right_answer_choice4_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice4_mc_formulas_basic_5 = 'Incorrect: This does not satisfy any of the conditions in the definition of algebraic expression.';
 
 var choice5_mc_formulas_basic_5 = '5';
 var answer_choice5_mc_formulas_basic_5 = 'true';
 var right_answer_choice5_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice5_mc_formulas_basic_5 = 'Incorrect: Numbers are algebraic expressions.';
 
 var choice6_mc_formulas_basic_5 = '-&theta';
 var answer_choice6_mc_formulas_basic_5 = 'true';
 var right_answer_choice6_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice6_mc_formulas_basic_5 = 'Incorrect: The opposite of theta is the same as the product of -1 and theta.  Products of numbers and variables are algebraic expressions.';
 
 var choice7_mc_formulas_basic_5 = 'x = 8';
 var answer_choice7_mc_formulas_basic_5 = 'false';
 var right_answer_choice7_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice7_mc_formulas_basic_5 = 'Incorrect: A variable is a letter.';
 
 var choice8_mc_formulas_basic_5 = '47/M<sub>k</sub>';
 var answer_choice8_mc_formulas_basic_5 = 'true';
 var right_answer_choice8_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice8_mc_formulas_basic_5 = 'Incorrect: Quotients are permitted.';
 
 var choice9_mc_formulas_basic_5 = 'x = length';
 var answer_choice9_mc_formulas_basic_5 = 'false';
 var right_answer_choice9_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice9_mc_formulas_basic_5 = 'Incorrect: Not only does this not satisfy the conditions in the definition of an algebraic expression, it is also grammatically incorrect.';
 
 var choice10_mc_formulas_basic_5 = '(4&lambda;)/(2xyz<sup>6</sup>)';
 var answer_choice10_mc_formulas_basic_5 = 'true';
 var right_answer_choice10_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice10_mc_formulas_basic_5 = 'Incorrect: .'; 
 
 var choice11_mc_formulas_basic_5 = ' <img src="../../image/complex_number_inverse_small.gif" alt="inverse of a complex number" border="0" align="absmiddle">';
 var answer_choice11_mc_formulas_basic_5 = 'true';
 var right_answer_choice11_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice11_mc_formulas_basic_5 = 'Incorrect: You should study the definition of algebraic expression.'; 
 
 var choice12_mc_formulas_basic_5 = ' <img src="../../image/radical_radicand_index_large.gif" alt="radical  nth root of b" border="0" align="absmiddle">';
 var answer_choice12_mc_formulas_basic_5 = 'true';
 var right_answer_choice12_mc_formulas_basic_5 = 'Correct';
 var wrong_answer_choice12_mc_formulas_basic_5 = 'Incorrect: You should study the definition of algebraic expression.'; 
 
  var choice_count_mc_formulas_basic_5 = 12; 
  
  
  var mc_formulas_basic_6 =
 ' Which of the following are algebraic expressions and are NOT variables?';
 var choice1_mc_formulas_basic_6 = 'x';
 var answer_choice1_mc_formulas_basic_6 = 'false';
 var right_answer_choice1_mc_formulas_basic_6 = 'Correct';
 var wrong_answer_choice1_mc_formulas_basic_6 = 'Incorrect: x is a varible.';
 
 var choice2_mc_formulas_basic_6 = '3x';
 var answer_choice2_mc_formulas_basic_6 = 'true';
 var right_answer_choice2_mc_formulas_basic_6 = 'Correct';
 var wrong_answer_choice2_mc_formulas_basic_6 = 'Incorrect: Products of variables and numbers are algebraic expressions but are not variables.';
 
 var choice3_mc_formulas_basic_6 = 'x + y';
 var answer_choice3_mc_formulas_basic_6 = 'true';
 var right_answer_choice3_mc_formulas_basic_6 = 'Correct';
 var wrong_answer_choice3_mc_formulas_basic_6 = 'Incorrect: Sums of variables are algebraic expressions but are not variables.';
 
 var choice4_mc_formulas_basic_6 = '<img src="../../image/square_root_of_5_small.gif" alt="square root of five" border="0" align="absmiddle">';
 var answer_choice4_mc_formulas_basic_6 = 'true';
 var right_answer_choice4_mc_formulas_basic_6 = 'Correct';
 var wrong_answer_choice4_mc_formulas_basic_6 = 'Incorrect: This is an algebraic expression but certainly is not a variable.';
 
 var choice5_mc_formulas_basic_6 = 'The circumference of a circle is the product of its diameter and pi.';
 var answer_choice5_mc_formulas_basic_6 = 'false';
 var right_answer_choice5_mc_formulas_basic_6 = 'Correct';
 var wrong_answer_choice5_mc_formulas_basic_6 = 'Incorrect: This satisfies none of the conditions in the definition of  algebraic expressions.';
 
 var choice6_mc_formulas_basic_6 = '-&theta';
 var answer_choice6_mc_formulas_basic_6 = 'true';
 var right_answer_choice6_mc_formulas_basic_6 = 'Correct';
 var wrong_answer_choice6_mc_formulas_basic_6 = 'Incorrect: The opposite of theta is the same as the product of -1 and theta.  Products of numbers and variables are algebraic expressions. Variables do not involve products.';
 
var choice_count_mc_formulas_basic_6 = 6; 


//insert equation_identify_clasify//
//note error in next group// 
 
var mc_equation_solution_solve_2 = ' Which of the following actions will generate an equation which is equivalent to the original equation ?';

var choice1_mc_equation_solution_solve_2 = 'Adding 23 to both sides of an equation.';
var answer_choice1_mc_equation_solution_solve_2 = 'true';
var right_answer_choice1_mc_equation_solution_solve_2 = 'Correct:';
var wrong_answer_choice1_mc_equation_solution_solve_2 = 'Incorrect:'; 
 
var choice2_mc_equation_solution_solve_2 = 'Multiplying both sides of an equation by 3x.';
var answer_choice2_mc_equation_solution_solve_2 = 'false';
var right_answer_choice2_mc_equation_solution_solve_2 = 'Correct:';
var wrong_answer_choice2_mc_equation_solution_solve_2 = 'Incorrect:'; 

var choice3_mc_equation_solution_solve_2 = 'Multiplying both sides of an equation by <img src="../../images/sq_root_7.gif" width="26" height="23" align="absmiddle">';
var answer_choice3_mc_equation_solution_solve_2 = 'true';
var right_answer_choice3_mc_equation_solution_solve_2 = 'Correct: ';
var wrong_answer_choice3_mc_equation_solution_solve_2 = 'Incorrect: ';

var choice4_mc_equation_solution_solve_2 = 'squaring both sides of an equation.';
var answer_choice4_mc_equation_solution_solve_2 = 'false';
var right_answer_choice4_mc_equation_solution_solve_2 = 'Correct: ';
var wrong_answer_choice4_mc_equation_solution_solve_2 = 'Incorrect: This myth will be dispelled later in the course.';

var choice5_mc_equation_solution_solve_2 = 'Adding 3x<sup>14</sup> + 5x<sup>4</sup> - 37 to both sides.';
var answer_choice5_mc_equation_solution_solve_2 = 'true';
var right_answer_choice5_mc_equation_solution_solve_2 = 'Correct: ';
var wrong_answer_choice5_mc_equation_solution_solve_2 = 'Incorrect: ';

var choice6_mc_equation_solution_solve_2 = 'Multiplying both sides by the lowest common denominator.';
var answer_choice6_mc_equation_solution_solve_2 = 'false';
var right_answer_choice6_mc_equation_solution_solve_2 = 'Correct: ';
var wrong_answer_choice6_mc_equation_solution_solve_2 = 'Incorrect: Another myth which will be busted later in the course.';
 
var choice_count_mc_equation_solution_solve_2 = 6; 
 
 
   //chapter1 section1 group3 equation_linear_one_variable //

var mc_equation_linear_one_variable_max_count = 1;
 
 
var mc_equation_linear_one_variable_1 = ' Which of the following are linear equations in one variable ?';

var choice1_mc_equation_linear_one_variable_1 = '3x + 2 = 0';
var answer_choice1_mc_equation_linear_one_variable_1 = 'true';
var right_answer_choice1_mc_equation_linear_one_variable_1 = 'Correct: ';
var wrong_answer_choice1_mc_equation_linear_one_variable_1 = 'Incorrect:  '; 
  
var choice2_mc_equation_linear_one_variable_1 = '3x -7 = 0';
var answer_choice2_mc_equation_linear_one_variable_1 = 'true';
var right_answer_choice2_mc_equation_linear_one_variable_1 = 'Correct: ';
var wrong_answer_choice2_mc_equation_linear_one_variable_1 = 'Incorrect:  ';  
 
var choice3_mc_equation_linear_one_variable_1 = '3x<sup>2</sup> + 2 = 0';
var answer_choice3_mc_equation_linear_one_variable_1 = 'false';
var right_answer_choice3_mc_equation_linear_one_variable_1 = 'Correct: ';
var wrong_answer_choice3_mc_equation_linear_one_variable_1 = 'Incorrect:  ';  
 
var choice4_mc_equation_linear_one_variable_1 = '-4x = 3';
var answer_choice4_mc_equation_linear_one_variable_1 = 'true';
var right_answer_choice4_mc_equation_linear_one_variable_1 = 'Correct: ';
var wrong_answer_choice4_mc_equation_linear_one_variable_1 = 'Incorrect:  ';  
 
var choice5_mc_equation_linear_one_variable_1 = '5 = 3 + 2';
var answer_choice5_mc_equation_linear_one_variable_1 = 'false';
var right_answer_choice5_mc_equation_linear_one_variable_1 = 'Correct: ';
var wrong_answer_choice5_mc_equation_linear_one_variable_1 = 'Incorrect:  ';  
 
var choice6_mc_equation_linear_one_variable_1 = '5x - 4 = 3x + 8';
var answer_choice6_mc_equation_linear_one_variable_1 = 'true';
var right_answer_choice6_mc_equation_linear_one_variable_1 = 'Correct: ';
var wrong_answer_choice6_mc_equation_linear_one_variable_1 = 'Incorrect:  ';  
 
var choice7_mc_equation_linear_one_variable_1 = 'y = 3x + 5';
var answer_choice7_mc_equation_linear_one_variable_1 = 'false';
var right_answer_choice7_mc_equation_linear_one_variable_1 = 'Correct: ';
var wrong_answer_choice7_mc_equation_linear_one_variable_1 = 'Incorrect:  ';  
 
var choice8_mc_equation_linear_one_variable_1 = '3x + 2 = 0';
var answer_choice8_mc_equation_linear_one_variable_1 = 'true';
var right_answer_choice8_mc_equation_linear_one_variable_1 = 'Correct: ';
var wrong_answer_choice8_mc_equation_linear_one_variable_1 = 'Incorrect:  ';  
 
var choice_count_mc_equation_linear_one_variable_1 = 8;  
 
 
 
   //chapter1 section3 group2 equation_quadratic_one_variable //

var mc_equation_quadratic_one_variable_max_count = 4;
 
 
var mc_equation_quadratic_one_variable_1 = ' Which of the following are quadratic equations in one variable ?';

var choice1_mc_equation_quadratic_one_variable_1 = '3x + 2 = 0';
var answer_choice1_mc_equation_quadratic_one_variable_1 = 'false';
var right_answer_choice1_mc_equation_quadratic_one_variable_1 = 'Correct: ';
var wrong_answer_choice1_mc_equation_quadratic_one_variable_1 = 'Incorrect:  '; 
  
var choice2_mc_equation_quadratic_one_variable_1 = '3x<sup>2</sup> -7 = 0';
var answer_choice2_mc_equation_quadratic_one_variable_1 = 'true';
var right_answer_choice2_mc_equation_quadratic_one_variable_1 = 'Correct: ';
var wrong_answer_choice2_mc_equation_quadratic_one_variable_1 = 'Incorrect:  ';  
 
var choice3_mc_equation_quadratic_one_variable_1 = '3x<sup>2</sup> + 2x - 17 = 0';
var answer_choice3_mc_equation_quadratic_one_variable_1 = 'true';
var right_answer_choice3_mc_equation_quadratic_one_variable_1 = 'Correct: ';
var wrong_answer_choice3_mc_equation_quadratic_one_variable_1 = 'Incorrect:  ';  
 
var choice4_mc_equation_quadratic_one_variable_1 = '-4x<sup>2</sup> = 3x + 5';
var answer_choice4_mc_equation_quadratic_one_variable_1 = 'true';
var right_answer_choice4_mc_equation_quadratic_one_variable_1 = 'Correct: ';
var wrong_answer_choice4_mc_equation_quadratic_one_variable_1 = 'Incorrect:  ';  
 
var choice5_mc_equation_quadratic_one_variable_1 = '5 = 3 + 2';
var answer_choice5_mc_equation_quadratic_one_variable_1 = 'false';
var right_answer_choice5_mc_equation_quadratic_one_variable_1 = 'Correct: ';
var wrong_answer_choice5_mc_equation_quadratic_one_variable_1 = 'Incorrect:  ';  
 
var choice6_mc_equation_quadratic_one_variable_1 = '5x<sup>2</sup> - 4 = 3x + 8';
var answer_choice6_mc_equation_quadratic_one_variable_1 = 'true';
var right_answer_choice6_mc_equation_quadratic_one_variable_1 = 'Correct: ';
var wrong_answer_choice6_mc_equation_quadratic_one_variable_1 = 'Incorrect:  ';  
 
var choice7_mc_equation_quadratic_one_variable_1 = 'y = 3x<sup>2</sup> - 5x + 3';
var answer_choice7_mc_equation_quadratic_one_variable_1 = 'false';
var right_answer_choice7_mc_equation_quadratic_one_variable_1 = 'Correct: ';
var wrong_answer_choice7_mc_equation_quadratic_one_variable_1 = 'Incorrect:  ';  
 
var choice8_mc_equation_quadratic_one_variable_1 = '(x + 4)(x - 5)= 9';
var answer_choice8_mc_equation_quadratic_one_variable_1 = 'true';
var right_answer_choice8_mc_equation_quadratic_one_variable_1 = 'Correct: ';
var wrong_answer_choice8_mc_equation_quadratic_one_variable_1 = 'Incorrect:  ';  
 
var choice_count_mc_equation_quadratic_one_variable_1 = 8;  
  
 

var mc_equation_quadratic_one_variable_2 = ' Which of the following quadratic equations have exactly one real solution ?';

var choice1_mc_equation_quadratic_one_variable_2 = 'x<sup>2</sup> + 2x + 1 = 0';
var answer_choice1_mc_equation_quadratic_one_variable_2 = 'true';
var right_answer_choice1_mc_equation_quadratic_one_variable_2 = 'Correct: ';
var wrong_answer_choice1_mc_equation_quadratic_one_variable_2 = 'Incorrect:  '; 
  
var choice2_mc_equation_quadratic_one_variable_2 = '3x<sup>2</sup> + 5x + 1 = 0';
var answer_choice2_mc_equation_quadratic_one_variable_2 = 'false';
var right_answer_choice2_mc_equation_quadratic_one_variable_2 = 'Correct: ';
var wrong_answer_choice2_mc_equation_quadratic_one_variable_2 = 'Incorrect:  ';  
 
var choice3_mc_equation_quadratic_one_variable_2 = 'x<sup>2</sup> + 6x + 9 = 0';
var answer_choice3_mc_equation_quadratic_one_variable_2 = 'true';
var right_answer_choice3_mc_equation_quadratic_one_variable_2 = 'Correct: ';
var wrong_answer_choice3_mc_equation_quadratic_one_variable_2 = 'Incorrect:  ';  
 
var choice4_mc_equation_quadratic_one_variable_2 = 'x<sup>2</sup> - 2x + 1 = 0';
var answer_choice4_mc_equation_quadratic_one_variable_2 = 'true';
var right_answer_choice4_mc_equation_quadratic_one_variable_2 = 'Correct: ';
var wrong_answer_choice4_mc_equation_quadratic_one_variable_2 = 'Incorrect:  ';  
 
var choice5_mc_equation_quadratic_one_variable_2 = '-2x<sup>2</sup> + 8x - 8 = 0';
var answer_choice5_mc_equation_quadratic_one_variable_2 = 'true';
var right_answer_choice5_mc_equation_quadratic_one_variable_2 = 'Correct: ';
var wrong_answer_choice5_mc_equation_quadratic_one_variable_2 = 'Incorrect:  ';  
 
var choice6_mc_equation_quadratic_one_variable_2 = '(x - 5)<sup>2</sup> = 0';
var answer_choice6_mc_equation_quadratic_one_variable_2 = 'true';
var right_answer_choice6_mc_equation_quadratic_one_variable_2 = 'Correct: ';
var wrong_answer_choice6_mc_equation_quadratic_one_variable_2 = 'Incorrect:  ';  
 
var choice_count_mc_equation_quadratic_one_variable_2 = 6; 
 
 
 

var mc_equation_quadratic_one_variable_3 = '{2, 5} is the solution set for which of the following quadratic equations. ?';

var choice1_mc_equation_quadratic_one_variable_3 = 'x<sup>2</sup> -7x + 10 = 0';
var answer_choice1_mc_equation_quadratic_one_variable_3 = 'true';
var right_answer_choice1_mc_equation_quadratic_one_variable_3 = 'Correct: ';
var wrong_answer_choice1_mc_equation_quadratic_one_variable_3 = 'Incorrect:  '; 
  
var choice2_mc_equation_quadratic_one_variable_3 = 'x<sup>2</sup> + 3x - 10 = 0 ';
var answer_choice2_mc_equation_quadratic_one_variable_3 = 'false';
var right_answer_choice2_mc_equation_quadratic_one_variable_3 = 'Correct: ';
var wrong_answer_choice2_mc_equation_quadratic_one_variable_3 = 'Incorrect:  ';  
 
var choice3_mc_equation_quadratic_one_variable_3 = 'x<sup>2</sup> + 20x + 10 = 0';
var answer_choice3_mc_equation_quadratic_one_variable_3 = 'false';
var right_answer_choice3_mc_equation_quadratic_one_variable_3 = 'Correct: ';
var wrong_answer_choice3_mc_equation_quadratic_one_variable_3 = 'Incorrect:  ';  
 
var choice4_mc_equation_quadratic_one_variable_3 = '(x - 2)(x - 5) = 0';
var answer_choice4_mc_equation_quadratic_one_variable_3 = 'true';
var right_answer_choice4_mc_equation_quadratic_one_variable_3 = 'Correct: ';
var wrong_answer_choice4_mc_equation_quadratic_one_variable_3 = 'Incorrect:  ';  
 
var choice5_mc_equation_quadratic_one_variable_3 = '(x -2)(x + 5) = 0';
var answer_choice5_mc_equation_quadratic_one_variable_3 = 'true';
var right_answer_choice5_mc_equation_quadratic_one_variable_3 = 'Correct: ';
var wrong_answer_choice5_mc_equation_quadratic_one_variable_3 = 'Incorrect:  ';

var choice6_mc_equation_quadratic_one_variable_3 = '3x<sup>2</sup> -21x + 30 ';
var answer_choice6_mc_equation_quadratic_one_variable_3 = 'true';
var right_answer_choice6_mc_equation_quadratic_one_variable_3 = 'Correct: ';
var wrong_answer_choice6_mc_equation_quadratic_one_variable_3 = 'Incorrect:  ';

var choice_count_mc_equation_quadratic_one_variable_3 = 6;
 
 
 
var mc_equation_quadratic_one_variable_4 = 'Which of the following are solutions of 2x<sup>2</sup> + 7x + 3 ?';

var choice1_mc_equation_quadratic_one_variable_4 = '3';
var answer_choice1_mc_equation_quadratic_one_variable_4 = 'false';
var right_answer_choice1_mc_equation_quadratic_one_variable_4 = 'Correct: ';
var wrong_answer_choice1_mc_equation_quadratic_one_variable_4 = 'Incorrect:  '; 
  
var choice2_mc_equation_quadratic_one_variable_4 = '-1/2';
var answer_choice2_mc_equation_quadratic_one_variable_4 = 'true';
var right_answer_choice2_mc_equation_quadratic_one_variable_4 = 'Correct: ';
var wrong_answer_choice2_mc_equation_quadratic_one_variable_4 = 'Incorrect:  ';  
 
var choice3_mc_equation_quadratic_one_variable_4 = '1/2 and -1/2';
var answer_choice3_mc_equation_quadratic_one_variable_4 = 'false';
var right_answer_choice3_mc_equation_quadratic_one_variable_4 = 'Correct: ';
var wrong_answer_choice3_mc_equation_quadratic_one_variable_4 = 'Incorrect:  ';  
 
var choice4_mc_equation_quadratic_one_variable_4 = '-3';
var answer_choice4_mc_equation_quadratic_one_variable_4 = 'true';
var right_answer_choice4_mc_equation_quadratic_one_variable_4 = 'Correct: ';
var wrong_answer_choice4_mc_equation_quadratic_one_variable_4 = 'Incorrect:  ';  
 
var choice5_mc_equation_quadratic_one_variable_4 = '3 and -3';
var answer_choice5_mc_equation_quadratic_one_variable_4 = 'true';
var right_answer_choice5_mc_equation_quadratic_one_variable_4 = 'Correct: ';
var wrong_answer_choice5_mc_equation_quadratic_one_variable_4 = 'Incorrect:  ';

var choice6_mc_equation_quadratic_one_variable_4 = '-3 and -1/2';
var answer_choice6_mc_equation_quadratic_one_variable_4 = 'true';
var right_answer_choice6_mc_equation_quadratic_one_variable_4 = 'Correct: ';
var wrong_answer_choice6_mc_equation_quadratic_one_variable_4 = 'Incorrect:  ';

var choice_count_mc_equation_quadratic_one_variable_4 = 6;