//chapter2 section 5 group 1 percent //
var tf_percent_max_count =1;
var tf_percent_1 = 'COMING SOON.';
var answer_tf_percent_1 = 'false';
var feedback_right_tf_percent_1 = 'CORRECT:';
var feedback_wrong_tf_percent_1 = 'INCORRECT:';


//chapter3 section 3 group 1 graph_linear_equations_inequalities_two_variables //
var tf_graph_linear_equations_inequalities_two_variables_max_count =9;
var tf_graph_linear_equations_inequalities_two_variables_1 = 'The graph of an equation of the form x = k is a vertical line through the point (0, k).';
var answer_tf_graph_linear_equations_inequalities_two_variables_1 = 'true';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_1 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_1 = 'INCORRECT:';

var tf_graph_linear_equations_inequalities_two_variables_2 = 'The boundary curve for a linear inequality in two variables is a line.';
var answer_tf_graph_linear_equations_inequalities_two_variables_2 = 'true';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_2 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_2 = 'INCORRECT:';

var tf_graph_linear_equations_inequalities_two_variables_3 = 'If the inequality symbol in an inequality in two variables is replaced with an equality symbol, the graph of the resulting equation is called the boundary curve for the inequality.';
var answer_tf_graph_linear_equations_inequalities_two_variables_3 = 'true';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_3 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_3 = 'INCORRECT:';

var tf_graph_linear_equations_inequalities_two_variables_4 = 'A linear equation in two variables is an equation that can be written in the form y = mx + b  where m and b are real numbers.';
var answer_tf_graph_linear_equations_inequalities_two_variables_4 = 'true';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_4 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_4 = 'INCORRECT:';

var tf_graph_linear_equations_inequalities_two_variables_5 = 'The boundary curve for a linear inequality in two variables is a half-plane.';
var answer_tf_graph_linear_equations_inequalities_two_variables_5 = 'false';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_5 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_5 = 'INCORRECT:';

var tf_graph_linear_equations_inequalities_two_variables_6 = 'The equation for the vertical line through the point (0, k) is x = k.';
var answer_tf_graph_linear_equations_inequalities_two_variables_6 = 'true';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_6 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_6 = 'INCORRECT:';

var tf_graph_linear_equations_inequalities_two_variables_7 = '3x + 2y > 7 is a linear inequality in two variables.';
var answer_tf_graph_linear_equations_inequalities_two_variables_7 = 'true';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_7 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_7 = 'INCORRECT:';

var tf_graph_linear_equations_inequalities_two_variables_8 = 'The equation for the vertical line through the point (0, k) is y = k.';
var answer_tf_graph_linear_equations_inequalities_two_variables_8 = 'false';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_8 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_8 = 'INCORRECT:';

var tf_graph_linear_equations_inequalities_two_variables_9 = 'The graph of an inequality consists of all the points, and only those points, whose coordinates are solutions of the inequality. ';
var answer_tf_graph_linear_equations_inequalities_two_variables_9 = 'true';
var feedback_right_tf_graph_linear_equations_inequalities_two_variables_9 = 'CORRECT:';
var feedback_wrong_tf_graph_linear_equations_inequalities_two_variables_9 = 'INCORRECT:';

//chapter3 section 4 group 1 slope_line //
var tf_slope_line_max_count =12;
var tf_slope_line_1 = 'A vertical line has no slope.';
var answer_tf_slope_line_1 = 'true';
var feedback_right_tf_slope_line_1 = 'CORRECT:';
var feedback_wrong_tf_slope_line_1 = 'INCORRECT:';

var tf_slope_line_2 = 'Some non-vertical lines have no slope.';
var answer_tf_slope_line_2 = 'false';
var feedback_right_tf_slope_line_2 = 'CORRECT:';
var feedback_wrong_tf_slope_line_2 = 'INCORRECT:';

var tf_slope_line_3 = 'The slope of a vertical line is 0.';
var answer_tf_slope_line_3 = 'false';
var feedback_right_tf_slope_line_3 = 'CORRECT:';
var feedback_wrong_tf_slope_line_3 = 'INCORRECT:';

var tf_slope_line_4 = 'If two line have the same slope, they are parallel.';
var answer_tf_slope_line_4 = 'false';
var feedback_right_tf_slope_line_4 = 'CORRECT:';
var feedback_wrong_tf_slope_line_4 = 'INCORRECT:';

var tf_slope_line_5 = 'If the slope of a line is 0, the line is horizontal.';
var answer_tf_slope_line_5 = 'true';
var feedback_right_tf_slope_line_5 = 'CORRECT:';
var feedback_wrong_tf_slope_line_5 = 'INCORRECT:';

var tf_slope_line_6 = 'The slope of a line through two points is the quotient of the difference in first coordinates divided by the quotient of the second coordinates.';
var answer_tf_slope_line_6 = 'true';
var feedback_right_tf_slope_line_6 = 'CORRECT:';
var feedback_wrong_tf_slope_line_6 = 'INCORRECT:';

var tf_slope_line_7 = 'A horizontal line has no slope.';
var answer_tf_slope_line_7 = 'false';
var feedback_right_tf_slope_line_7 = 'CORRECT:';
var feedback_wrong_tf_slope_line_7 = 'INCORRECT:';

var tf_slope_line_8 = 'Two non-vertical lines are parallel if they have the same slope and different y-intercepts.';
var answer_tf_slope_line_8 = 'true';
var feedback_right_tf_slope_line_8 = 'CORRECT:';
var feedback_wrong_tf_slope_line_8 = 'INCORRECT:';

var tf_slope_line_9 = 'If the slope of one line is 3 and a second line has slope -3, the lines are perpendicular.';
var answer_tf_slope_line_9 = 'false';
var feedback_right_tf_slope_line_9 = 'CORRECT:';
var feedback_wrong_tf_slope_line_9 = 'INCORRECT:';

var tf_slope_line_10 = 'The slope of a line through two points is the quotient of the difference in second coordinates divided by the quotient of the first coordinates.';
var answer_tf_slope_line_10 = 'false';
var feedback_right_tf_slope_line_10 = 'CORRECT:';
var feedback_wrong_tf_slope_line_10 = 'INCORRECT:';

var tf_slope_line_11 = 'Two non-vertical lines are perpendicular if their slopes are negative reciprocals of each other.';
var answer_tf_slope_line_11 = 'true';
var feedback_right_tf_slope_line_11 = 'CORRECT:';
var feedback_wrong_tf_slope_line_11 = 'INCORRECT:';

var tf_slope_line_12 = 'The slope of a line through two points is given by the formula <img src="../../image/slope_formula.gif">.';
var answer_tf_slope_line_12 = 'false';
var feedback_right_tf_slope_line_12 = 'CORRECT:';
var feedback_wrong_tf_slope_line_12 = 'INCORRECT:';

//chapter3 section 5 group 1 equations_of_lines //
var tf_equations_of_lines_max_count =13;
var tf_equations_of_lines_1 = 'Ax + By = C is called the slope-intercept form.';
var answer_tf_equations_of_lines_1 = 'false';
var feedback_right_tf_equations_of_lines_1 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_1 = 'INCORRECT:';

var tf_equations_of_lines_2 = 'A linear equation in two variables may be written in the form y = mx + b where m is the slope and b is the y-intercept..';
var answer_tf_equations_of_lines_2 = 'true';
var feedback_right_tf_equations_of_lines_2 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_2 = 'INCORRECT:';

var tf_equations_of_lines_3 = 'The equation of any non-vertical line can be written ing the form y = mx + b.';
var answer_tf_equations_of_lines_3 = 'true';
var feedback_right_tf_equations_of_lines_3 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_3 = 'INCORRECT:';

var tf_equations_of_lines_4 = 'The slope of a line through two points is given by the formula <img src="../../image/slope_formula.gif">.';
var answer_tf_equations_of_lines_4 = 'true';
var feedback_right_tf_equations_of_lines_4 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_4 = 'INCORRECT:';

var tf_equations_of_lines_5 = 'y = mx + b is called the slope-intercept form.';
var answer_tf_equations_of_lines_5 = 'true';
var feedback_right_tf_equations_of_lines_5 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_5 = 'INCORRECT:';

var tf_equations_of_lines_6 = 'y - y<sub>1</sub> = m(x - x<sub>1</sub>) is called the slope-intercept form.';
var answer_tf_equations_of_lines_6 = 'false';
var feedback_right_tf_equations_of_lines_6 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_6 = 'INCORRECT:';

var tf_equations_of_lines_7 = 'The graph of y = x<sup>2</sup> + 3x - 6 is a line.';
var answer_tf_equations_of_lines_7 = 'false';
var feedback_right_tf_equations_of_lines_7 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_7 = 'INCORRECT:';

var tf_equations_of_lines_8 = 'In the equation y = mx + b, the number b is the x-intercept.';
var answer_tf_equations_of_lines_8 = 'false';
var feedback_right_tf_equations_of_lines_8 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_8 = 'INCORRECT:';

var tf_equations_of_lines_9 = 'To find the x-intercept of the graph of y = 3x - 6, set x = 0 and solve for y.';
var answer_tf_equations_of_lines_9 = 'false';
var feedback_right_tf_equations_of_lines_9 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_9 = 'INCORRECT:';

var tf_equations_of_lines_10 = 'y - y<sub>1</sub> = m(x - x<sub>1</sub>) is the point-slope form of the equation of a line.';
var answer_tf_equations_of_lines_10 = 'true';
var feedback_right_tf_equations_of_lines_10 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_10 = 'INCORRECT:';

var tf_equations_of_lines_11 = 'In the equation y = mx + b, the number b is the y-intercept.';
var answer_tf_equations_of_lines_11 = 'true';
var feedback_right_tf_equations_of_lines_11 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_11 = 'INCORRECT:';

var tf_equations_of_lines_12 = 'To find the x-intercept of the graph of y = 3x - 6, set y = 0 and solve for x.';
var answer_tf_equations_of_lines_12 = 'true';
var feedback_right_tf_equations_of_lines_12 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_12 = 'INCORRECT:';

var tf_equations_of_lines_13 = 'The slope of the line through (2, 1) and (11 ,4) is 3.';
var answer_tf_equations_of_lines_13 = 'false';
var feedback_right_tf_equations_of_lines_13 = 'CORRECT:';
var feedback_wrong_tf_equations_of_lines_13 = 'INCORRECT:';













//chapter3 section 1 group 1 graph_equations_two_variables //
var tf_graph_equations_two_variables_max_count =10;
var tf_graph_equations_two_variables_1 = 'In a Cartesian coordinate system, the horizontal line is usually called the x-axis.';
var answer_tf_graph_equations_two_variables_1 = 'true';
var feedback_right_tf_graph_equations_two_variables_1 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_1 = 'INCORRECT:';

var tf_graph_equations_two_variables_2 = 'In a Cartesian coordinate system, the vertical line is usually called the x-axis.';
var answer_tf_graph_equations_two_variables_2 = 'false';
var feedback_right_tf_graph_equations_two_variables_2 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_2 = 'INCORRECT:';

var tf_graph_equations_two_variables_3 = 'In a Cartesian coordinate system, the point of intersection of the two number lines is called the origin.';
var answer_tf_graph_equations_two_variables_3 = 'true';
var feedback_right_tf_graph_equations_two_variables_3 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_3 = 'INCORRECT:';

var tf_graph_equations_two_variables_4 = 'The solution of an equation in two variables is an ordered pair of numbers.';
var answer_tf_graph_equations_two_variables_4 = 'true';
var feedback_right_tf_graph_equations_two_variables_4 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_4 = 'INCORRECT:';

var tf_graph_equations_two_variables_5 = 'The solution of an inequality in two variables is a region of the Cartesian coordinate system.';
var answer_tf_graph_equations_two_variables_5 = 'true';
var feedback_right_tf_graph_equations_two_variables_5 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_5 = 'INCORRECT:';

var tf_graph_equations_two_variables_6 = 'The solution of an inequality in two variables is an ordered pair of numbers.';
var answer_tf_graph_equations_two_variables_6 = 'true';
var feedback_right_tf_graph_equations_two_variables_6 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_6 = 'INCORRECT:';

var tf_graph_equations_two_variables_7 = 'A point is on the x-axis if and only if its second coordinate y is zero.';
var answer_tf_graph_equations_two_variables_7 = 'true';
var feedback_right_tf_graph_equations_two_variables_7 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_7 = 'INCORRECT:';

var tf_graph_equations_two_variables_8 = 'A point is on the x-axis if and only if its second coordinate x is zero.';
var answer_tf_graph_equations_two_variables_8 = 'false';
var feedback_right_tf_graph_equations_two_variables_8 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_8 = 'INCORRECT:';

var tf_graph_equations_two_variables_9 = 'A point is on the y-axis if and only if its second coordinate y is zero.';
var answer_tf_graph_equations_two_variables_9 = 'false';
var feedback_right_tf_graph_equations_two_variables_9 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_9 = 'INCORRECT:';

var tf_graph_equations_two_variables_10 = 'The equation of a circle with radius r and center at the origin is x<sup>2</sup> + y<sup>2</sup> = r<sup>2</sup>.';
var answer_tf_graph_equations_two_variables_10 = 'true';
var feedback_right_tf_graph_equations_two_variables_10 = 'CORRECT:';
var feedback_wrong_tf_graph_equations_two_variables_10 = 'INCORRECT:';



//chapter2 section 5 group 2 compound _inequalities //

 var tf_compound_inequalities_max_count =10;
 
var tf_compound_inequalities_1 = 'Every compound inequality can be written in compact form.';
var answer_tf_compound_inequalities_1 = 'false';
var feedback_right_tf_compound_inequalities_1 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_1 = 'INCORRECT:';
 
var tf_compound_inequalities_2 = 'Every compound inequality consists of two inequalities joined with the conjuction or.';
var answer_tf_compound_inequalities_2 = 'false';
var feedback_right_tf_compound_inequalities_2 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_2 = 'INCORRECT:';
 
var tf_compound_inequalities_3 = 'Every compound inequality consists of two inequalities joined with the conjuction and or the conjuction or.';
var answer_tf_compound_inequalities_3 = 'true';
var feedback_right_tf_compound_inequalities_3 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_3 = 'INCORRECT:';
 
var tf_compound_inequalities_4 = 'The solution set for the compound inequality 3 < x and x < 5 is (-&#8734;, 5) &#8745; (3, &#8734;).';
var answer_tf_compound_inequalities_4 = 'true';
var feedback_right_tf_compound_inequalities_4 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_4 = 'INCORRECT:';
 
var tf_compound_inequalities_5 = 'The solution set for the compound inequality -4 < x and x < 5 is (-&#8734;, 5) &#8746; (-4, &#8734;).';
var answer_tf_compound_inequalities_5 = 'false';
var feedback_right_tf_compound_inequalities_5 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_5 = 'INCORRECT:';
 
var tf_compound_inequalities_6 = '2 < x < 9 is a compact compound inequality.';
var answer_tf_compound_inequalities_6 = 'true';
var feedback_right_tf_compound_inequalities_6 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_6 = 'INCORRECT:';
 
var tf_compound_inequalities_7 = '2 < 3x + 2 < 9 is a compact compound inequality.';
var answer_tf_compound_inequalities_7 = 'true';
var feedback_right_tf_compound_inequalities_7 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_7 = 'INCORRECT:';
 
var tf_compound_inequalities_8 = '2 < 3x + 2 > 9 is a compact compound inequality.';
var answer_tf_compound_inequalities_8 = 'false';
var feedback_right_tf_compound_inequalities_8 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_8 = 'INCORRECT:';
 
var tf_compound_inequalities_9 = '2 < 3x + 2 and 5x < 9 is a compact compound inequality.';
var answer_tf_compound_inequalities_9 = 'false';
var feedback_right_tf_compound_inequalities_9 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_9 = 'INCORRECT:';

var tf_compound_inequalities_10 = '2 > 3x + 2 > 9 is a compact compound inequality.';
var answer_tf_compound_inequalities_10 = 'false';
var feedback_right_tf_compound_inequalities_10 = 'CORRECT:';
var feedback_wrong_tf_compound_inequalities_10 = 'INCORRECT:';


//chapter1 section 3 group 3 exponents_and_roots //

 var tf_exponents_and_roots_max_count =10;
 
 var tf_exponents_and_roots_1 =
 '-84<sup>2</sup> is positive.';
 var answer_tf_exponents_and_roots_1 =
 'false';
  var feedback_right_tf_exponents_and_roots_1 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_1 =
 'INCORRECT:  ';

 var tf_exponents_and_roots_2 =
 'In the expression -3<sup>2</sup> the base is 3.';
 var answer_tf_exponents_and_roots_2 =
 'true';
  var feedback_right_tf_exponents_and_roots_2 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_2 =
 'INCORRECT:  ';
 
  var tf_exponents_and_roots_3 =
 'In the expression (-3)<sup>2</sup> the base is -3.';
 var answer_tf_exponents_and_roots_3 =
 'true';
  var feedback_right_tf_exponents_and_roots_3 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_3 =
 'INCORRECT:  ';
 
  var tf_exponents_and_roots_4 =
 'In the expression -3<sup>2</sup> the base is 2.';
 var answer_tf_exponents_and_roots_4 =
 'false';
  var feedback_right_tf_exponents_and_roots_4 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_4 =
 'INCORRECT:  ';
 
  var tf_exponents_and_roots_5 =
 'In the expression -3<sup>2</sup> the exponent is 2.';
 var answer_tf_exponents_and_roots_5 =
 'true';
  var feedback_right_tf_exponents_and_roots_5 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_5 =
 'INCORRECT:  ';
 
  var tf_exponents_and_roots_6 =
 '(-3)<sup>2</sup> is positive.';
 var answer_tf_exponents_and_roots_6 =
 'true';
  var feedback_right_tf_exponents_and_roots_6 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_6 =
 'INCORRECT:  ';

  var tf_exponents_and_roots_7 =
 '(-2)<sup>3</sup> is positive.';
 var answer_tf_exponents_and_roots_7 =
 'false';
  var feedback_right_tf_exponents_and_roots_7 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_7 =
 'INCORRECT:  ';

  var tf_exponents_and_roots_8 =
 '-2<sup>3</sup> is positive.';
 var answer_tf_exponents_and_roots_8 =
 'false';
  var feedback_right_tf_exponents_and_roots_8 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_8 =
 'INCORRECT:  ';

  var tf_exponents_and_roots_9 =
 '(-274)<sup>31</sup> is negative.';
 var answer_tf_exponents_and_roots_9 =
 'true';
  var feedback_right_tf_exponents_and_roots_9 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_9 =
 'INCORRECT:  ';

 var tf_exponents_and_roots_10 =
 '-57<sup>13</sup> is positive.';
 var answer_tf_exponents_and_roots_10 =
 'false';
  var feedback_right_tf_exponents_and_roots_10 =
 'CORRECT:  ';
  var feedback_wrong_tf_exponents_and_roots_10 =
 'INCORRECT:  ';

//chapter1 section 3 group 1 numbers_real_operations //

 var tf_numbers_real_operations_max_count =21;
 
 var tf_numbers_real_operations_1 =
 'An inequality is a mathematical statement which contains an inequality symbol.';
 var answer_tf_numbers_real_operations_1 =
 'true';
  var feedback_right_tf_numbers_real_operations_1 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_1 =
 'INCORRECT:  ';

 var tf_numbers_real_operations_2 =
 'To add a positive real number b to a real number a start at a and move to the right b units.';
 var answer_tf_numbers_real_operations_2 =
 'true';
  var feedback_right_tf_numbers_real_operations_2 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_2 =
 'INCORRECT:  ';
 
  var tf_numbers_real_operations_3 =
 'To add a negative real number b to a real number a start at a and move to the right b units.';
 var answer_tf_numbers_real_operations_3 =
 'false';
  var feedback_right_tf_numbers_real_operations_3 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_3 =
 'INCORRECT:  ';
 
  var tf_numbers_real_operations_4 =
 'To add a negative real number b to a real number a start at a and move to the left the absolute value of  b units.';
 var answer_tf_numbers_real_operations_4 =
 'true';
  var feedback_right_tf_numbers_real_operations_4 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_4 =
 'INCORRECT:  ';
 
  var tf_numbers_real_operations_5 =
 'Subtraction is defined by a conversion to addition.';
 var answer_tf_numbers_real_operations_5 =
 'true';
  var feedback_right_tf_numbers_real_operations_5 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_5 =
 'INCORRECT:  ';
 
  var tf_numbers_real_operations_6 =
 'Division is defined by a conversion to multiplication.';
 var answer_tf_numbers_real_operations_6 =
 'false';
  var feedback_right_tf_numbers_real_operations_6 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_6 =
 'INCORRECT:  ';
 
  var tf_numbers_real_operations_7 =
 'Subtraction is defined by adding the minuend and the opposite of the subtrahend.';
 var answer_tf_numbers_real_operations_7 =
 'true';
  var feedback_right_tf_numbers_real_operations_7 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_7 =
 'INCORRECT:  ';
 
  var tf_numbers_real_operations_8 =
 'Subtraction is defined by adding the subtrahend and the opposite of the minuend.';
 var answer_tf_numbers_real_operations_8 =
 'false';
  var feedback_right_tf_numbers_real_operations_8 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_8 =
 'INCORRECT:  ';

  var tf_numbers_real_operations_9 =
 'Division is defined by multiplying the divisor and the inverse of the dividend.';
 var answer_tf_numbers_real_operations_9 =
 'false';
  var feedback_right_tf_numbers_real_operations_9 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_9 =
 'INCORRECT:  ';
 
  var tf_numbers_real_operations_10 =
 'Division is defined by multiplying the dividend and the opposite of the divisor.';
 var answer_tf_numbers_real_operations_10 =
 'false';
  var feedback_right_tf_numbers_real_operations_10 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_10 =
 'INCORRECT:  ';
 
   var tf_numbers_real_operations_11 =
 'On the number line < means to the left of.';
 var answer_tf_numbers_real_operations_11 =
 'true';
  var feedback_right_tf_numbers_real_operations_11 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_11 =
 'INCORRECT:  ';
 
 var tf_numbers_real_operations_12 =
 'On the number line > means to the left of.';
 var answer_tf_numbers_real_operations_12 =
 'false';
 var feedback_right_tf_numbers_real_operations_12 =
 'CORRECT:  ';
 var feedback_wrong_tf_numbers_real_operations_12 =
 'INCORRECT:  ';
  
 var tf_numbers_real_operations_13 =
 'On the number line < means to the right of.';
 var answer_tf_numbers_real_operations_13 =
 'false';
  var feedback_right_tf_numbers_real_operations_13 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_13 =
 'INCORRECT:  ';
  
 var tf_numbers_real_operations_14 =
 'On the number line > means to the right of.';
 var answer_tf_numbers_real_operations_14 =
 'false';
  var feedback_right_tf_numbers_real_operations_14 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_14 =
 'INCORRECT:  ';
 
 var tf_numbers_real_operations_15 =
 'Two real numbers a and b are equal if they represent the same point on the number line.';
 var answer_tf_numbers_real_operations_15 =
 'true';
  var feedback_right_tf_numbers_real_operations_15 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_15 =
 'INCORRECT:  ';
 
 var tf_numbers_real_operations_16 =
 'For every real number there corresponds exactly one point on the line.';
 var answer_tf_numbers_real_operations_16 =
 'true';
  var feedback_right_tf_numbers_real_operations_16 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_16 =
 'INCORRECT:  ';
   
 var tf_numbers_real_operations_17 =
 'for every point on the line there corresponds exactly one real number.';
 var answer_tf_numbers_real_operations_17 =
 'true';
  var feedback_right_tf_numbers_real_operations_17 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_17 =
 'INCORRECT:  ';

 var tf_numbers_real_operations_18 =
 'The product of two negative real numbers is negative.';
 var answer_tf_numbers_real_operations_18 =
 'false';
  var feedback_right_tf_numbers_real_operations_18 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_18 =
 'INCORRECT:  ';
 
 var tf_numbers_real_operations_19 =
 'The quotient of a negtive number divided by a positive number is negative.';
 var answer_tf_numbers_real_operations_19 =
 'true';
  var feedback_right_tf_numbers_real_operations_19 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_19 =
 'INCORRECT:  ';
 
 var tf_numbers_real_operations_20 =
 '0 divided by 5 is not defined.';
 var answer_tf_numbers_real_operations_20 =
 'false';
  var feedback_right_tf_numbers_real_operations_20 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_20 =
 'INCORRECT:  ';
 
 var tf_numbers_real_operations_21 =
 'Division by 0 is undefined.';
 var answer_tf_numbers_real_operations_21 =
 'true';
  var feedback_right_tf_numbers_real_operations_21 =
 'CORRECT:  ';
  var feedback_wrong_tf_numbers_real_operations_21 =
 'INCORRECT:  '; 
 
 
//chapter1 section 2 group 3 absolute_value //

 var tf_absolute_value_max_count =15;
 
 var tf_absolute_value_1 =
 'The absolute value of a real number is a real number.';
 var answer_tf_absolute_value_1 =
 'true';
  var feedback_right_tf_absolute_value_1 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_1 =
 'INCORRECT:  ';
 
 var tf_absolute_value_2 =
 'The absolute value of an integer is a whole number.';
 var answer_tf_absolute_value_2 =
 'true';
  var feedback_right_tf_absolute_value_2 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_2 =
 'INCORRECT:  ';
  
 var tf_absolute_value_3 =
 'The absolute value of a natural number is a natural number.';
 var answer_tf_absolute_value_3 =
 'true';
  var feedback_right_tf_absolute_value_3 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_3 =
 'INCORRECT:  ';
  
 var tf_absolute_value_4 =
 'The absolute value of a integer is a whole number.';
 var answer_tf_absolute_value_4 =
 'true';
  var feedback_right_tf_absolute_value_4 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_4 =
 'INCORRECT:  ';
  
 var tf_absolute_value_5 =
 'The absolute value of a rational number is a rational number.';
 var answer_tf_absolute_value_5 =
 'true';
  var feedback_right_tf_absolute_value_5 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_5 =
 'INCORRECT:  ';
 
  var tf_absolute_value_6 =
 'The absolute value of a real number is positive.';
 var answer_tf_absolute_value_6 =
 'false';
  var feedback_right_tf_absolute_value_6 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_6 =
 'INCORRECT:  ';
 
  var tf_absolute_value_7 =
 'The absolute value of a positive real number is itself.';
 var answer_tf_absolute_value_7 =
 'true';
  var feedback_right_tf_absolute_value_7 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_7 =
 'INCORRECT:  ';

 var tf_absolute_value_8 =
 'The absolute value of a negative real number is itself.';
 var answer_tf_absolute_value_8 =
 'false';
  var feedback_right_tf_absolute_value_8 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_8 =
 'INCORRECT:  ';

 var tf_absolute_value_9 =
 'The absolute value of a negative real number is its opposite.';
 var answer_tf_absolute_value_9 =
 'true';
  var feedback_right_tf_absolute_value_9 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_9 =
 'INCORRECT:  ';

 var tf_absolute_value_10 =
 'The opposite of a negative real number is a natural number.';
 var answer_tf_absolute_value_10 =
 'false';
  var feedback_right_tf_absolute_value_10 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_10 =
 'INCORRECT:  ';
 
 var tf_absolute_value_11 =
 'The opposite of real number is negative.';
 var answer_tf_absolute_value_11 =
 'false';
  var feedback_right_tf_absolute_value_11 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_11 =
 'INCORRECT:  ';
 
 var tf_absolute_value_12 =
 'The opposite of an integer is a natural number.';
 var answer_tf_absolute_value_12 =
 'false';
  var feedback_right_tf_absolute_value_12 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_12 =
 'INCORRECT:  ';
 
 var tf_absolute_value_13 =
 'The nuber zero does not have an opposite.';
 var answer_tf_absolute_value_13 =
 'false';
  var feedback_right_tf_absolute_value_13 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_13 =
 'INCORRECT:  ';

 var tf_absolute_value_14 =
 'The opposite of a real number is a real number.';
 var answer_tf_absolute_value_14 =
 'true';
  var feedback_right_tf_absolute_value_14 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_14 =
 'INCORRECT:  ';

 var tf_absolute_value_15 =
 'The opposite of an irrational number is an irrational number.';
 var answer_tf_absolute_value_15 =
 'true';
  var feedback_right_tf_absolute_value_15 =
 'CORRECT:  ';
  var feedback_wrong_tf_absolute_value_15 =
 'INCORRECT:  ';


//chapter1 section 2 group 2 sets_of_numbers //

 var tf_sets_of_numbers_max_count =14;
 
 var tf_sets_of_numbers_1 =
 'Every natural number is a real number.';
 var answer_tf_sets_of_numbers_1 =
 'true';
  var feedback_right_tf_sets_of_numbers_1 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_of_numbers_1 =
 'INCORRECT:  Check the chain of subsets for the sets of real numbers.';
 
 var tf_sets_of_numbers_2 =
 'Every rational number is an integer.';
 var answer_tf_sets_of_numbers_2 =
 'false';
  var feedback_right_tf_sets_of_numbers_2 =
 'CORRECT:  Can you give an example of a rational number which is not an integer?';
  var feedback_wrong_tf_sets_of_numbers_2 =
 'INCORRECT:  The rational number three fourths is certainly not an integer.';
 
 var tf_sets_of_numbers_3 =
 'Every real number is either a rational number or an irrational number.';
 var answer_tf_sets_of_numbers_3 =
 'true';
  var feedback_right_tf_sets_of_numbers_3 =
 'CORRECT:  Can you give an example of both a rational number and an irrational number?';
  var feedback_wrong_tf_sets_of_numbers_3 =
 'INCORRECT:  Review the definition of real numbers.';
 
 var tf_sets_of_numbers_4 =
 '1 is a prime number.';
 var answer_tf_sets_of_numbers_4 =
 'false';
  var feedback_right_tf_sets_of_numbers_4 =
 'CORRECT:  Why is that?';
  var feedback_wrong_tf_sets_of_numbers_4 =
 'INCORRECT:  The first phrase of the definition of prime number excludes 1.';  
 
 var tf_sets_of_numbers_5 =
 '0 is a Natural Number.';
 var answer_tf_sets_of_numbers_5 =
 'false';
  var feedback_right_tf_sets_of_numbers_5 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_of_numbers_5 =
 'INCORRECT:  The Natural Numbers are the ordinary counting numbers and do not include 0.'; 
 
 var tf_sets_of_numbers_6 =
 '0 is an Integer.';
 var answer_tf_sets_of_numbers_6 =
 'true';
  var feedback_right_tf_sets_of_numbers_6 =
 'CORRECT: ';
  var feedback_wrong_tf_sets_of_numbers_6 =
 'INCORRECT:  0 is a Whole Number which is a subset of the Integers and therefore 0 is an Integer.'; 
 
 var tf_sets_of_numbers_7 =
 '<b>Q</b> &sub; <b>N</b>';
 var answer_tf_sets_of_numbers_7 =
 'false';
  var feedback_right_tf_sets_of_numbers_7 =
 'CORRECT:  Can you give examples of element of <b>Q</b> whihc are not elements of <b>N</b>?';
  var feedback_wrong_tf_sets_of_numbers_7 =
 'INCORRECT:  <b>N</b> is a subset of <b>Q</b> but not <b>Q</b> &sub; <b>N</b>'; 

  var tf_sets_of_numbers_8 =
 ' {0} &sub; <b>N</b> ';
 var answer_tf_sets_of_numbers_8 =
 'false';
  var feedback_right_tf_sets_of_numbers_8 =
 'CORRECT:  Why is that?';
  var feedback_wrong_tf_sets_of_numbers_8 =
 'INCORRECT:  0 is not a natural number.'; 
 
  var tf_sets_of_numbers_9 =
 '{0} = &empty;';
 var answer_tf_sets_of_numbers_9 =
 'false';
  var feedback_right_tf_sets_of_numbers_9 =
 'CORRECT:  Why is that?';
  var feedback_wrong_tf_sets_of_numbers_9 =
 'INCORRECT: {0} is not empty.  It has one element -- the number 0.'; 
 
  var tf_sets_of_numbers_10 =
 '<b>Q</b> &sub; <b>R</b>.';
 var answer_tf_sets_of_numbers_10 =
 'true';
  var feedback_right_tf_sets_of_numbers_10 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_of_numbers_10 =
 'INCORRECT:  Look at the chain of subsets provided in the Chapter Summary.'; 
 
  var tf_sets_of_numbers_11 =
 '<b>Z</b> &sub; <b>R</b>';
 var answer_tf_sets_of_numbers_11 =
 'true';
  var feedback_right_tf_sets_of_numbers_11 =
 'CORRECT:  Why is that?';
  var feedback_wrong_tf_sets_of_numbers_11 =
 'INCORRECT:  Examine the chain of subsets provided in the Chapter Summary.'; 
 
   var tf_sets_of_numbers_12 =
 '(3,5) = {x|3 < x < 5}';
 var answer_tf_sets_of_numbers_12 =
 'true';
  var feedback_right_tf_sets_of_numbers_12 =
 'CORRECT:  Why is that?';
  var feedback_wrong_tf_sets_of_numbers_12 =
 'INCORRECT:  '; 
 
   var tf_sets_of_numbers_13 =
 '{x|x is an odd natural number less than 10} = {1,3,5,7,9}';
 var answer_tf_sets_of_numbers_13 =
 'true';
  var feedback_right_tf_sets_of_numbers_13 =
 'CORRECT:  Why is that?';
  var feedback_wrong_tf_sets_of_numbers_13 =
 'INCORRECT:  '; 
 
 var tf_sets_of_numbers_14 =
 '(5,8] = {6,7,8}';
 var answer_tf_sets_of_numbers_14 =
 'false';
 var feedback_right_tf_sets_of_numbers_14 =
 'CORRECT:  Why is that?';
 var feedback_wrong_tf_sets_of_numbers_14 =
 'INCORRECT:  It is true that 5 is not in (5,8] and that 6, 7, and 8 are.  However, there are infinitely many rational and irrational numbers between 5 and 8 which are also in the set (5,8] and not in {6,7,8}.'; 

//chapter1 section 1 group 2 sets_intro //

 var tf_sets_intro_max_count =12;
 
 var tf_sets_intro_1 =
 'A set is a collection of objects.';
 var answer_tf_sets_intro_1 =
 'true';
  var feedback_right_tf_sets_intro_1 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_1 =
 'INCORRECT:  Check the definition of set.';

 var tf_sets_intro_2 =
 'The null set is the set with no elements.';
 var answer_tf_sets_intro_2 =
 'true';
  var feedback_right_tf_sets_intro_2 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_2 =
 'INCORRECT:  Check the definition of set.';

 var tf_sets_intro_3 =
 '5 is an element of {2, 9, 4, 3, 5}';
 var answer_tf_sets_intro_3 =
 'true';
  var feedback_right_tf_sets_intro_3 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_3 =
 'INCORRECT:  Check the definition of set.';

var tf_sets_intro_4 =
 '5 is subset of {2, 9, 4, 3, 5}';
 var answer_tf_sets_intro_4 =
 'false';
  var feedback_right_tf_sets_intro_4 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_4 =
 'INCORRECT:  subset is a relation between sets and 5 is not a set.';

var tf_sets_intro_5 =
 '{5} is subset of {2, 9, 4, 3, 5}';
 var answer_tf_sets_intro_5 =
 'true';
  var feedback_right_tf_sets_intro_5 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_5 =
 'INCORRECT:  {5} is a set, {2, 9, 4, 3, 5} is a set, and every element of {5} is an element of {2, 9, 4, 3, 5}.';

var tf_sets_intro_6 =
 '5 and {5} are the same thing.';
 var answer_tf_sets_intro_6 =
 'false';
  var feedback_right_tf_sets_intro_6 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_6 =
 'INCORRECT:  5 is a number and {5} is a set containing a number.  Certainly you would not say a room containing a student is the same as the student.  Do not do it with sets and elements of sets.';

 var tf_sets_intro_7 =
 '<img src="../../image/symbol_set_null_small.gif" alt="null set" border="0" align="absmiddle"> <img src="../../image/symbol_set_isin_small.gif" alt="is an element of" border="0" align="absmiddle"> {8, 22, -8, 9, 0}.';
 var answer_tf_sets_intro_7 =
 'false';
  var feedback_right_tf_sets_intro_7 =
 'CORRECT:  Can you explain why not?';
  var feedback_wrong_tf_sets_intro_7 =
 'INCORRECT:  <img src="../../image/symbol_set_null_small.gif" alt="null set" border="0" align="absmiddle"> is a set and each of the elements of {8, 22, -8, 9, 0} is a number.';

 var tf_sets_intro_8 =
 '<img src="../../image/symbol_set_null_small.gif" alt="null set" border="0" align="absmiddle"> <img src="../../image/symbol_set_subset_proper_small.gif" alt="is a subset of" border="0" align="absmiddle"> {8, 22, -8, 9, 0}.';
 var answer_tf_sets_intro_8 =
 'true';
  var feedback_right_tf_sets_intro_8 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_8 =
 'INCORRECT:  The empty set is a subset of every set so it is a subset of {8, 22, -8, 9, 0}.';

 var tf_sets_intro_9 =
 'If A <img src="../../image/symbol_set_subset_proper_small.gif" alt="is a subset of" border="0" align="absmiddle"> B and B <img src="../../image/symbol_set_subset_proper_small.gif" alt="is a subset of" border="0" align="absmiddle"> A Then A = B. ';
 var answer_tf_sets_intro_9 =
 'true';
  var feedback_right_tf_sets_intro_9 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_9 =
 'INCORRECT:  Check the definition of equality of sets.';

 var tf_sets_intro_10 =
 ' {2, 9, 4, 3, 5} is the roster method of writing a set';
 var answer_tf_sets_intro_10 =
 'true';
  var feedback_right_tf_sets_intro_10 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_10 =
 'INCORRECT:  ';
 
  var tf_sets_intro_11 =
 ' {x|x is a natural number} = {1, 2, 3, &hellip;}';
 var answer_tf_sets_intro_11 =
 'true';
  var feedback_right_tf_sets_intro_11 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_11 =
 'INCORRECT:  ';
 
   var tf_sets_intro_12 =
 ' {x|x is a natural number} is the roster method of writing a set';
 var answer_tf_sets_intro_12 =
 'false';
  var feedback_right_tf_sets_intro_12 =
 'CORRECT:  ';
  var feedback_wrong_tf_sets_intro_12 =
 'INCORRECT:  A roster is a list so the roster method is like {2, 3, 5, 19, 9, 0}.  The example in the question is  set-builder notation';
 
 
//chapter1 section 1 group 1 formulas_basic //

 var tf_formulas_basic_max_count = 15;
 
 var tf_formulas_basic_1 =
 'Every rectangle is a square.';
 var answer_tf_formulas_basic_1 =
 'false';
  var feedback_right_tf_formulas_basic_1 =
 'CORRECT:  Can you give an example of a rectangle which is not a square?';
  var feedback_wrong_tf_formulas_basic_1 =
 'INCORRECT:  There are many rectangles which are not squares.  '
 +'Any rectangle whose length is not equal to its width is not a square. '
+'For example the rectangle with length 5 and width 2 is not a square. '
+'Insure that you can provide additional examples of rectangles which are not squares.';
  
 var tf_formulas_basic_2 =
 'The area of a rectangle is the product of its length and its width.';
 var answer_tf_formulas_basic_2 =
 'true';
  var feedback_right_tf_formulas_basic_2 =
 'CORRECT:  Can you relate this fact with the formula for the area of a parallelogram?';
  var feedback_wrong_tf_formulas_basic_2 =
 'INCORRECT:  You should probably review the formulas for the areas of basic geometric shapes.  '
 +'Make sure you understand what the formula "says".  Simply memorizing a bunch of '
 +'letters is of little value.';
 
  var tf_formulas_basic_3 =
 'The area of a triangle is the product of its base and its height.';
 var answer_tf_formulas_basic_3 =
 'false';
  var feedback_right_tf_formulas_basic_3 =
 'CORRECT:  What relation between rectangles and triangles can help you remember the '
 +'formula for the area of a triangle?';
  var feedback_wrong_tf_formulas_basic_3 =
 'INCORRECT:  The area of a triangle is half the product of its base and its height. '
 +'Try to think of a right triangle as half of a rectangle to help remember the formula '
 +'for the area of a triangle.';
 
 var tf_formulas_basic_4 =
 'The formula for the area of a trapezoid is <img src="../../image/formula_trapezoid_area_small.gif" alt="formula for the area of a trapezoid" border="0" align="absmiddle">';
 var answer_tf_formulas_basic_4 =
 'true';
 var feedback_right_tf_formulas_basic_4 =
 'CORRECT:  Can you create an example of a trapezoid and compute its area?';
 var feedback_wrong_tf_formulas_basic_4 =
 'INCORRECT:  You should probably review the formulas for the areas of basic geometric shapes.  '
 +'Make sure you understand what the formula says.  Simply memorizing a bunch of '
 +'letters is of little value.';
 
var tf_formulas_basic_5 = ' 2<img src="../../image/pi_small.gif" width="16" height="15" align="absmiddle">r is the formula for the circumference of a circle.';
 var answer_tf_formulas_basic_5 = 'false';
 var feedback_right_tf_formulas_basic_5 =
 'CORRECT: This is not even a formula.  A formula must be an equation.';
 var feedback_wrong_tf_formulas_basic_5 =
 'INCORRECT:  This is not a formula.  A formula must be an equation.';  
  
var tf_formulas_basic_6 = 'A = 2<img src="../../image/pi_small.gif"  align="absmiddle">r is the formula for the area of a circle.';
 var answer_tf_formulas_basic_6 = 'false';
 var feedback_right_tf_formulas_basic_6 =
 'CORRECT: 2<img src="../../image/pi_small.gif"  align="absmiddle">r produces the circumference of a circle';
 var feedback_wrong_tf_formulas_basic_6 =
 'INCORRECT:  2<img src="../../image/pi_small.gif"  align="absmiddle">r produces the circumference of a circle'; 
   
var tf_formulas_basic_7 = 'The perimeter of a rectangle is twice the sum of its length and width.';
 var answer_tf_formulas_basic_7 = 'true';
 var feedback_right_tf_formulas_basic_7 =
 'CORRECT: ';
 var feedback_wrong_tf_formulas_basic_7 =
 'INCORRECT:  ';   
  
var tf_formulas_basic_8 = 'The area of a triangle is one half the product of its base and height.';
 var answer_tf_formulas_basic_8 = 'true';
 var feedback_right_tf_formulas_basic_8 =
 'CORRECT: ';
 var feedback_wrong_tf_formulas_basic_8 =
 'INCORRECT:  Try to think of a right triangle as half of a rectangle to help remember the formula '
 +'for the area of a triangle.';  
  
 var tf_formulas_basic_9 = 'Each formula for area involves the product of two linear measures.';
 var answer_tf_formulas_basic_9 = 'true';
 var feedback_right_tf_formulas_basic_9 =
 'CORRECT: In fact this is why the units for area are square units (or units squared).';
 var feedback_wrong_tf_formulas_basic_9 =
 'INCORRECT:  Reexamine the formulas';  
 
 var tf_formulas_basic_10 = 'The area of a rectangle can be an irrational number.';
 var answer_tf_formulas_basic_10 = 'true';
 var feedback_right_tf_formulas_basic_10 =
 'CORRECT: Can you construct a rectangle whose area is an irrational number?';
 var feedback_wrong_tf_formulas_basic_10 =
 'INCORRECT:  There is nothing unusual about an irrational area.  For example, '
 +'the area of the rectangle with length 6 and width '
 +'<img src="../../image/square_root_of_5_small.gif" alt="square root of five" border="0" align="absmiddle"> '
 +' is 6<img src="../../image/square_root_of_5_small.gif" alt="square root of five" border="0" align="absmiddle"> '
+' which is an irrational number.' ;   
 
 var tf_formulas_basic_11 = 'Each variable is an algebraic expression.';
 var answer_tf_formulas_basic_11 = 'true';
 var feedback_right_tf_formulas_basic_11 =
 'CORRECT: The definition of algebraic expression explicitly includes variables.';
 var feedback_wrong_tf_formulas_basic_11 =
 'INCORRECT:  Look at the first few words of the definition of algebraic expression. Memorize the definition of algebraic expression. Think about what is included and what is excluded.';  
 
 var tf_formulas_basic_12 = 'Each algebraic expression is a product of variables.';
 var answer_tf_formulas_basic_12 = 'false';
 var feedback_right_tf_formulas_basic_12 =
 'CORRECT: Can you construct five distinctly different algebraic expressions which are not products of variables?';
 var feedback_wrong_tf_formulas_basic_12 =
 'INCORRECT:  The expression x + 5 is an algebraic expression and it is not the product of variables. Memorize the definition of algebraic expression. Think about what is included and what is excluded.'; 
 
 var tf_formulas_basic_13 = 'Some numbers are variables.';
 var answer_tf_formulas_basic_13 = 'false';
 var feedback_right_tf_formulas_basic_13 =
 'CORRECT: A variable is a letter.';
 var feedback_wrong_tf_formulas_basic_13 =
 'INCORRECT:  A variable is a letter.  That excludes numbers.'; 
 
 var tf_formulas_basic_14 = 'Each algebraic expression is a variable.';
 var answer_tf_formulas_basic_14 = 'false';
 var feedback_right_tf_formulas_basic_14 =
 'CORRECT: Can you construct an algebraic expression which is not a variable?';
 var feedback_wrong_tf_formulas_basic_14 =
 'INCORRECT:  Some algebraic expressions are variables, but many algebraic expresions are not variables.'; 
 
 var tf_formulas_basic_15 = 'An algebraic expression can involve square roots.';
 var answer_tf_formulas_basic_15 = 'true';
 var feedback_right_tf_formulas_basic_15 =
 'CORRECT: Can you write the definition of algebraic expression precisely as stated in this chapter summary?';
 var feedback_wrong_tf_formulas_basic_15 =
 'INCORRECT:  Square roots are explicitly included by the definition of algebraic expression.';  
 
 
 
 
// var tf_equation_identify_classify_5 =
// 'The equation 2x = x is a conditional equation.';
// var answer_tf_equation_identify_classify_5 =
// 'true';
// var feedback_right_tf_equation_identify_classify_5 =
// 'CORRECT:  How many numbers will make the equation true when substituted for the variable x?';
// var feedback_wrong_tf_equation_identify_classify_5 =
// 'INCORRECT:  Clearly this equation is true if 0 is substituted for x, so the equation is not a contradiction. <br> '
// +'Just as easily one can determine that the equation is false if 5 is substituted for x, so the equation is not an identity.<br>'
// +'  That leaves only one possibility, the equation must be a conditional equation.'; 
// 
// 
//var tf_equation_identify_classify_6 =
// 'The statement x < x + 2 is a identity.';
// var answer_tf_equation_identify_classify_6 =
// 'false';
// var feedback_right_tf_equation_identify_classify_6 =
// 'CORRECT:  What change could you make to this statement to convert it to an identity ?';
// var feedback_wrong_tf_equation_identify_classify_6 =
// 'INCORRECT:  This statement is not an equation, so it certainly is not an identity.<br>'
// +'Remember identities are equations.'; 
//  
//var tf_equation_identify_classify_7 =
// 'Some conditional equations are identities.';
// var answer_tf_equation_identify_classify_7 =
// 'false';
// var feedback_right_tf_equation_identify_classify_7 =
// 'CORRECT: ';
// var feedback_wrong_tf_equation_identify_classify_7 =
// 'INCORRECT:  The set of conditional equations, the set of identities, and the set of contradictions are '
// +'disjoint sets.  That is, no two of the sets have elements in common.';   
// 
//var tf_equation_identify_classify_8 =
// 'The mathematical expression x<sup>2</sup>+ 5x + 6 is a conditional equation.';
// var answer_tf_equation_identify_classify_8 =
// 'false';
// var feedback_right_tf_equation_identify_classify_8 =
// 'CORRECT: Can you write a two step deductive argument which concludes that x<sup>2</sup>+ 5x + 6 is not a '
// +'conditional equation?';
// var feedback_wrong_tf_equation_identify_classify_8 =
// 'INCORRECT:  A conditional equation is an equation and therefore must contain an equal symbol.  '
// +'Clearly, the expression x<sup>2</sup>+ 5x + 6 contains no = symbol.  Therefore x<sup>2</sup>+ 5x + 6 is not an equation '
// +'and if it is not an equation it certainly cannot be a conditional equation.';   
  
  
  
 //chapter1 section 1 group 2 equation_solution_solve //

 var tf_equation_solution_solve_max_count = 6;


var tf_equation_solution_solve_1 =
 'A solution of the equation x<sup>2</sup> + 5x - 6 = 0 is 1.';
 var answer_tf_equation_solution_solve_1 =
 'true';
 var feedback_right_tf_equation_solution_solve_1 =
 'CORRECT: Can you write an brief sentence/paragraph explaining how you came to this conclusion?';
 var feedback_wrong_tf_equation_solution_solve_1 =
 'INCORRECT:  If x is replaced with the number 1, a true statement results.  Therefore 1 satisfies the definition '
 +'of solution of the given equation.'; 
 
 var tf_equation_solution_solve_2 =
 'The number -1 is a solution of the equation x<sup>3</sup> + x<sup>2</sup> + x<sup>5</sup> + 1 = 0';
 var answer_tf_equation_solution_solve_2 =
 'true';
 var feedback_right_tf_equation_solution_solve_2 =
 'CORRECT: Can you write a brief sentence/paragraph explaining how you came to this conclusion?';
 var feedback_wrong_tf_equation_solution_solve_2 =
 'INCORRECT:  If x is replaced with the number -1, a true statement results.  Therefore -1 satisfies the definition '
 +'of solution of the given equation.'; 
 
 var tf_equation_solution_solve_3 =
 'The numbers 1 and -5 are solutions of x<sup>2</sup> + 5x = 6.';
 var answer_tf_equation_solution_solve_3 = 'false';
 var feedback_right_tf_equation_solution_solve_3 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_solution_solve_3 =
 'INCORRECT:  If x is replaced with the number 1, a true statement results.Therefore 1 satisfies the '
 +'definition of solution of the given equation.<br>'
 +'However, if x is replaced with the number -5, a false statement results. Therefore -5 does not satisfy the '
 +'definition of solution of the given equation.';
 
  var tf_equation_solution_solve_4 =
 'If x<sup>3</sup> - 12 is added to both sides of the equation 5x - 3 = 7, the resulting equation is '
 +'equivalent to the original equation';
 var answer_tf_equation_solution_solve_4 =
 'true';
 var feedback_right_tf_equation_solution_solve_4 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_solution_solve_4 =
 'INCORRECT:  If any expression is added to both sides of an equation, the resulting equation is '
 +'equivalent to the original equation.  Please review the two Properties of Equations.';
 
 var tf_equation_solution_solve_5 =
 'The equation 3x = 6 is a simplest equation.';
 var answer_tf_equation_solution_solve_5 =
 'false';
 var feedback_right_tf_equation_solution_solve_5 =
 'CORRECT: Compare the equation 3x = 6 to the definition of simplest equation and 3x = 6 fails the test.';
 var feedback_wrong_tf_equation_solution_solve_5 =
 'INCORRECT:  A simplest equation has ONLY a variable on one sie and ONLY a number on the other side.  '
 +'This equation has both a variable x and a number 3 on one side of the equation.';
 
 var tf_equation_solution_solve_6 =
 'The two statements<br>Equation 1 and Equation 2 are equivalent equations.<br>Equation 1 and Equation 2 have the same solution sets.<br> say the same thing.';
 var answer_tf_equation_solution_solve_6 =
 'true';
 var feedback_right_tf_equation_solution_solve_6 =
 'CORRECT: Two equations are equivalent if and only if they have the same solution sets.';
 var feedback_wrong_tf_equation_solution_solve_6 =
 'INCORRECT:  Two equations are equivalent if and only if they have the same solution sets.'; 
 
 
 //chapter1 section1 group3 equation_linear_one_variable //

 var tf_equation_linear_one_variable_max_count = 10;


var tf_equation_linear_one_variable_1 = '18x + 7 = 4 is a linear equation in one variable.';
 var answer_tf_equation_linear_one_variable_1 = 'true';
 var feedback_right_tf_equation_linear_one_variable_1 =
 'CORRECT: Can you explain why ?';
 var feedback_wrong_tf_equation_linear_one_variable_1 =
 'INCORRECT:  This is an equation in one variable.  It is not in the form ax + b = 0, but it can be written '
 +'in that form by adding -4 to both sides of the equation.';  
 
var tf_equation_linear_one_variable_2 = 'Every linear equation in one variable has a solution.';
 var answer_tf_equation_linear_one_variable_2 = 'false';
 var feedback_right_tf_equation_linear_one_variable_2 =
 'CORRECT: Can you create a linearequation in one variable which has no solution ?';
 var feedback_wrong_tf_equation_linear_one_variable_2 =
 'INCORRECT:  The equation 3x + 7 = 3x - 4 is a linear equation in one variable which has no solution.';  
 
var tf_equation_linear_one_variable_3 = 'The graph of a linear equation in one variable is a point on the Real Number line.';
 var answer_tf_equation_linear_one_variable_3 = 'false';
 var feedback_right_tf_equation_linear_one_variable_3 =
 'CORRECT: Can you create a linear equation whose graph is not a point on the Real Number line ?';
 var feedback_wrong_tf_equation_linear_one_variable_3 =
 'INCORRECT:  The graph of the linear equation in one variable 10x + 5 = 5(2x + 1) is the entire real number line <b>R</b>';   
 
var tf_equation_linear_one_variable_4 = 'The graph of a linear equation in one variable is a line.';
 var answer_tf_equation_linear_one_variable_4 = 'false';
 var feedback_right_tf_equation_linear_one_variable_4 =
 'CORRECT: What is the graph of a linear equation ?';
 var feedback_wrong_tf_equation_linear_one_variable_4 =
 'INCORRECT:  Because the equation involves only one variable, its graph must be a subset of the Real Number line';    
 
var tf_equation_linear_one_variable_5 = 'The solution set for 3x + 2 = 14 is {4}.';
 var answer_tf_equation_linear_one_variable_5 = 'true';
 var feedback_right_tf_equation_linear_one_variable_5 =
 'CORRECT: What is the graph of the equation ?';
 var feedback_wrong_tf_equation_linear_one_variable_5 =
 'INCORRECT:  Please study the process for solving a linear equation in one variable.';    
 
var tf_equation_linear_one_variable_6 = 'The solution for 5x + 7 = 1 is a negative number.';
 var answer_tf_equation_linear_one_variable_6 = 'true';
 var feedback_right_tf_equation_linear_one_variable_6 =
 'CORRECT: What kind of number is the solution ?';
 var feedback_wrong_tf_equation_linear_one_variable_6 =
 'INCORRECT:  Please study the process for solving a linear equation in one variable.';   
 
var tf_equation_linear_one_variable_7 = 'The solution set for 2x + 2 = 14 is {7}.';
 var answer_tf_equation_linear_one_variable_7 = 'false';
 var feedback_right_tf_equation_linear_one_variable_7 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_linear_one_variable_7 =
 'INCORRECT:  Please study the process for solving a linear equation in one variable.';   
 
var tf_equation_linear_one_variable_8 = 'The solution for 3x + 2 = 0 is a negative rational number.';
 var answer_tf_equation_linear_one_variable_8 = 'true';
 var feedback_right_tf_equation_linear_one_variable_8 =
 'CORRECT: What is the graph of the equation ?';
 var feedback_wrong_tf_equation_linear_one_variable_8 =
 'INCORRECT:  Please study the process for solving a linear equation in one variable.';   
 
var tf_equation_linear_one_variable_9 = 'The interval (3, 4) can be the solution set for a linear equation in one variable.';
 var answer_tf_equation_linear_one_variable_9 = 'false';
 var feedback_right_tf_equation_linear_one_variable_9 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_linear_one_variable_9 =
 'INCORRECT:  ';   
 
var tf_equation_linear_one_variable_10 = 'The set {3, 5, 6} can be the solution set for a linear equation in one variable.';
 var answer_tf_equation_linear_one_variable_10 = 'false';
 var feedback_right_tf_equation_linear_one_variable_10 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_linear_one_variable_10 =
 'INCORRECT:  ';    
 
 
 //chapter1 section 1 group 5 equation_important_formulas //

 var tf_equation_important_formulas_max_count = 11;


var tf_equation_important_formulas_1 = ' 2<img src="../../image/pi.gif" width="16" height="15" align="absmiddle">r is the formula for the circumference of a circle.';
 var answer_tf_equation_important_formulas_1 = 'false';
 var feedback_right_tf_equation_important_formulas_1 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_1 =
 'INCORRECT:  This is not a formula.  A formula must be an equation.';  
  
var tf_equation_important_formulas_2 = 'A = 2<img src="../../image/pi.gif" width="16" height="15" align="absmiddle">r is the formula for the area of a circle.';
 var answer_tf_equation_important_formulas_2 = 'false';
 var feedback_right_tf_equation_important_formulas_2 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_2 =
 'INCORRECT:  ';   
 
var tf_equation_important_formulas_3 = 'The volume of a cylinder is the area of its base times its height.';
 var answer_tf_equation_important_formulas_3 = 'true';
 var feedback_right_tf_equation_important_formulas_3 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_3 =
 'INCORRECT:  ';   
  
var tf_equation_important_formulas_4 = 'The perimeter of a rectangle is twice the sum of its length and width.';
 var answer_tf_equation_important_formulas_4 = 'true';
 var feedback_right_tf_equation_important_formulas_4 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_4 =
 'INCORRECT:  ';   
  
var tf_equation_important_formulas_5 = 'The area of a triangle is the product of its base and height.';
 var answer_tf_equation_important_formulas_5 = 'false';
 var feedback_right_tf_equation_important_formulas_5 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_5 =
 'INCORRECT:  ';    
 
var tf_equation_important_formulas_6 = 'The volume of a cone is the area of its base times its height.';
 var answer_tf_equation_important_formulas_6 = 'false';
 var feedback_right_tf_equation_important_formulas_6 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_6 =
 'INCORRECT:  ';   
 
var tf_equation_important_formulas_7 = 'The volume of a cone is the one-half the area of its base times its height.';
 var answer_tf_equation_important_formulas_7 = 'false';
 var feedback_right_tf_equation_important_formulas_7 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_7 =
 'INCORRECT:  ';  
 
 var tf_equation_important_formulas_8 = 'The volume of a cone is the one-third the area of its base times its height.';
 var answer_tf_equation_important_formulas_8 = 'true';
 var feedback_right_tf_equation_important_formulas_8 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_8 =
 'INCORRECT:  '; 
 
 var tf_equation_important_formulas_8 = 'The volume of a sphere is 4/3 times its area.';
 var answer_tf_equation_important_formulas_8 = 'false';
 var feedback_right_tf_equation_important_formulas_8 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_8 =
 'INCORRECT:  '; 
 
 var tf_equation_important_formulas_9 = 'If a and b are the lengths of the legs of a right triangle with hypotenuse of length c, <br>then a<sup>2</sup> - b<sup>2</sup> = c<sup>2</sup>';
 var answer_tf_equation_important_formulas_9 = 'false';
 var feedback_right_tf_equation_important_formulas_9 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_important_formulas_9 =
 'INCORRECT:  That should be a + symbol not a - symbol.  Recall the Pythagorean Theorem.';  
 
 var tf_equation_important_formulas_10 = 'Each formula for area involves the product of two linear measures.';
 var answer_tf_equation_important_formulas_10 = 'true';
 var feedback_right_tf_equation_important_formulas_10 =
 'CORRECT: In fact this is why the units for are are square units (or units squared).';
 var feedback_wrong_tf_equation_important_formulas_10 =
 'INCORRECT:  Reexamine the formulas';   

 var tf_equation_important_formulas_11 = 'Each formula for volume involves the product of three linear measures.';
 var answer_tf_equation_important_formulas_11 = 'true';
 var feedback_right_tf_equation_important_formulas_11 =
 'CORRECT: In fact this is why the units for volume are cubic units (or units cubed).';
 var feedback_wrong_tf_equation_important_formulas_11 =
 'INCORRECT: Reexamine the formulas ';   



 //chapter1 section3 group1 equation_quadratic_one_variable //

 var tf_equation_quadratic_one_variable_max_count = 20;


var tf_equation_quadratic_one_variable_1 = '3x + 5 = 0 is a quadratic equation. ';
 var answer_tf_equation_quadratic_one_variable_1 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_1 =
 'CORRECT: Can you explain why this is not a quadratic equation?';
 var feedback_wrong_tf_equation_quadratic_one_variable_1 =
 'INCORRECT:  This is a linear equation.  Review the definitions of both linear and quadratic equations.';  

var tf_equation_quadratic_one_variable_2 = '3x<sup>2</sup> + 5 = 0 is a quadratic equation. ';
 var answer_tf_equation_quadratic_one_variable_2 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_2 =
 'CORRECT: Can you explain why this is a quadratic equation?';
 var feedback_wrong_tf_equation_quadratic_one_variable_2 =
 'INCORRECT:  This is a quadratic equation.  It has the right form with a = 3, b = 0, and c = 5.'; 
 
var tf_equation_quadratic_one_variable_3 = '-7x<sup>2</sup> - 5x + 4 = 0 is a quadratic equation. ';
 var answer_tf_equation_quadratic_one_variable_3 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_3 =
 'CORRECT: Can you identify the three constants a, b, and c used in the definition of quadratic equation ?';
 var feedback_wrong_tf_equation_quadratic_one_variable_3 =
 'INCORRECT:  This is a quadratic equation.  Review the definition quadratic equations.';   

var tf_equation_quadratic_one_variable_4 = '-7x<sup>2</sup> - 5x + 4 is a quadratic equation. ';
 var answer_tf_equation_quadratic_one_variable_4 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_4 =
 'CORRECT: Can you explain why this is not a quadratic equation ?';
 var feedback_wrong_tf_equation_quadratic_one_variable_4 =
 'INCORRECT:  This is not a quadratic equation.  Because -7x<sup>2</sup> - 5x + 4 does not contain an = symbol it is not an equation and therefore it cannot be a quadratic equation.';   

var tf_equation_quadratic_one_variable_5 = 'Every quadratic equation in one variable can be solved with the Quadratic Formula.';
 var answer_tf_equation_quadratic_one_variable_5 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_5 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_5 =
 'INCORRECT:  ';   

var tf_equation_quadratic_one_variable_6 = 'Every quadratic equation in one variable can be solved by factoring combined with The Zero Factor Property.';
 var answer_tf_equation_quadratic_one_variable_6 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_6 =
 'CORRECT: Can you give an example of a quadratic equation in one variable that cannot be solved by factoring combined with The Zero Factor Property ?';
 var feedback_wrong_tf_equation_quadratic_one_variable_6 =
 'INCORRECT:  Lots of quadratic equations cannot be factore.<br>  For example the quadratic equation x<sup>2</sup> + x + 1 cannot be factored.';   

var tf_equation_quadratic_one_variable_7 = 'If the discrimminant of a quadratic equation in one variable is negative, the equation has no real solution.';
 var answer_tf_equation_quadratic_one_variable_7 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_7 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_7 =
 'INCORRECT:  ';  
 
var tf_equation_quadratic_one_variable_8 = 'If the discrimminant of a quadratic equation in one variable is negative, the equation has two complex solutions.';
 var answer_tf_equation_quadratic_one_variable_8 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_8 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_8 =
 'INCORRECT:  '; 
 
var tf_equation_quadratic_one_variable_9 = 'If the discrimminant of a quadratic equation in one variable is positive, the equation has two real solutions.';
 var answer_tf_equation_quadratic_one_variable_9 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_9 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_9 =
 'INCORRECT:  ';  
 
 var tf_equation_quadratic_one_variable_10 = 'If the discrimminant of a quadratic equation in one variable is positive, the equation has no real solutions.';
 var answer_tf_equation_quadratic_one_variable_10 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_10 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_10 =
 'INCORRECT:  ';  
 
var tf_equation_quadratic_one_variable_11 = 'If the discrimminant of a quadratic equation in one variable is positive, the equation has exactly one real solution.';
 var answer_tf_equation_quadratic_one_variable_11 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_11 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_11 =
 'INCORRECT:  ';  
 
 var tf_equation_quadratic_one_variable_12 = 'If the discrimminant of a quadratic equation in one variable is zero, the equation has exactly one real solution.';
 var answer_tf_equation_quadratic_one_variable_12 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_12 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_12 =
 'INCORRECT:  ';  
 
var tf_equation_quadratic_one_variable_13 = 'If the discrimminant of a quadratic equation in one variable is zero, the equation has two real solutions.';
 var answer_tf_equation_quadratic_one_variable_13 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_13 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_13 =
 'INCORRECT:  ';  
 
 var tf_equation_quadratic_one_variable_14 = 'If a quadratic equation in one variable has exactly one real solution, then its discriminant is positive.';
 var answer_tf_equation_quadratic_one_variable_14 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_14 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_14 =
 'INCORRECT:  ';  
 
  var tf_equation_quadratic_one_variable_15 = 'If a quadratic equation in one variable has two real solutions, then its discriminant is negative.';
 var answer_tf_equation_quadratic_one_variable_15 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_15 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_15 =
 'INCORRECT:  ';  
 
 var tf_equation_quadratic_one_variable_16 = 'If a quadratic equation in one variable has exactly two complex solutions, then those solutions are conjugates of each other.';
 var answer_tf_equation_quadratic_one_variable_16 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_16 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_16 =
 'INCORRECT:  ';  
 
  var tf_equation_quadratic_one_variable_16 = 'If a quadratic equation in one variable has exactly two complex solutions, then its discriminant is negative.';
 var answer_tf_equation_quadratic_one_variable_16 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_16 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_16 =
 'INCORRECT:  ';
 
  var tf_equation_quadratic_one_variable_17 = 'If a quadratic equation in one variable has exactly two complex solutions, then its discriminant is positive.';
 var answer_tf_equation_quadratic_one_variable_17 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_17 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_17 =
 'INCORRECT:  '; 
 
   var tf_equation_quadratic_one_variable_18 = 'The Zero Factor Property is a property of quadratic equations.';
 var answer_tf_equation_quadratic_one_variable_18 = 'false';
 var feedback_right_tf_equation_quadratic_one_variable_18 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_18 =
 'INCORRECT:  The Zero Factor Property is a property of the Real Numbers.'; 
 
var tf_equation_quadratic_one_variable_19 = 'The Zero Factor Property is a property of real numbers.';
 var answer_tf_equation_quadratic_one_variable_19 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_19 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_19 =
 'INCORRECT:  '; 
 
var tf_equation_quadratic_one_variable_20 = 'A quadratic equation is a second degree polynomial equation';
 var answer_tf_equation_quadratic_one_variable_20 = 'true';
 var feedback_right_tf_equation_quadratic_one_variable_20 =
 'CORRECT: ';
 var feedback_wrong_tf_equation_quadratic_one_variable_20 =
 'INCORRECT:  '; 



   //chapter1 section4 group1 complex_numbers //

 var tf_complex_numbers_max_count = 21;

var tf_complex_numbers_1 = '3 + 5i is a complex number. ';
 var answer_tf_complex_numbers_1 = 'true';
 var feedback_right_tf_complex_numbers_1 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_1 =
 'INCORRECT:  ';  
  
var tf_complex_numbers_2 = '3 - 5i is a complex number. ';
 var answer_tf_complex_numbers_2 = 'true';
 var feedback_right_tf_complex_numbers_2 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_2 =
 'INCORRECT:  '; 
 
  
var tf_complex_numbers_3 = '- 5i is a complex number. ';
 var answer_tf_complex_numbers_3 = 'true';
 var feedback_right_tf_complex_numbers_3 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_3 =
 'INCORRECT:  ';  
 
  
var tf_complex_numbers_4 = '13 is a complex number. ';
 var answer_tf_complex_numbers_4 = 'true';
 var feedback_right_tf_complex_numbers_4 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_4 =
 'INCORRECT:  ';  
 
var tf_complex_numbers_5 = 'The conjugate of a complex number is a real number. ';
 var answer_tf_complex_numbers_5 = 'false';
 var feedback_right_tf_complex_numbers_5 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_5 =
 'INCORRECT:  ';  
 
var tf_complex_numbers_6 = 'The norm of a complex number is a real number';
 var answer_tf_complex_numbers_6 = 'true';
 var feedback_right_tf_complex_numbers_6 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_6 =
 'INCORRECT:  ';  
 
var tf_complex_numbers_7 = 'The multiplicative inverse of a complex number is its reciprocal';
 var answer_tf_complex_numbers_7 = 'false';
 var feedback_right_tf_complex_numbers_7 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_7 =
 'INCORRECT:  ';  
 
 var tf_complex_numbers_8 = 'The multiplicative inverse of a complex number is its norm divided by its conjugate.';
 var answer_tf_complex_numbers_8 = 'false';
 var feedback_right_tf_complex_numbers_8 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_8 =
 'INCORRECT:  '; 
 
 var tf_complex_numbers_9 = 'The multiplicative inverse of a complex number is its conjugate divided by its norm.';
 var answer_tf_complex_numbers_9 = 'true';
 var feedback_right_tf_complex_numbers_9 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_9 =
 'INCORRECT:  '; 

 var tf_complex_numbers_10 = 'The additive inverse of a complex number is its opposite.';
 var answer_tf_complex_numbers_10 = 'true';
 var feedback_right_tf_complex_numbers_10 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_10 =
 'INCORRECT:  '; 

 var tf_complex_numbers_11 = 'The product of two complex numbers is a real number.';
 var answer_tf_complex_numbers_11 = 'false';
 var feedback_right_tf_complex_numbers_11 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_11 =
 'INCORRECT:  '; 

 var tf_complex_numbers_12 = 'The product of two complex numbers is a complex number.';
 var answer_tf_complex_numbers_12 = 'true';
 var feedback_right_tf_complex_numbers_12 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_12 =
 'INCORRECT:  '; 

 var tf_complex_numbers_13 = '(2 - 7i) + (-5 + 8i) = -3 + i.';
 var answer_tf_complex_numbers_13 = 'true';
 var feedback_right_tf_complex_numbers_13 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_13 =
 'INCORRECT:  '; 

 var tf_complex_numbers_13 = '(2 - 7i) - (-5 - 8i) = -3 + i.';
 var answer_tf_complex_numbers_13 = 'false';
 var feedback_right_tf_complex_numbers_13 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_13 =
 'INCORRECT:  '; 

  var tf_complex_numbers_14 = '(2 - 7i) - (-5 - 8i) = 3 + i.';
 var answer_tf_complex_numbers_14 = 'false';
 var feedback_right_tf_complex_numbers_14 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_14 =
 'INCORRECT:  ';
 
  var tf_complex_numbers_15 = '(2 - 7i) - (-5 + 8i) = 8 - 15i.';
 var answer_tf_complex_numbers_15 = 'true';
 var feedback_right_tf_complex_numbers_15 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_15 =
 'INCORRECT:  '; 
 
  var tf_complex_numbers_16 = 'i = -1.';
 var answer_tf_complex_numbers_16 = 'false';
 var feedback_right_tf_complex_numbers_16 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_16 =
 'INCORRECT:  '; 
 
  var tf_complex_numbers_16 = 'i<sup>2</sup> = -1.';
 var answer_tf_complex_numbers_16 = 'true';
 var feedback_right_tf_complex_numbers_16 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_16 =
 'INCORRECT:  '; 
 
  var tf_complex_numbers_17 = 'i<sup>3</sup> = i.';
 var answer_tf_complex_numbers_17 = 'true';
 var feedback_right_tf_complex_numbers_17 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_17 =
 'INCORRECT:  ';  
 
  var tf_complex_numbers_17 = 'i<sup>4</sup> = 1.';
 var answer_tf_complex_numbers_17 = 'true';
 var feedback_right_tf_complex_numbers_17 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_17 =
 'INCORRECT:  ';  
 
  var tf_complex_numbers_18 = '(2 - 3i)(5 + 6i) = 28 - 3i.';
 var answer_tf_complex_numbers_18 = 'true';
 var feedback_right_tf_complex_numbers_18 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_18 =
 'INCORRECT:  '; 
 
  var tf_complex_numbers_19 = 'The norm of 2 - 3i is -5.';
 var answer_tf_complex_numbers_19 = 'true';
 var feedback_right_tf_complex_numbers_19 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_19 =
 'INCORRECT:  ';  
 
  var tf_complex_numbers_20 = 'The multiplicative inverse of 7 + 2i is -7 - 2i divided by 53.';
 var answer_tf_complex_numbers_20 = 'false';
 var feedback_right_tf_complex_numbers_20 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_20 =
 'INCORRECT:  '; 
 
  var tf_complex_numbers_21 = 'The multiplicative inverse of 7 + 2i is 7 - 2i divided by 53.';
 var answer_tf_complex_numbers_21 = 'true';
 var feedback_right_tf_complex_numbers_21 =
 'CORRECT: ';
 var feedback_wrong_tf_complex_numbers_21 =
 'INCORRECT:  ';