//chapter3 section 1 group 1 percent //
 var san_percent_max_count = 1;
 var san_percent_1 = 'COMING SOON.';
 var answer_san_percent_1 = 'SOMETIMES ALWAYS NEVER';
 var feedback_right_san_percent_1 = 'CORRECT:  ';
 var feedback_wrong_san_percent_1 = 'INCORRECT: '; 




//chapter3 section 3 group 1 graph_linear_equations_inequalities_two_variables //
 var san_graph_linear_equations_inequalities_two_variables_max_count = 1;
 var san_graph_linear_equations_inequalities_two_variables_1 = 'COMING SOON.';
 var answer_san_graph_linear_equations_inequalities_two_variables_1 = 'SOMETIMES ALWAYS NEVER';
 var feedback_right_san_graph_linear_equations_inequalities_two_variables_1 = 'CORRECT:  ';
 var feedback_wrong_san_graph_linear_equations_inequalities_two_variables_1 = 'INCORRECT: '; 

//chapter3 section 4 group 1 slope_line //
 var san_slope_line_max_count = 1;
 var san_slope_line_1 = 'COMING SOON.';
 var answer_san_slope_line_1 = 'SOMETIMES ALWAYS NEVER';
 var feedback_right_san_slope_line_1 = 'CORRECT:  ';
 var feedback_wrong_san_slope_line_1 = 'INCORRECT: '; 

//chapter3 section 5 group 1 percent //
 var san_equations_of_lines_max_count = 1;
 var san_equations_of_lines_1 = 'COMING SOON.';
 var answer_san_equations_of_lines_1 = 'SOMETIMES ALWAYS NEVER';
 var feedback_right_san_equations_of_lines_1 = 'CORRECT:  ';
 var feedback_wrong_san_equations_of_lines_1 = 'INCORRECT: ';  
  

//chapter3 section 1 group 1 graph_equations_two_variables //
 var san_graph_equations_two_variables_max_count = 10;
 
 var san_graph_equations_two_variables_1 = 'An ordered pair of real numbers corresponds to exactly one point in the Cartesian coordinate system.';
 var answer_san_graph_equations_two_variables_1 = 'ALWAYS';
 var feedback_right_san_graph_equations_two_variables_1 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_1 = 'INCORRECT: '; 

 var san_graph_equations_two_variables_2 = 'Each point in the Cartesian coordinate system corresponds to exactly one ordered pair of real numbers.';
 var answer_san_graph_equations_two_variables_2 = 'ALWAYS';
 var feedback_right_san_graph_equations_two_variables_2 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_2 = 'INCORRECT: '; 
  
 var san_graph_equations_two_variables_3 = 'If a point is above the x-axis, its second coordinate is positive.';
 var answer_san_graph_equations_two_variables_3 = 'ALWAYS';
 var feedback_right_san_graph_equations_two_variables_3 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_3 = 'INCORRECT: '; 
  
 var san_graph_equations_two_variables_4 = 'If a point is above the x-axis, it first coordiante is positive.';
 var answer_san_graph_equations_two_variables_4 = 'SOMETIMES';
 var feedback_right_san_graph_equations_two_variables_4 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_4 = 'INCORRECT: '; 
 
 var san_graph_equations_two_variables_5 = 'If a point is below the x-axis, it first coordinate is negative.';
 var answer_san_graph_equations_two_variables_5 = 'SOMETIMES';
 var feedback_right_san_graph_equations_two_variables_5 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_5 = 'INCORRECT: '; 

 var san_graph_equations_two_variables_6 = 'If a point is below the x-axis, it second coordinate is negative.';
 var answer_san_graph_equations_two_variables_6 = 'ALWAYS';
 var feedback_right_san_graph_equations_two_variables_6 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_6 = 'INCORRECT: '; 
 
 var san_graph_equations_two_variables_7 = 'If a point is on the y-axis, its first coordinate is positive.';
 var answer_san_graph_equations_two_variables_7 = 'NEVER';
 var feedback_right_san_graph_equations_two_variables_7 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_7 = 'INCORRECT: '; 
 
 var san_graph_equations_two_variables_8 = 'If a point is on the x-axis, its second coordinate is positive.';
 var answer_san_graph_equations_two_variables_8 = 'NEVER';
 var feedback_right_san_graph_equations_two_variables_8 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_8 = 'INCORRECT: '; 
 
 var san_graph_equations_two_variables_9 = 'If any expression is added to both sides of an equation the resulting equation is equivalent to the original equation.';
 var answer_san_graph_equations_two_variables_9 = 'ALWAYS';
 var feedback_right_san_graph_equations_two_variables_9 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_9 = 'INCORRECT: '; 
 
 var san_graph_equations_two_variables_10 = 'If both sides of an inequality are multiplied by the same real number, the resulting inequality is equivalent to the original inequality.';
 var answer_san_graph_equations_two_variables_10 = 'SOMETIMES';
 var feedback_right_san_graph_equations_two_variables_10 = 'CORRECT:  ';
 var feedback_wrong_san_graph_equations_two_variables_10 = 'INCORRECT: '; 



//chapter2 section 5 group 2 compound _inequalities //
 var san_compound_inequalities_max_count = 1;
 
 var san_compound_inequalities_1 = 'COMING SOON.';
 var answer_san_compound_inequalities_1 = 'SOMETIMES ALWAYS NEVER';
  var feedback_right_san_compound_inequalities_1 = 'CORRECT:  ';
  var feedback_wrong_san_compound_inequalities_1 = 'INCORRECT: ';
 
 

 
 
 
 
 

//chapter1 section 2 group 3 absolute_value //
 var san_absolute_value_max_count = 9;
 
 var san_absolute_value_1 =
 'The opposite of a real number is negative.';
 var answer_san_absolute_value_1 =
 'sometimes';
  var feedback_right_san_absolute_value_1 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_1 =
 'INCORRECT: ';

 var san_absolute_value_2 =
 'The opposite of a natural number is negative.';
 var answer_san_absolute_value_2 =
 'always';
  var feedback_right_san_absolute_value_2 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_2 =
 'INCORRECT: ';
 
  var san_absolute_value_3 =
 'The absolute value of a real number is its opposite.';
 var answer_san_absolute_value_3 =
 'sometimes';
  var feedback_right_san_absolute_value_3 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_3 =
 'INCORRECT: ';
 
  var san_absolute_value_4 =
 'The opposite of a real number is a real number.';
 var answer_san_absolute_value_4 =
 'always';
  var feedback_right_san_absolute_value_4 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_4 =
 'INCORRECT: ';
 
  var san_absolute_value_5 =
 'The absolute value of a positive real number is its opposite.';
 var answer_san_absolute_value_5 =
 'never';
  var feedback_right_san_absolute_value_5 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_5 =
 'INCORRECT: ';
 
  var san_absolute_value_6 =
 'The absolute value of a real number is non-negative.';
 var answer_san_absolute_value_6 =
 'always';
  var feedback_right_san_absolute_value_6 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_6 =
 'INCORRECT: ';

  var san_absolute_value_7 =
 'The absolute value of a negative irrational number is a positive real number.';
 var answer_san_absolute_value_7 =
 'always';
  var feedback_right_san_absolute_value_7 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_7 =
 'INCORRECT: ';
 
  var san_absolute_value_8 =
 'If x and y are real numbers and x is the opposite of y, then y is the opposite of x.';
 var answer_san_absolute_value_8 =
 'always';
  var feedback_right_san_absolute_value_8 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_8 =
 'INCORRECT: '; 
 
   var san_absolute_value_9 =
 'If x and y are real numbers and x is the absolute value of y, then y is the absolute value of x.';
 var answer_san_absolute_value_9 =
 'sometimes';
  var feedback_right_san_absolute_value_9 =
 'CORRECT:  ';
  var feedback_wrong_san_absolute_value_9 =
 'INCORRECT: ';
 
//chapter1 section 2 group 2 sets_of_numbers //

 var san_sets_of_numbers_max_count = 9;
 
 var san_sets_of_numbers_1 =
 'A rational number is a prime number.';
 var answer_san_sets_of_numbers_1 =
 'never';
  var feedback_right_san_sets_of_numbers_1 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_1 =
 'INCORRECT: ';
 
 var san_sets_of_numbers_2 =
 'A real number is a rational number.';
 var answer_san_sets_of_numbers_2 =
 'sometimes';
  var feedback_right_san_sets_of_numbers_2 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_2 =
 'INCORRECT: ';

 var san_sets_of_numbers_3 =
 'A real number is an irrational number.';
 var answer_san_sets_of_numbers_3 =
 'sometimes';
  var feedback_right_san_sets_of_numbers_3 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_3 =
 'INCORRECT: ';
 
  var san_sets_of_numbers_4 =
 'A whole number is a rational number.';
 var answer_san_sets_of_numbers_4 =
 'sometimes';
  var feedback_right_san_sets_of_numbers_4 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_4 =
 'INCORRECT: ';
 
  var san_sets_of_numbers_5 =
 'An integer is a natural number.';
 var answer_san_sets_of_numbers_5 =
 'sometimes';
  var feedback_right_san_sets_of_numbers_5 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_5 =
 'INCORRECT: ';
 
  var san_sets_of_numbers_6 =
 'An interval can contain exactly two elements.';
 var answer_san_sets_of_numbers_6 =
 'never';
  var feedback_right_san_sets_of_numbers_6 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_6 =
 'INCORRECT: ';
 
  var san_sets_of_numbers_7 =
 'Prime numbers are odd.';
 var answer_san_sets_of_numbers_7 =
 'sometimes';
  var feedback_right_san_sets_of_numbers_7 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_7 =
 'INCORRECT: ';

  var san_sets_of_numbers_8 =
 'A rational number is an irrational number.';
 var answer_san_sets_of_numbers_8 =
 'never';
  var feedback_right_san_sets_of_numbers_8 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_8 =
 'INCORRECT: ';
 
   var san_sets_of_numbers_9 =
 'An irrational number can be written as a terminating or repeating decimal.';
 var answer_san_sets_of_numbers_9 =
 'never';
  var feedback_right_san_sets_of_numbers_9 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_of_numbers_9 =
 'INCORRECT: ';
 
 
 
  
  //chapter1 section1 group2 sets_intro //

 var san_sets_intro_max_count = 6;
 
 var san_sets_intro_1 =
 'A set is a collection of objects.';
 var answer_san_sets_intro_1 =
 'always';
  var feedback_right_san_sets_intro_1 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_intro_1 =
 'INCORRECT:  This is in fact the definition of set.';
 
 
var san_sets_intro_2 =
 'Sets are written with the roster method.';
 var answer_san_sets_intro_2 =
 'sometimes';
  var feedback_right_san_sets_intro_2 =
 'CORRECT: Can you give other examples of wriutting sets?';
  var feedback_wrong_san_sets_intro_2 =
 'INCORRECT:  Sometimes sets are written by using standard symbols/letters and sometimes they are written with set builder notation.'; 

 var san_sets_intro_3 =
 'Sets have subsets.';
 var answer_san_sets_intro_3 =
 'always';
  var feedback_right_san_sets_intro_3 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_intro_3 =
 'INCORRECT:  .';

 var san_sets_intro_4 =
 'Sets are designated with capital letters.';
 var answer_san_sets_intro_4 =
 'sometimes';
  var feedback_right_san_sets_intro_4 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_intro_4 =
 'INCORRECT:  .';
 
 var san_sets_intro_5 =
 'The null set has elements.';
 var answer_san_sets_intro_5 =
 'never';
  var feedback_right_san_sets_intro_5 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_intro_5 =
 'INCORRECT:  .'; 
 
  var san_sets_intro_6 =
 'If A = B, then A is a subset of B and B is a subset of A.';
 var answer_san_sets_intro_6 =
 'never';
  var feedback_right_san_sets_intro_6 =
 'CORRECT:  ';
  var feedback_wrong_san_sets_intro_6 =
 'INCORRECT:  .'; 
  
//chapter1 section1 group1 formula_basic //

 var san_formulas_basic_max_count = 9;
 
 var san_formulas_basic_1 =
 'A formula is an equation.';
 var answer_san_formulas_basic_1 =
 'always';
  var feedback_right_san_formulas_basic_1 =
 'CORRECT:  A common error (which you avoided) is to think of the "right side" of the formula as the formula '
 +'when in fact the formula is a statement of equality.';
  var feedback_wrong_san_formulas_basic_1 =
 'INCORRECT:  A formula must contain an equal symbol and is therefore an equation.';
 
 
var san_formulas_basic_2 =
 'A rectangle is a square.';
 var answer_san_formulas_basic_2 =
 'sometimes';
  var feedback_right_san_formulas_basic_2 =
 'CORRECT:  Only if the length and width of a rectangle are equal, is the rectangle is a square.';
  var feedback_wrong_san_formulas_basic_2 =
 'INCORRECT:  If the length and width of a rectangle are equal, the rectangle is a square. '
 +'If the length and width of a rectangle are not equal, the rectangle is not a square.'; 

  var san_formulas_basic_3 =
 'A variable is a letter or a subscripted variable.';
 var answer_san_formulas_basic_3 =
 'always';
  var feedback_right_san_formulas_basic_3 =
 'CORRECT:  The definition of variable is quite clear on this point.';
  var feedback_wrong_san_formulas_basic_3 =
 'INCORRECT:  The definition of variable requires all letters and subscripted letters to be a variable.';
 
var san_formulas_basic_4 =
 'The area of a triangle is a fraction.';
 var answer_san_formulas_basic_4 =
 'sometimes';
  var feedback_right_san_formulas_basic_4 =
 'CORRECT:  Can you create a triangle whose area is a fraction?  Can you create a triangle '
 +'whose area is not a fraction?';
  var feedback_wrong_san_formulas_basic_4 =
 'INCORRECT:  The area of the triangle with base 5 and height 7 is a fraction but the area of the triangle with base 4 and height 5 is not a fraction.'; 
 
 var san_formulas_basic_5 =
 'The area of a parallelogram is the product of its length and its height.';
 var answer_san_formulas_basic_5 =
 'always';
  var feedback_right_san_formulas_basic_5 =
 'CORRECT:  That is what the formula states.';
  var feedback_wrong_san_formulas_basic_5 =
 'INCORRECT: Perhaps you should review the basic formulas and definitions of the terms.';
 
  var san_formulas_basic_6 =
 'An algebraic expression is a variable.';
 var answer_san_formulas_basic_6 =
 'sometimes';
  var feedback_right_san_formulas_basic_6 =
 'CORRECT:  Can you create an algebraic expression which is not a variable?  Can you create and algebraic expresion whihc is a variable?';
  var feedback_wrong_san_formulas_basic_6 =
 'INCORRECT: The definition of algebraic expression allows for it to be a variable, but also permits many other things.';
 
 var san_formulas_basic_7 =
 '<img src="../../image/pi_small.gif" alt="the symbol for pi" border="0" align="absmiddle"> = 3.14';
 var answer_san_formulas_basic_7 =
 'never';
  var feedback_right_san_formulas_basic_7 =
 'CORRECT: Can you provide a logically sound reason for your answer.';
  var feedback_wrong_san_formulas_basic_7 =
 'INCORRECT:  The number pi is an irrational number and therefore cannot be equal to any decimal.'; 
 
 var san_formulas_basic_8 =
 'The product of 3 and (x + y) is an algebraic expression.';
 var answer_san_formulas_basic_8 =
 'always';
  var feedback_right_san_formulas_basic_8 =
 'CORRECT: Can you provide a logically sound reason for your answer.';
  var feedback_wrong_san_formulas_basic_8 =
 'INCORRECT:  The definition of algebraic expression permits sums and products of numbers and variables';
 
 var san_formulas_basic_9 =
 'A number is a variable.';
 var answer_san_formulas_basic_9 =
 'never';
  var feedback_right_san_formulas_basic_9 =
 'CORRECT: Can you provide a logically sound reason for your answer.';
  var feedback_wrong_san_formulas_basic_9 =
 'INCORRECT:  The definition of varible requires that it be a letter or a subscripted variable.';

//insert equation_identify_clasify//


 //chapter1 section1 group2 equation_solution_solve //
 
 var san_equation_solution_solve_max_count = 6;
  
   
  var san_equation_solution_solve_1 =
 'An equation has a solution.';
 var answer_san_equation_solution_solve_1 =
 'sometimes';
  var feedback_right_san_equation_solution_solve_1 =
 'CORRECT:';
  var feedback_wrong_san_equation_solution_solve_1 =
 'INCORRECT:  A contradiction is an equation and it has no solutions.'; 
 
  var san_equation_solution_solve_2 =
 'If 17 is added to both sides of an equation, the resulting equation has the same solution set as '
 +'the original equation.';
 var answer_san_equation_solution_solve_2 =
 'always';
  var feedback_right_san_equation_solution_solve_2 =
 'CORRECT: ';
  var feedback_wrong_san_equation_solution_solve_2 =
 'INCORRECT:  The first property of equations states that if an expression (17 is an expression) '
 +'is added to both sides of an equation, the resulting equation is equivalent to the original and the definition '
 +'of equivalent equations states that two equations are equivalent if they have the same solution set.  '
 +'Consequently adding 17 to both sides of an equation yields an equation with the same solution set as '
 +'the original.';  
 
  var san_equation_solution_solve_3 =
 'If 3 - 5x is added to both sides of an equation, the resulting equation has the same solution set as '
 +'the original equation.';
 var answer_san_equation_solution_solve_3 =
 'always';
  var feedback_right_san_equation_solution_solve_3 =
 'CORRECT: ';
  var feedback_wrong_san_equation_solution_solve_3 =
 'INCORRECT:  The first property of equations states that if an expression (3 - 5x is an expression) '
 +'is added to both sides of an equation, the resulting equation is equivalent to the original and the definition '
 +'of equivalent equations states that two equations are equivalent if they have the same solution set.  '
 +'Consequently adding 3 - 5x to both sides of an equation yields an equation with the same solution set as '
 +'the original.';  
 
 
  var san_equation_solution_solve_4 =
 'If both sides of an equation are multiplied by 17, the resulting equation has the same solution set as '
 +'the original equation.';
 var answer_san_equation_solution_solve_4 =
 'always';
  var feedback_right_san_equation_solution_solve_4 =
 'CORRECT: ';
  var feedback_wrong_san_equation_solution_solve_4 =
 'INCORRECT:  The second property of equations states that if both sides of an equation are multiplied by a non-zero '
 +'real number (17 is a non-zero real number), the resulting equation is equivalent to the original '
 +'and the definition of equivalent equations states that two equations are equivalent if they have the same '
 +'solution set. Consequently multiplying both sides of an equation by 17 yields an equation which has the same solution '
 +'set as the original equation.';  
 
 var san_equation_solution_solve_5 =
 'If both sides of an equation are multiplied by 3x, the resulting equation has the same solution set as '
 +'the original equation.';
 var answer_san_equation_solution_solve_5 =
 'sometimes';
  var feedback_right_san_equation_solution_solve_5 =
 'CORRECT: ';
  var feedback_wrong_san_equation_solution_solve_5 =
 'INCORRECT:  The second property of equations states that if both sides of an equation are multiplied by a non-zero '
 +'real number (3x is NOT a non-zero real number).  There is no property which states that multiplication by a '
 +'variable expression will yield an equivalent equation. In fact multiplying both sides of an equation by a variable '
 +'expression sometimes yields an equation which has the same solution set as the original equation AND sometimes yields '
 +'an equation which has a different solution set.';  
 
  var san_equation_solution_solve_6 =
 'If 7 is solution of two different equations, then those two equations are equivalent.';
 var answer_san_equation_solution_solve_6 =
 'sometimes';
  var feedback_right_san_equation_solution_solve_6 =
 'CORRECT: ';
  var feedback_wrong_san_equation_solution_solve_6 =
 'INCORRECT:  Two equations are equivalent if they have the same solution sets.  Simply sharing a solution '
+'a solution is not sufficient to make to equations equivalent.'; 


 //chapter1 section 1 group 3 equation_linear_one_variable //
 
 var san_equation_linear_one_variable_max_count = 4;
  
   
  var san_equation_linear_one_variable_1 =
 'A linear equation in one variable has no solution.';
 var answer_san_equation_linear_one_variable_1 =
 'sometimes';
  var feedback_right_san_equation_linear_one_variable_1 =
 'CORRECT:  What are the other possibilities ?';
  var feedback_wrong_san_equation_linear_one_variable_1 =
 'INCORRECT:  Some linear equation in one variable have no solutions, others have one solution, and others have infinitiy many solutions.'; 
 
  var san_equation_linear_one_variable_2 =
 'A linear equation in one variable has one solution.';
 var answer_san_equation_linear_one_variable_2 =
 'sometimes';
  var feedback_right_san_equation_linear_one_variable_2 =
 'CORRECT:  What are the other possibilities ?';
  var feedback_wrong_san_equation_linear_one_variable_2 =
 'INCORRECT:  Some linear equation in one variable have no solutions, others have one solution, and others have infinitiy many solutions.'; 
 
  
 var san_equation_linear_one_variable_3 =
 'A linear equation in one variable has infinitly many solutions.';
 var answer_san_equation_linear_one_variable_3 =
 'sometimes';
  var feedback_right_san_equation_linear_one_variable_3 =
 'CORRECT:  What are the other possibilities ?';
  var feedback_wrong_san_equation_linear_one_variable_3 =
 'INCORRECT:  Some linear equation in one variable have no solutions, others have one solution, and others have infinitiy many solutions.'; 
  
 var san_equation_linear_one_variable_4 =
 'A linear equation in one variable has a graph.';
 var answer_san_equation_linear_one_variable_4 =
 'sometimes';
  var feedback_right_san_equation_linear_one_variable_4 =
 'CORRECT:  Can you construct a linear equation in one variable which has no graph ?';
  var feedback_wrong_san_equation_linear_one_variable_4 =
 'INCORRECT:  A linear equation in one variable which has no solution has no graph while any other linear equation in one variable does have a graph.'; 
   
 
 //chapter1 section3 group1 equation_quadratic_one_variable //
 
 var san_equation_quadratic_one_variable_max_count = 7;
     
var san_equation_quadratic_one_variable_1 = 'A quadratic equation in one variable has no real solution.';
var answer_san_equation_quadratic_one_variable_1 = 'sometimes';
var feedback_right_san_equation_quadratic_one_variable_1 = 'CORRECT:  What are the other possibilities ?';
var feedback_wrong_san_equation_quadratic_one_variable_1 = 'INCORRECT:  Some quadratic equations in one variable have no real solutions, others have one real solution, and others two real solutions.'; 
 
  var san_equation_quadratic_one_variable_2 =
 'A quadratic equation in one variable has one solution.';
 var answer_san_equation_quadratic_one_variable_2 =
 'sometimes';
  var feedback_right_san_equation_quadratic_one_variable_2 =
 'CORRECT:  What are the other possibilities ?';
  var feedback_wrong_san_equation_quadratic_one_variable_2 =
 'INCORRECT:  Some quadratic equations in one variable have no real solutions, others have one real solution, and others two real solutions.'; 
 
  
 var san_equation_quadratic_one_variable_3 =
 'A quadratic equation in one variable can be solved with the Quadratic Formula.';
 var answer_san_equation_quadratic_one_variable_3 =
 'always';
  var feedback_right_san_equation_quadratic_one_variable_3 =
 'CORRECT:  ';
  var feedback_wrong_san_equation_quadratic_one_variable_3 =
 'INCORRECT: '; 
  
 var san_equation_quadratic_one_variable_4 =
 'A quadratic equation in one variable can be solve by factoring in conjunction with The Zero Factor Property.';
 var answer_san_equation_quadratic_one_variable_4 =
 'sometimes';
  var feedback_right_san_equation_quadratic_one_variable_4 =
 'CORRECT:  Can you construct a quadratic equation in one variable which cannot be factored ?';
  var feedback_wrong_san_equation_quadratic_one_variable_4 =
 'INCORRECT:  '; 
   
 var san_equation_quadratic_one_variable_5 =
 'The graph of a quadratic equation in one variable is on the Real Number Line';
 var answer_san_equation_quadratic_one_variable_5 =
 'always';
  var feedback_right_san_equation_quadratic_one_variable_5 =
 'CORRECT:  ';
  var feedback_wrong_san_equation_quadratic_one_variable_5 =
 'INCORRECT:  ';  
 
 var san_equation_quadratic_one_variable_6 =
 'The discriminant of a quadratic equation in one variable is a complex number.';
 var answer_san_equation_quadratic_one_variable_6 =
 'never';
  var feedback_right_san_equation_quadratic_one_variable_6 =
 'CORRECT:  ';
  var feedback_wrong_san_equation_quadratic_one_variable_6 =
 'INCORRECT:  If a, b, and c are real numbers then b<sup>2 - 4ac is a real number.';   
 
 
 var san_equation_quadratic_one_variable_7 =
 'One solution of a quadratic equation in one variable is a real number and another solution of the same equation is a complex number.';
 var answer_san_equation_quadratic_one_variable_7 =
 'never';
  var feedback_right_san_equation_quadratic_one_variable_7 =
 'CORRECT:  ';
  var feedback_wrong_san_equation_quadratic_one_variable_7 =
 'INCORRECT:  '; 
 
 
   //chapter1 section4 group1 complex_numbers // 
 
  var san_complex_numbers_max_count = 11;
     
var san_complex_numbers_1 = 'A complex number is a real number.';
var answer_san_complex_numbers_1 = 'sometimes';
var feedback_right_san_complex_numbers_1 = 'CORRECT: ';
var feedback_wrong_san_complex_numbers_1 = 'INCORRECT:  '; 
 
var san_complex_numbers_2 = 'A real number is a complex number.';
var answer_san_complex_numbers_2 = 'always';
var feedback_right_san_complex_numbers_2 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_2 = 'INCORRECT:  '; 
 
  
var san_complex_numbers_3 = 'The norm of a complex number is a real number.';
var answer_san_complex_numbers_3 = 'always';
var feedback_right_san_complex_numbers_3 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_3 = 'INCORRECT: '; 
  
var san_complex_numbers_4 = 'i<sup>2</sup> is a real number.';
var answer_san_complex_numbers_4 = 'always';
var feedback_right_san_complex_numbers_4 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_4 = 'INCORRECT:  '; 
   
var san_complex_numbers_5 = 'The opposite of a non-real complex number is a non-real complex number.';
var answer_san_complex_numbers_5 = 'always';
var feedback_right_san_complex_numbers_5 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_5 = 'INCORRECT:  ';  
 
var san_complex_numbers_6 = 'The square of a complex number is a non-negative real number.';
var answer_san_complex_numbers_6 = 'sometimes';
var feedback_right_san_complex_numbers_6 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_6 = 'INCORRECT: ';   
 
 
var san_complex_numbers_7 = 'A complex number may be solved.';
var answer_san_complex_numbers_7 = 'never';
var feedback_right_san_complex_numbers_7 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_7 = 'INCORRECT:  '; 
 
var san_complex_numbers_8 = 'The product of two complex numbers is a real number.';
var answer_san_complex_numbers_8 = 'sometimes';
var feedback_right_san_complex_numbers_8 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_8 = 'INCORRECT:  ';  
 
var san_complex_numbers_9 = 'The sum of two complex numbers is a real number.';
var answer_san_complex_numbers_9 = 'sometimes';
var feedback_right_san_complex_numbers_9 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_9 = 'INCORRECT:  ';   
 
var san_complex_numbers_10 = 'The complex component of a complex number is a real number.';
var answer_san_complex_numbers_10 = 'always';
var feedback_right_san_complex_numbers_10 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_10 = 'INCORRECT:  ';   
 
var san_complex_numbers_11 = 'The product of a complex number and its conjugate is its norm.';
var answer_san_complex_numbers_11 = 'always';
var feedback_right_san_complex_numbers_11 = 'CORRECT:  ';
var feedback_wrong_san_complex_numbers_11 = 'INCORRECT:  ';