//chapter1 section 1 group 1 equation_identify_classify //

 var tf_equation_identify_classify_max_count = 8;
 
 var tf_equation_identify_classify_1 =
 'Every mathematical statement is an equation.';
 var answer_tf_equation_identify_classify_1 =
 'false';
  var feedback_right_tf_equation_identify_classify_1 =
 'CORRECT:  Can you give an example of a mathematical statement which is not an equation?';
  var feedback_wrong_tf_equation_identify_classify_1 =
 'INCORRECT:  There are many mathematical statements which are not equations.  '
+'For example the mathematical statement 4 < 9 is not an equation.';
 
 
 var tf_equation_identify_classify_2 =
 'Every equation is a mathematical statement.';
 var answer_tf_equation_identify_classify_2 =
 'true';
  var feedback_right_tf_equation_identify_classify_2 =
 'CORRECT:  ';
  var feedback_wrong_tf_equation_identify_classify_2 =
 'INCORRECT:  You should probably review the definition of equation to observe that an equation is a mathematical statement.';
 
  var tf_equation_identify_classify_3 =
 'Every equation is true for some value of the variables.';
 var answer_tf_equation_identify_classify_3 =
 'false';
  var feedback_right_tf_equation_identify_classify_3 =
 'CORRECT:  ';
  var feedback_wrong_tf_equation_identify_classify_3 =
 'INCORRECT:  Some equations such as 3 + 4 = 7 do not even have variables.<br>'
 +'Some equations like x<sup>2</sup> = -4 are contradictions; that is they are false for every value of x.';
 
 var tf_equation_identify_classify_4 =
 'The equation x + 5 = x + 2 is a contradiction.';
 var answer_tf_equation_identify_classify_4 =
 'true';
 var feedback_right_tf_equation_identify_classify_4 =
 'CORRECT:  Can you demonstrate this on the number line?';
 var feedback_wrong_tf_equation_identify_classify_4 =
 'INCORRECT:  If x is any number then 5 plus that number is certainly not equal to 2 plus that number.';
 
 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:  ';