//chapter2 section 5 group 1 percent //
 var fib_percent_max_count =1 ; 
 var fib_percent_1 ='COMING SOON';
 var answer_fib_percent_1 = 'COMING SOON';
 
 
 



//chapter3 section 3 group 1 graph_linear_equations_inequalities_two_variables //
 var fib_graph_linear_equations_inequalities_two_variables_max_count =12 ; 
 var fib_graph_linear_equations_inequalities_two_variables_1 ='The <input name="answer"> of an equation of the form x = k is a vertical line through the point (0, k).';
 var answer_fib_graph_linear_equations_inequalities_two_variables_1 = 'graph';
 var fib_graph_linear_equations_inequalities_two_variables_2 ='A linear equation in two variables is an equation that can be written in the form <input name="answer">  where m and b are real numbers.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_2 = 'y=mx+b';
 var fib_graph_linear_equations_inequalities_two_variables_3 ='The equation for the <input name="answer"> line through the point (0, k) is x = k.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_3 = 'vertical';
 var fib_graph_linear_equations_inequalities_two_variables_4 ='A solution of an equation in two variables is an ordered pair of Real Numbers whose coordinates make the equation <input name="answer"> when substituted for the variables.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_4 = 'true';
 var fib_graph_linear_equations_inequalities_two_variables_5 ='The graph of an equation consists of all the points, and only those points, whose <input name="answer"> are solutions of the equation.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_5 = 'coordinates';
 var fib_graph_linear_equations_inequalities_two_variables_6 ='A solution of an inequality in two variables is an <input name="answer"> pair of Real Numbers whose coordinates make the inequality true when substituted for the variables.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_6 = 'ordered';
 var fib_graph_linear_equations_inequalities_two_variables_7 ='The boundary curve for a linear inequality in two variables is a <input name="answer">.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_7 = 'line';
 var fib_graph_linear_equations_inequalities_two_variables_8 ='The graph of every linear equation in two variables is a <input name="answer"> line. ';
 var answer_fib_graph_linear_equations_inequalities_two_variables_8 = 'non-vertical';
 var fib_graph_linear_equations_inequalities_two_variables_9 ='The graph of a linear inequality in two variables is a half-plane bounded by the graph of the corresponding <input name="answer"> equation.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_9 = 'boundary';
 var fib_graph_linear_equations_inequalities_two_variables_10 ='If a test point is a solution of an inequality, every point in that half-plane is a <input name="answer"> of the inequality.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_10 = 'solution';
 var fib_graph_linear_equations_inequalities_two_variables_11 ='If a test point is not a solution of an inequality, every point in the <input name="answer"> half-plane is a solution of the inequality.';
 var answer_fib_graph_linear_equations_inequalities_two_variables_11 = 'other';
 var fib_graph_linear_equations_inequalities_two_variables_12 ='To graph a linear equation in two variables it is only necessary to plot <input name="answer"> points on the graph and draw the line through those points. ';
 var answer_fib_graph_linear_equations_inequalities_two_variables_12 = 'two';

//chapter3 section 4 group 1 slope_line //
 var fib_slope_line_max_count =6 ; 
 var fib_slope_line_1 ='Two non-vertical lines are <input name="answer"> if they have the same slope and different y-intercepts.';
 var answer_fib_slope_line_1 = 'parallel'; 
 var fib_slope_line_2 ='A <input name="answer"> line has no slope.';
 var answer_fib_slope_line_2 = 'vertical';
 var fib_slope_line_3 ='Two non-vertical lines are <input name="answer"> if their slopes are negative reciprocals of each other.';
 var answer_fib_slope_line_3 = 'perpendicular'; 
 var fib_slope_line_4 ='The slope of a <input name="answer"> line is 0.';
 var answer_fib_slope_line_4 = 'horizontal'; 
 var fib_slope_line_5 ='Two non-vertical lines are perpendicular if their slopes are negative <input name="answer"> of each other.';
 var answer_fib_slope_line_5 = 'reciprocals'; 
 var fib_slope_line_6 ='Two non-vertical lines are <input name="answer"> if they have the same slope and different y-intercepts.';
 var answer_fib_slope_line_6 = 'parallel';  
 
 
 
 
 
 
 
 
 
 
//chapter3 section 5 group 1 equations_of_lines //
 var fib_equations_of_lines_max_count =1 ; 
 var fib_equations_of_lines_1 ='COMING SOON';
 var answer_fib_equations_of_lines_1 = 'COMING SOON'; 

//chapter3 section 1 group 1 graph_equations_two_variables //
 var fib_graph_equations_two_variables_max_count =10 ; 
 var fib_graph_equations_two_variables_1 ='A rectangular coordinate system (Cartesian coordinate system) consists of two perpendicular <input name="answer"> lines. ';
 var answer_fib_graph_equations_two_variables_1 = 'number';
 var fib_graph_equations_two_variables_2 ='The point of intersection of the two number lines in a Cartesian coordinate system is called the <input name="answer"> of the coordinate system.';
 var answer_fib_graph_equations_two_variables_2 = 'origin';
 var fib_graph_equations_two_variables_3 ='Each ordered pair of real numbers corresponds to exactly one <input name="answer"> in the Cartesian coordinate system.';
 var answer_fib_graph_equations_two_variables_3 = 'point'; 
 var fib_graph_equations_two_variables_4 ='Each point in the Cartesian coordinate system corresponds to exactly one <input name="answer"> of real numbers.';
 var answer_fib_graph_equations_two_variables_4 = 'ordered pair'; 
 var fib_graph_equations_two_variables_5 ='An x-intercept of a graph in the Cartesian Coordinate System is a point where the graph <input name="answer"> the x-axis.';
 var answer_fib_graph_equations_two_variables_5 = 'intersects';  
 var fib_graph_equations_two_variables_6 ='A point is on the x-axis if and only if its <input name="answer"> coordinate y is zero.';
 var answer_fib_graph_equations_two_variables_6 = 'second';  
 var fib_graph_equations_two_variables_7 ='A <input name="answer"> of a graph in the Cartesian Coordinate System is a point where the graph intersects the y-axis.';
 var answer_fib_graph_equations_two_variables_7 = 'y-intercept';  
 var fib_graph_equations_two_variables_8 ='A point is on the y-axis if and only if its first coordinate x is <input name="answer">.';
 var answer_fib_graph_equations_two_variables_8 = 'zero'; 
 var fib_graph_equations_two_variables_9 ='To find the <input name="answer"> of a graph we let x = 0 and solve for y.';
 var answer_fib_graph_equations_two_variables_9 = 'y-intercepts';  
 var fib_graph_equations_two_variables_10 ='To find the <input name="answer"> of a graph we let y = 0 and solve for x.';
 var answer_fib_graph_equations_two_variables_10 = 'x-intercepts';  




//chapter2 section 5 group 2 compound _inequalities //
var fib_compound_inequalities_max_count =10; 

var fib_compound_inequalities_1 ='A compound inequality is two inequalities joined by either the conjunction <input name="answer"> or the conjunction or.';
var answer_fib_compound_inequalities_1 = 'and';
 
var fib_compound_inequalities_2 ='A compound inequality is two inequalities joined by either the conjunction and or the conjunction <input name="answer">.';
var answer_fib_compound_inequalities_2 = 'or';
 
var fib_compound_inequalities_3 ='A <input name="answer"> is two inequalities joined by either the conjunction and or the conjunction or.';
var answer_fib_compound_inequalities_3 = 'compound inequality'; 

var fib_compound_inequalities_4 ='The solution set of a compound inequality formed with the word and is the  <input name="answer">  of the solution sets of the two inequalities.';
var answer_fib_compound_inequalities_4 = 'intersection'; 

var fib_compound_inequalities_5 ='The solution set of a compound inequality formed with the word or is the <input name="answer"> of the solution sets of the two inequalities.';
var answer_fib_compound_inequalities_5 = 'union'; 

var fib_compound_inequalities_6 ='A compact compound inequality is a compound inequality which can be written in the form <input name="answer">.';
var answer_fib_compound_inequalities_6 = 'a<x<b'; 

var fib_compound_inequalities_7 ='A <input name="answer"> is a compound inequality which can be written in the form a < x < b.';
var answer_fib_compound_inequalities_7 = 'compact compound inequality'; 

var fib_compound_inequalities_8 ='The solution set of a compound inequality formed with the word <input name="answer"> is the union of the solution sets of the two inequalities.';
var answer_fib_compound_inequalities_8 = 'or'; 

var fib_compound_inequalities_9 ='The solution set of a compound inequality formed with the word <input name="answer"> is the intersection of the solution sets of the two inequalities.';
var answer_fib_compound_inequalities_9 = 'and'; 

var fib_compound_inequalities_10 ='The compound inequality 2 < x AND x < 9 can be written in compact form as <input name="answer">.';
var answer_fib_compound_inequalities_10 = '2<x<9'; 


//chapter1 section 3 group 2 fractions //

 var fib_fractions_max_count =7 ; 

 var fib_fractions_1 =
 'A <input name="answer"> of two fractions <IMG src="../../image/fraction_a_over_b_small.gif"> and <IMG src="../../image/fraction_c_over_d_small.gif"> is a number which is divisible by both the denominators b and d.';
 var answer_fib_fractions_1 = 'common denominator';

 var fib_fractions_2 =
 'A <input name="answer"> consists of a numerator (top), a denominator (bottom), and the indicated division of the numerator by the denominator.';
 var answer_fib_fractions_2 = 'fraction';

 var fib_fractions_3 =
 'The sign of the fraction, the sign of the numerator, and the sign of the denominator produce <input name="answer"> equivalent forms of every fraction.';
 var answer_fib_fractions_3 = 'four';
 
 var fib_fractions_4 =
 'The sign of the <input name="answer">, the sign of the numerator, and the sign of the denominator produce four equivalent forms of every fraction.';
 var answer_fib_fractions_4 = 'fraction'; 
 
 var fib_fractions_5 =
 'The sign of the fraction, the sign of the <input name="answer">, and the sign of the denominator produce four equivalent forms of every fraction.';
 var answer_fib_fractions_5 = 'numerator'; 
 
 var fib_fractions_6 =
 'The sign of the fraction, the sign of the numerator, and the sign of the <input name="answer"> produce four equivalent forms of every fraction.';
 var answer_fib_fractions_6 = 'denominator'; 
 
 var fib_fractions_7 =
 'If <IMG src="../../image/fraction_a_over_b_small.gif"> and <IMG src="../../image/fraction_c_over_d_small.gif">  are fractions, then their <input name="answer"> is defined by <IMG src="../../image/fraction_product_small.gif">.';
 var answer_fib_fractions_7 = ' product';  
 
//chapter1 section 4 group 1 equality_and_inequality //

 var fib_equality_and_inequality_max_count =7 ; 

 var fib_equality_and_inequality_1 =
 'A binary <input name="answer"> is a calculation involving two operands.';
 var answer_fib_equality_and_inequality_1 = 'operation';

 var fib_equality_and_inequality_2 =
 'A binary <input name="answer"> is a comparison of two operands.';
 var answer_fib_equality_and_inequality_2 = 'relation';

 var fib_equality_and_inequality_3 =
 'Two real numbers a and b are equal if they represent the <input name="answer"> on the number line.';
 var answer_fib_equality_and_inequality_3 = 'same point';

 var fib_equality_and_inequality_4 =
 'An inequality is a mathematical statement which contains an <input name="answer"> symbol.';
 var answer_fib_equality_and_inequality_4 = 'inequality';

 var fib_equality_and_inequality_5 =
 'The real number a is <input name="answer"> than b if a is to the left of b on the number line.';
 var answer_fib_equality_and_inequality_5 = 'less';

 var fib_equality_and_inequality_6 =
 'The real number a is greater than b if a is to the <input name="answer"> of b on the number line.';
 var answer_fib_equality_and_inequality_6 = 'right'; 

 var fib_equality_and_inequality_7 =
 'The expression a > b means a - b is <input name="answer">.';
 var answer_fib_equality_and_inequality_7 = 'positive'; 


//chapter1 section 3 group 1 exponents_and_roots //

 var fib_exponents_and_roots_max_count =7; 

 var fib_exponents_and_roots_1 =
 'An expression of the form a<sup>n</sup> is called an <input name="answer"> expression.';
 var answer_fib_exponents_and_roots_1 = 'exponential';

 var fib_exponents_and_roots_2 =
 'In the exponential expression a<sup>n</sup>, n is the <input name="answer">.';
 var answer_fib_exponents_and_roots_2 = 'exponent';
 
 var fib_exponents_and_roots_3 =
 'In the exponential expression a<sup>n</sup>, a is the <input name="answer">.';
 var answer_fib_exponents_and_roots_3 = 'base';
 
 var fib_exponents_and_roots_4 =
 'When n is a natural number, the exponential expression a<sup>n</sup> is used to indicate that the base a is <input name="answer"> times itself n times.';
 var answer_fib_exponents_and_roots_4 = 'multiplied';
 
 var fib_exponents_and_roots_5 =
 'In the exponential expression a<sup>n</sup>, <input name="answer"> is the base.';
 var answer_fib_exponents_and_roots_5 = 'a';

 
 var fib_exponents_and_roots_6 =
 'In the exponential expression a<sup>n</sup>, <input name="answer"> is the exponent.';
 var answer_fib_exponents_and_roots_6 = 'n';
 
 var fib_exponents_and_roots_7 =
 'If k is a positive real number then the <input name="answer"> square root  of k is a positive number whose square is k.';
 var answer_fib_exponents_and_roots_7 = 'principal'; 


//chapter1 section 2 group 3 absolute_value //

 var fib_absolute_value_max_count =5; 

 var fib_absolute_value_1 =
 'The absolute value of a number is its <input name="answer"> from 0 on the number line.';
 var answer_fib_absolute_value_1 = 'distance';

 var fib_absolute_value_2 =
 'The <input name="answer"> of a real number is the number which is equidistant from zero but on the opposite side of zero.';
 var answer_fib_absolute_value_2 = 'opposite';
 
 var fib_absolute_value_3 =
 'The <input name="answer"> of a number is its distance from 0 on the number line.';
 var answer_fib_absolute_value_3 = 'absolute value';
 
 var fib_absolute_value_4 =
 'The opposite of a real number is the number which is <input name="answer"> from zero but on the opposite side of zero.';
 var answer_fib_absolute_value_4 = 'equidistant';
 
 var fib_absolute_value_5 =
 'A precise algebraic definition of  <input name="answer"> of a number is <img src="../../image/absolute_value_def_small.gif" alt="absolute vaue definition">.';
 var answer_fib_absolute_value_5 = 'absolute value';

//chapter1 section 2 group 2 sets_of_numbers //

 var fib_sets_of_numbers_max_count =7; 

 var fib_sets_of_numbers_1 =
 ' The set of Natural Numbers consists of the common <input name="answer"> numbers.';
 var answer_fib_sets_of_numbers_1 = 'counting';

 var fib_sets_of_numbers_2 = 'The set of <input name="answer"> Numbers consists of the set of Natural Numbers with the number 0 adjoined.';
 var answer_fib_sets_of_numbers_2 = 'Whole';
 
  var fib_sets_of_numbers_3 = 'The set of Integers consists of the Whole Numbers with their <input name="answer"> adjoined.  ';
 var answer_fib_sets_of_numbers_3 = 'opposites';
 
  var fib_sets_of_numbers_4 = 'The set of <input name="answer"> Numbers consists of all numbers which can be written as fractions. ';
 var answer_fib_sets_of_numbers_4 = 'Rational';
 
  var fib_sets_of_numbers_5 = 'The set of <input name="answer"> Numbers consists of the set of Rational Numbers with the set of Irrational Numbers adjoined. ';
 var answer_fib_sets_of_numbers_5 = 'Real';
 
  var fib_sets_of_numbers_6 = 'The set of Real Numbers consists of the set of <input name="answer"> Numbers with the set of Irrational Numbers adjoined. ';
 var answer_fib_sets_of_numbers_6 = 'Rational';

  var fib_sets_of_numbers_7 = 'The set of Real Numbers consists of the set of Rational Numbers with the set of <input name="answer"> Numbers adjoined. ';
 var answer_fib_sets_of_numbers_7 = 'Irrational';

//chapter1 section 1 group 2 sets_intro //

 var fib_sets_intro_max_count = 9;

 var fib_sets_intro_1 =
 ' The set A is a <input name="answer"> of the set B if every element of set A is an element of set B.';
 var answer_fib_sets_intro_1 = 'subset';

 var fib_sets_intro_2 =
 ' The <input name="answer"> of specifying a set consists of surrounding the collection of elements with braces.';
 var answer_fib_sets_intro_2 = 'roster method';

 var fib_sets_intro_3 =
 ' The <input name="answer"> is the set with no elements.';
 var answer_fib_sets_intro_3 = 'null set';

 var fib_sets_intro_4 =
 ' A set is a <input name="answer"> of objects.';
 var answer_fib_sets_intro_4 = 'collection';

 var fib_sets_intro_5 =
 ' An <input name="answer"> of a set is one of the objects in the set.';
 var answer_fib_sets_intro_5 = 'element';

 var fib_sets_intro_6 =
 ' In set builder notation the vertical bar is read as <input name="answer">.';
 var answer_fib_sets_intro_6 = 'such that';

 var fib_sets_intro_7 =
 ' An <input name="answer"> of a set is one of the objects in the set.';
 var answer_fib_sets_intro_7 = 'element';

 var fib_sets_intro_8 =
 ' The <input name="answer"> is a subset of every set.';
 var answer_fib_sets_intro_8 = 'null set';
  
 var fib_sets_intro_9 =
 ' Two sets are <input name="answer"> if they contain exactly the same elements.';
 var answer_fib_sets_intro_9 = 'equal';
 




 //chapter1 section 1 group 2 formulas_basic //
 var fib_formulas_basic_max_count = 11;

 var fib_formulas_basic_1 =
 ' <img src="../../image/formula_trapezoid_area_small.gif" alt="formula for the area of a trapezoid" border="0" align="absmiddle"> '
 +'is the formula for the area of a <input name="answer">.';
 var answer_fib_formulas_basic_1 =
 'trapezoid';

 var fib_formulas_basic_2 =
 ' A <input name="answer"> is a quadrilateral with four equal sides and four 90 degree angles.';
 var answer_fib_formulas_basic_2 =
 'square';
 
  var fib_formulas_basic_3 =
 ' A triangle is a <input name="answer"> sided polygon. '; 
  var answer_fib_formulas_basic_3 =
 'three';
 
   var fib_formulas_basic_4 =
 ' An <input name="answer"> is a number, a variable, or sums, differences, products, quotients, powers, or roots of variables and numbers '; 
  var answer_fib_formulas_basic_4 =
 'algebraic expression';
 
  var fib_formulas_basic_5 =
 'The area of a triangle whose base is 6 inches and whose height is 5 inches is '
+' <input name="answer"> sq. in.';
 var answer_fib_formulas_basic_5 =
 '15';

 var fib_formulas_basic_6 =
 ' A quadrilateral which has exactly two parallel sides is called a <input name="answer">.';
 var answer_fib_formulas_basic_6 =
 'trapezoid';
 
  var fib_formulas_basic_7 =
 '<img src="../../image/formula_circle_circumference.gif" alt="formula for the circumference of a circle" border="0" align="absmiddle"> '
 +'is the formula for the <input name="answer"> of a circle';
 var answer_fib_formulas_basic_7 =
 'circumference'; 
 
  var fib_formulas_basic_8 =
 ' What is the area of the rectangle which is 4 inches wide and 5 feet long? <input name="answer"> sq.in.';
 var answer_fib_formulas_basic_8 =
 '240';

  var fib_formulas_basic_9 =
 ' 14x - 5y is an <input name="answer">.';
 var answer_fib_formulas_basic_9 =
 'algebraic expression';

  var fib_formulas_basic_10 =
 ' Correct to 1 decimal place, what is the area of the circle with a 6 inch radius? '
+' <input name="answer"> sq.in.';
 var answer_fib_formulas_basic_10 =
 '113.0';
 
   var fib_formulas_basic_11 =
 'A variable is a <input name="answer"> which represents a number.';
 var answer_fib_formulas_basic_11 =
 'letter'; 
 
 
 //insert equation_identify_clasify//
 
 
 
   //chapter1 section 1 group 2 equation_solution_solve //
 
var fib_equation_solution_solve_max_count = 20;
  
var fib_equation_solution_solve_1 =
 ' A number (or numbers) that makes an equation <input name="answer"> when substituted for the variable (or variables) is '
 +'called a solution of the equation.';
var answer_fib_equation_solution_solve_1 = 'true';  

var fib_equation_solution_solve_2 =
 ' The collection of all <input name="answer"> of an equation is called the solution set of the equation';
var answer_fib_equation_solution_solve_2 = 'solutions';   
  
var fib_equation_solution_solve_3 =
 ' A number (or numbers) that makes an equation true when substituted for the variable (or variables) is '
 +'called a <input name="answer"> of the equation.';
var answer_fib_equation_solution_solve_3 = 'solution';   
  
var fib_equation_solution_solve_4 =
 ' Two equations are <input name="answer"> if they have the same solution sets.';
var answer_fib_equation_solution_solve_4 = 'equivalent';   
  
var fib_equation_solution_solve_5 =
 ' The process of finding all the solutions (the solution set) of an equation is called <input name="answer"> the equation.';
var answer_fib_equation_solution_solve_5 = 'solving';     
  
var fib_equation_solution_solve_6 =
 ' The collection of all solutions of an equation is called the solution <input name="answer"> of the equation';
var answer_fib_equation_solution_solve_6 = 'set';    
  
var fib_equation_solution_solve_7 =
 ' The process of finding <input name="answer"> the solutions (the solution set) of an equation is called solving the equation.';
var answer_fib_equation_solution_solve_7 = 'all';     
  
var fib_equation_solution_solve_8 =
 ' A <input name="answer"> equation is an equation which has a single variable on one side of the equal sign and a '
 +'single number on the other side.';
var answer_fib_equation_solution_solve_8 = 'simplest';  
  
var fib_equation_solution_solve_9 =
 ' Two equations are equivalent if they have the same <input name="answer"> sets.';
var answer_fib_equation_solution_solve_9 = 'solution';   
  
var fib_equation_solution_solve_10 =
 ' The collection of all solutions of an equation is called the <input name="answer"> set of the equation';
var answer_fib_equation_solution_solve_10 = 'solution';    
 
var fib_equation_solution_solve_11 =
 '  If any <input name="answer"> is added to both sides of an equation the resulting equation is equivalent '
 +'to the original equation.';
var answer_fib_equation_solution_solve_11 = 'expression';  

var fib_equation_solution_solve_12 =
 'If both sides of an equation are <input name="answer"> by the same non-zero real number, the resulting equation is '
 +'equivalent to the original equation.';
var answer_fib_equation_solution_solve_12 = 'multiplied';  

var fib_equation_solution_solve_13 =
 ' A <input name="answer"> equation is an equation which has a single variable on one side of the equal sign and a '
 +'single number on the other side.';
var answer_fib_equation_solution_solve_13 = 'simplest';    
  
var fib_equation_solution_solve_14 =
 '  If any expression is <input name="answer"> to both sides of an equation the resulting equation is equivalent '
 +'to the original equation.';
var answer_fib_equation_solution_solve_14 = 'added';   

var fib_equation_solution_solve_15 =
 'The <input name="answer"> of an equation consists of all the points, and only those points, whose coordinates '
 +'are solutions of the equation.';
var answer_fib_equation_solution_solve_15 = 'graph'; 

var fib_equation_solution_solve_16 =
 'If both sides of an equation are multiplied by the same non-zero real number, the resulting equation is '
 +'<input name="answer"> to the original equation.';
var answer_fib_equation_solution_solve_16 = 'equivalent'; 

var fib_equation_solution_solve_17 =
 '  If any expression is added to both sides of an equation the resulting equation is <input name="answer"> '
 +'to the original equation.';
var answer_fib_equation_solution_solve_17 = 'equivalent'; 

var fib_equation_solution_solve_18 =
 'The graph of an equation consists of all the points, and only those points, whose <input name="answer"> '
 +'are solutions of the equation.';
var answer_fib_equation_solution_solve_18 = 'coordinates'; 
  
var fib_equation_solution_solve_19 =
 'If both sides of an equation are multiplied by the same <input name="answer"> real number, the resulting equation is '
 +'equivalent to the original equation.';
var answer_fib_equation_solution_solve_19 = 'non-zero';   
  
 var fib_equation_solution_solve_20 =
 'The graph of an equation consists of all the points, and only those points, whose coordinates '
 +'are <input name="answer"> of the equation.';
var answer_fib_equation_solution_solve_20 = 'solutions';  


   //chapter1 section 1 group 3 equation_linear_one_variable //
 
var fib_equation_linear_one_variable_max_count = 8;
  
var fib_equation_linear_one_variable_1 =
 ' The process to solve a linear equation in one variable is to generate a sequence of equations '
 +'each <input name="answer"> to the previous equation until a simplest equation is obtained.';
var answer_fib_equation_linear_one_variable_1 = 'equivalent';  

var fib_equation_linear_one_variable_2 =
 ' The process to solve a linear equation in one variable is to generate a sequence of equations '
 +'each  equivalent to the previous equation until a  <input name="answer"> equation is obtained.';
var answer_fib_equation_linear_one_variable_2 = 'simplest'; 

var fib_equation_linear_one_variable_3 =
 ' A linear equation in one variable is an equation that can be written in the form <input name="answer"> '
 +'where a and b are real numbers with a not zero.';
var answer_fib_equation_linear_one_variable_3 = 'ax + b = 0'; 

var fib_equation_linear_one_variable_4 =
 ' The process to solve a linear equation in one variable is to generate a sequence of <input name="answer"> '
 +'each  equivalent to the previous equation until a simplest equation is obtained.';
var answer_fib_equation_linear_one_variable_4 = 'equations'; 

var fib_equation_linear_one_variable_5 =
 ' A  <input name="answer"> equation in one variable is an equation that can be written in the form ax + b = 0 '
 +'where a and b are real numbers with a not zero.';
var answer_fib_equation_linear_one_variable_5 = 'linear'; 

var fib_equation_linear_one_variable_6 =
 ' If the solution set for a linear equation in one variable is a set containing a single number, the '
 +'graph of that linear equation in one variable is a single <input name="answer"> on the Real Number Line.';
var answer_fib_equation_linear_one_variable_6 = 'point'; 

var fib_equation_linear_one_variable_7 =
 ' If the solution set for a linear equation in one variable is the <input name="answer"> set, that equation has no graph.';
var answer_fib_equation_linear_one_variable_7 = 'empty'; 

var fib_equation_linear_one_variable_8 =
 ' If the solution set for a linear equation in one variable is the empty  set, that equation has <input name="answer"> graph.';
var answer_fib_equation_linear_one_variable_8 = 'no'; 




   //chapter1 section3 group1 equation_quadratic_one_variable //
 
var fib_equation_quadratic_one_variable_max_count = 8;
  
var fib_equation_quadratic_one_variable_1 =
 'A <input name="answer"> is an equation which may be written in the form ax<sup>2</sup> + bx + c = 0 where a, b, and c are real numbers and a is not 0.';
var answer_fib_equation_quadratic_one_variable_1 = 'quadratic equation';  

var fib_equation_quadratic_one_variable_2 =
 'A quadratic equation is an <input name="answer"> which may be written in the form ax<sup>2</sup> + bx + c = 0 where a, b, and c are real numbers and a is not 0.';
var answer_fib_equation_quadratic_one_variable_2 = 'equation'; 

var fib_equation_quadratic_one_variable_3 =
 ' If the discriminant of a quadratic equation is negative, the equation will have <input name="answer"> real solutions.';
var answer_fib_equation_quadratic_one_variable_3 = 'no'; 

var fib_equation_quadratic_one_variable_4 =
 'If the discriminant of a quadratic equation is positive, the equation will have <input name="answer"> real solutions. ';
var answer_fib_equation_quadratic_one_variable_4 = 'two'; 

var fib_equation_quadratic_one_variable_5 =
 ' If a quadratic has two complex solutions those solutions are <input name="answer"> of each other.';
var answer_fib_equation_quadratic_one_variable_5 = 'conjugates'; 

var fib_equation_quadratic_one_variable_6 =
 'Every quadratic equation can be solved with the <input name="answer">.';
var answer_fib_equation_quadratic_one_variable_6 = 'quadratic formula'; 

var fib_equation_quadratic_one_variable_7 =
 'The graph of a quadratic equation in one variable with two real solutions consists of <input name="answer"> points on the real number line.';
var answer_fib_equation_quadratic_one_variable_7 = 'two'; 

var fib_equation_quadratic_one_variable_8 =
 'The graph of a quadratic equation in one variable is drawn on the <input name="answer">.';
var answer_fib_equation_quadratic_one_variable_8 = 'real number line'; 


   //chapter1 section4 group1 complex_numbers //
 
var fib_complex_numbers_max_count = 10;
  
var fib_complex_numbers_1 =
 'A <input name="answer"> is a number that can be written in the form a + bi where a and b are real numbers and i = <img src="../../images/square_root_of_negative_one.gif" width="38" height="29" align="absmiddle">';
var answer_fib_complex_numbers_1 = 'complex number';  

var fib_complex_numbers_2 =
 'The <input name="answer"> of the complex number a + bi is a<sup>2</sup> + b<sup>2</sup>. ';
var answer_fib_complex_numbers_2 = 'norm'; 

var fib_complex_numbers_3 =
 'The <input name="answer"> of the complex number a + bi is a - bi. ';
var answer_fib_complex_numbers_3 = 'conjugate';

var fib_complex_numbers_4 =
 'The <input name="answer"> of the complex number a + bi is -a - bi. ';
var answer_fib_complex_numbers_4 = 'opposite';

var fib_complex_numbers_5 =
 'The <input name="answer"> of the complex numbers 3 + 2i and 5 - 6i is 8 - 4i. ';
var answer_fib_complex_numbers_5 = 'sum';

var fib_complex_numbers_6 =
 'The norm of the complex number 5 - 6i is <input name="answer">. ';
var answer_fib_complex_numbers_6 = '61';

var fib_complex_numbers_7 =
 'The multiplicative inverse of a complex number is its <input name="answer"> divided by its norm. ';
var answer_fib_complex_numbers_7 = 'conjugate';

var fib_complex_numbers_8 =
 'The multiplicative inverse of a complex number is its conjugate divided by its <input name="answer">. ';
var answer_fib_complex_numbers_8 = 'conjugate';

var fib_complex_numbers_8 =
 'Two complex numbers a + bi and c + di are <input name="answer"> if a = c and b = d.';
var answer_fib_complex_numbers_8 = 'equal';

var fib_complex_numbers_9 =
 'The <input name="answer"> of the complex number 8  5i is 8.';
var answer_fib_complex_numbers_9 = 'real component';

var fib_complex_numbers_10 =
 'The multiplicative inverse of a complex number is its conjugate divided by its <input name="answer">. ';
var answer_fib_complex_numbers_10 = 'norm';