Extra Examples—ISTEP+/GQE

Extra Examples shows you additional worked-out examples that mimic the ones in your book. These requirements include the benchmarks from the Sunshine State Standards that are most relevant to this course. The benchmarks printed in regular type are required for this course. The portions printed in italic type are not required for this course.

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Standard 1 Operations with Real Numbers
Students simplify and compare expressions. They use rational exponents, and simplify square roots.
 A1.1.1 Compare real number expressions.
 A1.1.2 Simplify square roots using factors.
 A1.1.3 Understand and use the distributive, associative, and commutative properties.
 A1.1.4 Use the laws of exponents for rational exponents.
 A1.1.5 Use dimensional (unit) analysis to organize conversions and computations.
Standard 2 Linear Equations and Inequalities
Students solve linear equations and inequalities in one variable. They solve word problems that involve linear equations, inequalities, or formulas.
 A1.2.1 Solve linear equations.
1-3,3-2,3-3,3-4,3-5,7-2,7-3,7-4
 A1.2.2 Solve equations and formulas for a specified variable.
1-2, 3-8, 4-4, 5-3
 A1.2.3 Find solution sets of linear inequalities when possible numbers are given for the variable.
 A1.2.4 Solve linear inequalities using properties of order.
 A1.2.5 Solve combined linear inequalities.
 A1.2.6 Solve word problems that involve linear equations, formulas, and inequalities.
1-3, 7-5,3-2,3-3,3-4,3-5,4-5,4-6,6-1,6-2,6-3
Standard 3 Relations and Functions
Students sketch and interpret graphs representing given situations. They understand the concept of a function and analyze the graphs of functions.
 A1.3.1 Sketch a reasonable graph for a given relationship.
1-8
 A1.3.2 Interpret a graph representing a given situation.
 A1.3.3 Understand the concept of a function, decide if a given relation is a function, and link equations to functions.
 A1.3.4 Find the domain and range of a relation.
1-8, 4-3,4-4,4-5
Standard 4 Graphing Linear Equations and Inequalities
Students graph linear equations and inequalities in two variables. They write equations of lines and find and use the slope and y intercept of lines. They use linear equations to model real data.
 A1.4.1 Graph a linear equation.
4-5,5-2,5-3,7-1
 A1.4.2 Find the slope, x intercept and y intercept of a line given its graph, its equation, or two points on the line.
 A1.4.3 Write the equation of a line in slope intercept form. Understand how the slope and y intercept of the graph are related to the equation.
5-4
 A1.4.4 Write the equation of a line given appropriate information.
 A1.4.5 Write the equation of a line that models a data set and use the equation (or the graph of the equation) to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.
5-7
 A1.4.6 Graph a linear inequality in two variables.
Standard 5 Pairs of Linear Equations and Inequalities
Students solve pairs of linear equations using graphs and using algebra. They solve pairs of linear inequalities using graphs. They solve word problems involving pairs of linear equations.
 A1.5.1 Use a graph to estimate the solution of a pair of linear equations in two variables.
7-1
 A1.5.2 Use a graph to find the solution set of a pair of linear inequalities in two variables.
7-5
 A1.5.3 Understand and use the substitution method to solve a pair of linear equations in two variables.
 A1.5.4 Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.
 A1.5.5 Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.
7-4
 A1.5.6 Use pairs of linear equations to solve word problems.
7-1,7-2,7-3,7-4
Standard 6 Polynomials
 A1.6.2 Multiply and divide monomials.
 A1.6.3 Find powers and roots of monomials (only when the answer has an integer exponent).
 A1.6.4 Multiply polynomials.
 A1.6.5 Divide polynomials by monomials.
12-5
 A1.6.6 Find a common monomial factor in a polynomial.
 A1.6.7 Factor the difference of two squares and other quadratics.
9-3, 9-4,9-5,9-6
 A1.6.8 Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x intercepts of a graph, and the factors of a polynomial expression.
10-2
Standard 7 Algebraic Fractions
Students simplify algebraic ratios and solve algebraic proportions.
 A1.7.1 Simplify algebraic ratios.
 A1.7.2 Solve algebraic proportions.
Students graph and solve quadratic and radical equations. They graph cubic equations.
 A1.8.2 Solve quadratic equations by factoring.
9-2, 9-3, 9-4, 9-5, 9-6
 A1.8.3 Solve quadratic equations in which a perfect square equals a constant.
 A1.8.4 Complete the square to solve quadratic equations.
10-3
 A1.8.5 Derive the quadratic formula by completing the square.
11-1
10-4
 A1.8.7 Use quadratic equations to solve word problems.
 A1.8.8 Solve equations that contain radical expressions.
11-3
 A1.8.9 Use graphing technology to find approximate solutions of quadratic and cubic equations.
Standard 9 Mathematical Reasoning and Problem Solving
Students use a variety of strategies to solve problems.
 A1.9.1 Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guess and check, solving a simpler problem, writing an equation, and working backwards.
1-7, 3-1, 3-2, 3-3,
3-4,3-5,3-7,4-8,7-1,7-2,7-5,10-3,10-5
 A1.9.2 Decide whether a solution is reasonable in the context of the original situation.
4-4
Standard 9 Mathematical Reasoning and Problem Solving
Students develop and evaluate mathematical arguments and proofs.
 A1.9.3 Use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations.
1-2, 1-3, 1-4,1-5,1-6,3-4,3-5
 A1.9.4 Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.
1-7, 3-2, 3-3, 3-4,3-5, 11-3
 A1.9.5 Decide whether a given algebraic statement is true always, sometimes, or never (statements involving linear or quadratic expressions, equations, or inequalities).
 A1.9.6 Distinguish between inductive and deductive reasoning, identifying and providing examples of each.
 A1.9.7 Identify the hypothesis and conclusion in a logical deduction
1-7
 A1.9.8 Use counterexamples to show that statements are false, recognizing that a single counterexample is sufficient to prove a general statement false.
1-7, 3-5, 3-6, 4-3,
4-6,6-2,7-1,8-1,8-4,9-1,13-4

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