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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.
| Printer-Friendly
Version | |
| Academic
Standard |
Student Edition
Lesson(s) |
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. |
|
2-1,
2-7, 11-2 |
| A1.1.2 |
|
Simplify square roots
using factors. |
|
11-1,
11-2 |
| A1.1.3 |
|
Understand and use the
distributive, associative, and
commutative properties. |
|
1-5,1-6,6-3
|
| A1.1.4
|
|
Use the laws of exponents
for rational exponents. |
|
10-5,
11-1 |
| A1.1.5 |
|
Use dimensional (unit)
analysis to organize conversions
and computations. |
|
12-3,
12-4 |
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. |
|
1-3,
6-6, 7-1 |
| A1.2.4 |
|
Solve linear inequalities
using properties of order. |
|
1-3,
6-3 |
| A1.2.5 |
|
Solve combined linear
inequalities. |
|
6-4,
7-5 |
| 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. |
|
1-8,
1-9, 2-5,
13-2 |
| A1.3.3 |
|
Understand the concept
of a function, decide if a given relation is a function,
and link equations to functions. |
|
4-6,
10-2 |
| 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. |
|
4-5,
5-3,5-4 |
| 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. |
|
5-4,5-5 |
| 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. |
|
6-6,7-5 |
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. |
|
7-2,7-4 |
| A1.5.4
|
|
Understand and use the
addition or subtraction method to solve a pair of
linear equations in two variables. |
|
7-3,7-4 |
| 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
Students add, subtract, multiply, and divide polynomials.
They factor quadratics. |
| A1.6.1
|
|
Add and subtract polynomials. |
|
8-5,
3-8 |
| A1.6.2
|
|
Multiply and divide monomials. |
|
8-1,
8-2, 8-3,
12-2 |
| A1.6.3
|
|
Find powers and roots
of monomials (only when the answer has an integer
exponent). |
|
8-1,
11-1 |
| A1.6.4
|
|
Multiply polynomials. |
|
8-6,
8-7,8-8 |
| A1.6.5 |
|
Divide polynomials by
monomials. |
|
12-5 |
| A1.6.6
|
|
Find a common monomial
factor in a polynomial. |
|
9-2,
11-1 |
| 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. |
|
12-2,
12-3,12-4,12-5,12-6,12-7 |
| A1.7.2 |
|
Solve algebraic proportions. |
|
3-6,
12-9 |
Standard
8 Quadratic, Cubic, and Radical Equations
Students graph and solve quadratic and radical equations.
They graph cubic equations. |
| A1.8.1
|
|
Graph quadratic, cubic,
and radical equations. |
|
10-1,
10-2, 11-3 |
| 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. |
|
9-6,
10-3 |
| 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 |
| A1.8.6
|
|
Solve quadratic equations
by using the quadratic formula. |
|
10-4 |
| A1.8.7
|
|
Use quadratic equations
to solve word problems. |
|
10-2,10-3,10-4 |
| 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. |
|
10-2,10-4 |
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). |
|
3-2,
6-1, 6-5,
10-5,
10-7, 13-2 |
| A1.9.6
|
|
Distinguish between inductive
and deductive reasoning, identifying and providing
examples of each. |
|
1-7,
4-8, 8-3 |
| 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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—ISTEP+/GQE
Answer Sheet