The table of contents below shows the review topics (bulleted text) that are integrated into the Thinking Mathematically course. The Integrated Review includes worksheets, videos, and other materials designed to help students master these important topics.

1. Problem Solving and Critical Thinking

1.R Integrated Review

• 1.R.1 Translate English phrases into algebraic expressions
• 1.R.2 Find coordinates of points in the rectangular coordinate system
• 1.R.3 Evaluate algebraic expressions
• 1.R.4 Use the order of operations agreement

1.1 Inductive and Deductive Reasoning

1.2 Estimation, Graphs, and Mathematical Models

1.3 Problem Solving

2. Set Theory

2.R Integrated Review

• 2.R.1 Understand and use inequality symbols

2.1 Basic Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Set Operations and Venn Diagrams with Three Sets

2.5 Survey Problems

3. Logic

3.1 Statements, Negations, and Quantified Statements

3.2 Compound Statements and Connectives

3.3 Truth Tables for Negations, Conjunction, and Disjunction

3.4 Truth Tables for the Conditional and the Biconditional

3.5 Equivalent Statements and Variations of Conditional Statements

3.6 Negations of Conditional Statements and De Morgan's Laws

3.7 Arguments and Truth Tables

3.8 Arguments and Euler Diagrams

4. Number Representation and Calculation

4.1 Our Hindu-Arabic System and Early Positional Systems

4.2 Number Bases in Positional Systems

4.3 Computation in Positional Systems

4.4 Looking Back at Early Numeration Systems

5. Number Theory and the Real Number System

5.R Integrated Review

• 5.R.1 Evaluate exponential expressions
• 5.R.2 Use the multiplication property of equality to solve equations
• 5.R.3 Find square roots
• 5.R.4 Use a calculator to find decimal approximations for irrational square roots

5.1 Number Theory, Prime and Composite Numbers

5.2 The Integers; Order of Operations

5.3 The Rational Numbers

5.4 The Irrational Numbers

5.5 Real Numbers and Their Properties; Clock Addition

5.6 Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences

6. Algebra: Equations and Inequalities

6.R Integrated Review

• 6.R.1 Determine whether a number is a solution of an equation
• 6.R.2 Use the addition property of equality to solve equations
• 6.R.3 Translate English sentences into algebraic equations
• 6.R.4 Solve linear equations
• 6.R.5 Graph numbers on a number line
• 6.R.6 Combine like terms
• 6.R.7 Multiply monomials
• 6.R.8 Find the greatest common factor
• 6.R.9 Use the product rule
• 6.R.10 Use the power rule
• 6.R.11 Use the quotient rule
• 6.R.12 Simplify exponential expressions

6.1 Algebraic Expressions and Formulas

6.2 Linear Equations in One Variable and Proportions

6.3 Applications of Linear Equations

6.4 Linear Inequalities in One Variable

6.5 Quadratic Equations

7. Algebra: Graphs, Functions, and Linear Systems

7.R Integrated Review

• 7.R.1 Determine whether an ordered pair is a solution of an equation
• 7.R.2 Find solutions of an equation in two variables
• 7.R.3 Use a graph to identify intercepts
• 7.R.4 Graph equations in the rectangular coordinate system
• 7.R.5 Solve a formula for a variable
• 7.R.6 Determine whether an ordered pair is a solution of an inequality
• 7.R.7 Understand properties used to solve linear inequalities

7.1 Graphing and Functions

7.2 Linear Functions and Their Graphs

7.3 Systems of Linear Equations in Two Variables

7.4 Linear Inequalities in Two Variables

7.5 Linear Programming

7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions

8. Personal Finance

8.R Integrated Review

• 8.R.1 Use the percent formula

8.1 Percent, Sales Tax, and Discounts

8.2 Income Tax

8.3 Simple Interest

8.4 Compound Interest

8.5 Annuities, Methods of Savings, and Investments

8.6 Cars

8.7 The Cost of Home Ownership

8.8 Credit Cards

9. Measurement

9.R Integrated Review

• 9.R.1 Convert between mixed numbers and improper fractions
• 9.R.2 Convert from decimal to scientific notation
• 9.R.3 Convert from scientific to decimal notation

9.1 Measuring Length; The Metric System

9.2 Measuring Area and Volume

9.3 Measuring Weight and Temperature

10. Geometry

10.R Integrated Review

• 10.R.1 Solve problems involving proportions
• 10.R.2 Solve quadratic equations using the square root property

10.1 Points, Lines, Planes, and Angles

10.2 Triangles

10.3 Polygons, Perimeter, and Tessellations

10.4 Area and Circumference

10.5 Volume and Surface Area

10.6 Right Triangle Trigonometry

10.7 Beyond Euclidean Geometry

11. Counting Methods and Probability Theory

11.R Integrated Review

• 11.R.1 Reduce or simplify fractions
• 11.R.2 Express rational numbers as decimals
• 11.R.3 Multiply fractions
• 11.R.4 Add and subtract fractions with identical denominators
• 11.R.5 Add and subtract fractions with unlike denominators
• 11.R.6 Divide fractions

11.1 The Fundamental Counting Principle

11.2 Permutations

11.3 Combinations

11.4 Fundamentals of Probability

11.5 Probability with the Fundamental Counting principle, Permutations, and Combinations

11.6 Events Involving Not and Or; Odds

11.7 Events Involving And; Conditional Probability

11.8 Expected Value

12. Statistics

12.R Integrated Review

• 12.R.1 Plot ordered pairs in the rectangular coordinate system
• 12.R.2 Compute a line’s slope
• 12.R.3 Find a line’s slope and y-intercept from its equation
• 12.R.4 Graph lines in slope-intercept form
• 12.R.5 Use the rectangular coordinate system to visualize relationships between variables
• 12.R.6 Find a number’s absolute value

12.1 Sampling, Frequency Distributions, and Graphs

12.2 Measures of Central Tendency

12.3 Measures of Dispersion

12.4 The Normal Distribution

12.5 Problem Solving with the Normal Distribution

12.6 Scatter Plots, Correlation, and Regression Lines

13. Voting and Apportionment

13.1 Voting Methods

13.2 Flaws of Voting Methods

13.3 Apportionment Methods

13.4 Flaws of Apportionment Methods

14. Graph Theory

14.1 Graphs, Paths, and Circuits

14.2 Euler Paths and Euler Circuits

14.3 Hamilton Paths and Hamilton Circuits

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