## Table of Contents

**1. Critical Thinking Skills**

** Skill Review Topics**

Objective: Round to the nearest ten, hundred, or thousand

Objective: Translate phrases into mathematical expressions.

Objective: Evaluate expressions containing variables

Objective: Solve problems involving percents, rates, and statistics.

1.1 Inductive and Deductive Reasoning

1.2 Estimation

1.3 Problem Solving

**2. Sets**

** Skill Review Topics**

Objective: Evaluate expressions containing exponents.

Objective: Determine which is the greater of two numbers

Objective: Solve Equations using the additional principle.

2.1 Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets

2.5 Applications of Sets

2.6 Infinite Sets

**3. Logic**

3.1 Statements and Logical Connectives

3.2 Truth Tables for Negation, Conjunction, and Disjunction

3.3 Truth Tables for the Conditional and Biconditional

3.4 Equivalent Statements

3.5 Symbolic Arguments

3.6 Euler Diagrams and Syllogistic Arguments

3.7 Switching Circuits

**4. Systems of Numeration**

** Skill Review Topics**

Objective: Add whole numbers.

Objective: Subtract whole numbers.

Objective: Multiply whole numbers.

Objective: Divide whole numbers.

Objective: Convert between expanded and standard notation.

4.1 Additive, Multiplicative, and Ciphered Systems of Numeration

4.2 Place-Value or Positional-Value Numeration Systems

4.3 Other Bases

4.4 Computation in Other Bases

4.5 Early Computational Methods

**5. Number Theory and the Real Number System**

** Skill Review Topics**

Objective: Find square roots.

Objective: Use a formula to find the value of a variable.

5.1 Number Theory

5.2 The Integers

5.3 The Rational Numbers

5.4 The Irrational Numbers

5.5 Real Numbers and Their Properties

5.6 Rules of Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences

5.8 Fibonacci Sequence

**6. Algebra, Graphs, and Functions**

** Skill Review Topics**

Objective: Add real numbers using a number line.

Objective: Subtract numbers.

Objective: Multiply real numbers.

Objective: Divide real numbers.

Objective: Evaluate exponential notation.

Objective: Simplify square roots of squares such as the square root of 25.

6.1 Order of Operations and Solving Equations

6.2 Formulas

6.3 Applications of Algebra

6.4 Variation

6.5 Linear Inequalities

6.6 Graphing Linear Equations

6.7 Solving Systems of Linear Equations

6.8 Linear Inequalities and Systems of Linear Inequalities

6.9 Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula

6.10 Functions and Their Graphs

**7. The Metric System**

** Skill Review Topics**

Objective: Convert between mixed numerals and fraction notation.

Objective: Convert between decimal notation and fraction notation.

Objective: Multiply a fraction by a fraction, and multiply a fraction by an integer.

7.1 Basic Terms and Conversions Within the Metric System

7.2 Length, Area, and Volume

7.3 Mass and Temperature

7.4 Dimensional Analysis and Conversions to and from the Metric System

**8. Geometry**

** Skill Review Topics**

Objective: Determine the intersection and union of two sets.

Objective: Solve proportions using cross-multiplication.

Objective: Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand.

Objective: Approximate square roots.

8.1 Points, Lines, Planes, and Angles

8.2 Polygons

8.3 Perimeter and Area

8.4 Volume and Surface Area

8.5 Transformational Geometry, Symmetry, and Tessellations

8.6 Topology

8.7 Non-Euclidean Geometry and Fractal Geometry

**9. Mathematical Systems**

** Skill Review Topics**

Objective: Identify which numbers belong to a set.

Objective: Divide whole numbers, writing the quotient as a mixed numeral.

9.1 Groups

9.2 Finite Mathematical Systems

9.3 Modular Arithmetic

9.4 Matrices

** **

**10. Consumer Mathematics**

** Skill Review Topics**

Objective: Simplify expressions using the rules of order of operations.

Objective: Use the multiplication property to solve equations.

Objective: Convert from percent notation to decimal notation.

10.1 Percent

10.2 Personal Loans and Simple Interest

10.3 Compound Interest

10.4 Installment Buying

10.5 Buying a House with a Mortgage

10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments

**11. Probability**

** Skill Review Topics**

Objective: Simplify fractions.

Objective: Multiply fractions.

Objective: Add and subtract frations.

Objective: Divide fractions

Objective: Solve linear equations with a variable on only one side of the equals sign.

11.1 Empirical and Theoretical Probabilities

11.2 Odds

11.3 Expected Value (Expectation)

11.4 Tree Diagrams

11.5 OR and AND Problems

11.6 Conditional Probability

11.7 The Counting Principle and Permutations

11.8 Combinations

11.9 Solving Probability Problems by Using Combinations

11.10 Binomial Probability Formula

**12. Statistics**

** Skill Review Topics**

Objective: Find the absolute value of a number.

Objective: Plot points in the Cartesian coordinate system.

Objective: Determine the slope and *y-*intercept of the line represented by a given equation.

Objective: Graph a linear equation using the slope and *y-*intercept.

12.1 Sampling Techniques and Misuses of Statistics

12.2 Frequency Distributions and Statistical Graphs

12.3 Measures of Central Tendency

12.4 Measures of Dispersion

12.5 The Normal Curve

12.6 Linear Correlation and Regression

**13. Graph Theory**

13.1 Graphs, Paths, and Circuits

13.2 Euler Paths and Euler Circuits

13.3 Hamilton Paths and Hamilton Circuits

13.4 Trees

**14. Voting and Apportionment**

14.1 Voting Methods

14.2 Flaws and the Voting Methods

14.3 Apportionment Methods

14.4 Flaws of the Apportionment Methods