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Math Review

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Math Subtopics

Pre-algebra
Whole Numbers
1.2 Add Whole Numbers
1.3 Subtract Whole Numbers
1.4 Multiply Whole Numbers
1.5 Divide Whole Numbers


Language of Algebra
2.1 Use the Language of Algebra
2.2 Evaluate, Simplify, and Translate Expressions
2.3 Subtraction and Addition Properties of Equality
2.4 Find Multiples and Factors
2.5 Prime Factorization, Least Common Multiple (LCM)


Integers
3.2 Add Integers
3.3 Subtract Integers
3.4 Multiply and Divide Integers
3.5 Solve Equations Using Integers;
The Division Property of Equality


Fractions
4.1 Visualize Fractions
4.2 Multiply and Divide Fractions
4.3 Multiply and Divide Mixed Numbers and Complex Fractions
4.4 Add and Subtract Fractions, Common Denominators
4.5 Add and Subtract Fractions, Different Denominators
4.6 Add and Subtract Mixed Numbers
4.7 Solve Equations with Fractions


Decimals
5.2 Decimal Operations
5.3 Decimals and Fractions
5.4 Solve Equations with Decimals
5.5 Averages and Probability
5.6 Ratios and Rate
5.7 Simplify and Use Square Roots


Percent
6.1 Understand Percent
6.2 Solve General Applications of Percent
6.3 Solve Sales Tax, Commission, Discount Applications
6.4 Solve Simple Interest Applications
6.5 Solve Proportions and their Applications


Real Numbers
7.1 Rational and Irrational Numbers
7.2 Commutative and Associative Properties
7.3 Distributive Property
7.4 Properties of Identity, Inverses, and Zero
7.5 Systems of Measurement


Linear Equations
8.1 Solve Equations using Subtraction and Addition Properties of Equality
8.2 Solve Equations using Division and Multiplication Properties of Equality
8.3 Solve Equations with Variables and Constants on Both Sides
8.4 Solve Equations with Fraction or Decimal Coefficients


Geometry
9.1 Use a Problem Solving Strategy
9.2 Solve Money Applications
9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
9.4 Use Properties of Rectangles, Triangles, and Trapezoids
9.5 Solve Geometry Applications: Circles and Irregular Figures
9.6 Solve Geometry Applications: Volume and Surface Area
9.7 Solve a Formula for a Specific Variable


Polynomials
10.1 Add and Subtract Polynomials
10.2 Use Multiplication Properties of Exponents
10.3 Multiply Polynomials
10.4 Divide Monomials
10.5 Integer Exponents and Scientific Notation
10.6 Introduction to Factoring Polynomials


Graphs
11.1 Use the Rectangular Coordinate System
11.2 Graphing Linear Equations
11.3 Graphing with Intercepts
11.4 Understand Slope of a Line


Algebra
Solving Linear Equations
2.1 Solve Linear Equations
2.2 Problem Solving Strategy
2.3 Solve a Formula for a Specific Variable
2.4 Solve Mixture and Uniform Motion
2.5 Linear Inequalities
2.6 Compound Inequalities
2.7 Absolute Value Inequalities


Graphs
3.1 Graph Linear Equations in Two Variables
3.2 Slope of a Line
3.3 Find the Equation of a Line
3.4 Graph Linear Inequalities in Two Variables
3.5 Relations and Functions
3.6 Graphs of Functions


Linear Equations
4.1 Linear Equations with Two Variables
4.2 Systems of Equations
4.3 Solve Mixture Applications
4.4 Equations with Three Variables
4.5 Matrices
4.6 Determinants
4.7 Graphing Linear Inequalities


Polynomials
5.1 Add and Subtract Polynomials
5.2 Exponents and Scientific Notation
5.3 Multiply Polynomials
5.4 Dividing Polynomials


Factoring
6.1 Greatest Common Factor
6.2 Factor Trinomials
6.3 Factor Special Products
6.4 General Strategy for Factoring Polynomials
6.5 Polynomial Equations


Rational Expressions
7.1 Multiply and Divide Rational Expressions
7.2 Add and Subtract Rational Expressions
7.3 Simplify Complex Rational Expressions
7.4 Solve Rational Equations
7.5 Solve Applications with Rational Equations
7.6 Solve Rational Inequalities

Roots and Radicals
8.1 Simplify Expressions with Roots
8.2 Simplify Radical Expressions
8.3 Simplify Rational Exponents
8.4 Add, Subtract, and Multiply Radical Expressions
8.5 Divide Radical Expressions
8.6 Solve Radical Equations
8.7 Use Radicals in Functions
8.8 Use the Complex Number System


Quadratic Equations
9.1 Square Root Property
9.2 Completing the Square
9.3 Quadratic Formula
9.5 Solve Applications
9.6 Graph Quadratic Functions
9.8 Quadratic Inequalities


Exponents and Logarithm
10.1 Finding Composite and Inverse Functions
10.2 Evaluate and Graph Exponential Functions
10.3 Evaluate and Graph Logarithmic Functions
10.4 Use the Properties of Logarithms
10.5 Solve Exponential and Logarithmic Equations


Conics
11.1 Distance and Midpoint Formulas; Circles
11.2 Parabolas
11.3 Ellipses
11.4 Hyperbolas
11.5 Solve Systems of Nonlinear Equations


Sequences, Series
12.2 Arithmetic Sequences
12.3 Geometric Sequences and Series
12.4 Binomial Theorem


Statistics
Sampling and Data
1.1 Definitions of Statistics, Probability
1.2 Data, Sampling, and Variation
1.3 Frequency, Frequency Tables
1.4 Experimental Design and Ethics
1.5 Data Collection Experiment
1.6 Sampling Experiment


Descriptive Statistics
2.1 Stem-and-Leaf Graphs, Bar Graphs
2.2 Histograms, Frequency Polygons, Time Series Graphs
2.3 Measures of the Location of the Data
2.4 Box Plots
2.5 Measures of the Center of the Data
2.6 Skewness and the Mean, Median, and Mode
2.7 Measures of the Spread of the Data
2.8 Descriptive Statistics


Probability Topics
3.1 Terminology
3.2 Independent and Mutually Exclusive Events
3.3 Two Basic Rules of Probability
3.4 Contingency Tables
3.5 Tree and Venn Diagrams
3.6 Probability Topics


Discrete Random Variables
4.1 Probability Distribution Function
4.2 Mean or Expected Value and Standard Deviation
4.3 Binomial Distribution
4.4 Geometric Distribution
4.5 Hypergeometric Distribution
4.6 Poisson Distribution
4.7 Discrete Distribution (Playing Card Experiment)
4.8 Discrete Distribution (Lucky Dice Experiment)


Continuous Random Variables
5.1 Continuous Probability Functions
5.2 The Uniform Distribution
5.3 The Exponential Distribution
5.4 Continuous Distribution


The Normal Distribution
6.1 The Standard Normal Distribution
6.2 Using the Normal Distribution
6.3 Normal Distribution—Lap Times
6.4 Normal Distribution—Pinkie Length


The Central Limit Theorem
7.1 The Central Limit Theorem for Sample Means
7.2 The Central Limit Theorem for Sums
7.3 Using the Central Limit Theorem
7.4 Central Limit Theorem (Pocket Change)
7.5 Central Limit Theorem (Cookie Recipes)


Confidence Intervals
8.1 Normal Distribution
8.2 Student's t-Distribution
8.3 A Population Proportion
8.4 Confidence Interval (Home Costs)
8.5 Confidence Interval (Place of Birth)
8.6 Confidence Interval (Women's Heights)


Hypothesis Testing with One Sample
9.1 Null and Alternative Hypotheses
9.2 Outcomes and the Type I and Type II Errors
9.3 Distribution Needed for Hypothesis Testing
9.4 Rare Events, the Sample, and the Decision and Conclusion
9.5 Additional Information and Full Hypothesis Test Examples
9.6 Hypothesis Testing of a Single Mean and Single Proportion


Hypothesis Testing with Two Samples
10.1 Two Population Means, Unknown Standard Deviations
10.2 Two Population Means, Known Standard Deviations
10.3 Comparing Two Independent Population Proportions
10.4 Matched or Paired Samples
10.5 Hypothesis Testing for Two Means


The Chi-Square Distribution
11.1 Facts About the Chi-Square Distribution
11.2 Goodness-of-Fit Test
11.3 Test of Independence
11.4 Test for Homogeneity
11.5 Comparison of the Chi-Square Tests
11.6 Test of a Single Variance
11.7 Lab 1: Chi-Square Goodness-of-Fit
11.8 Lab 2: Chi-Square Test of Independence


Linear Regression and Correlation
12.1 Linear Equations
12.2 The Regression Equation
12.3 Correlation Coefficient
12.4 Prediction
12.5 Outliers
12.6 Regression (Distance from School)
12.7 Regression (Textbook Cost)
12.8 Regression (Fuel Efficiency)


F-Distribution and One-way Anova
13.1 One-Way ANOVA
13.2 The F Distribution and the F Ratio
13.3 Facts About the F Distribution
13.4 Test of Two Variances
13.5 Lab: One-Way ANOVA


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