AOPS Pre Algebra Syllabus
This course is offered exclusively as a one-on-one class and is not available in a small-group format.
Syllabus
1 Properties of Arithmetic
1.1 Start with Arithmetic
1.2 Addition
1.3 Multiplication
1.4 Negation
1.5 Subtraction
1.6 Reciprocals
1.7 Division
1.8 Summary
2 Exponents
2.1 Squares
2.2 Higher Exponents
2.3 Zero as an Exponent
2.4 Negative Exponents
2.5 Summary
3 Number Theory
3.1 Multiples
3.2 Divisibility Tests
3.3 Prime Numbers
3.4 Prime Factorization
3.5 Least Common Multiple
3.6 Divisors
3.7 Greatest Common Divisor
3.8 Summary
4 Fractions
4.1 What is a Fraction?
4.2 Multiplying Fractions
4.3 Dividing by a Fraction
4.4 Raising Fractions to Powers
4.5 Simplest Form of a Fraction
4.7 Adding and Subtracting Fractions
4.8 Mixed Numbers
4.9 Summary
5 Equations and Inequalities
5.1 Expressions
5.2 Solving Linear Equations I
5.3 Solving Linear Equations II
5.4 Word Problems
5.5 Inequalities
5.6 Summary
6 Decimals
6.1 Arithmetic with Decimals
6.2 Rounding
6.3 Decimals and Fractions
6.4 Repeating Decimals
6.5 Summary
7 Ratios, Conversions, and Rates
7.1 What is a Ratio
7.2 Multi-way Ratios
7.3 Proportions
7.4 Conversions
7.5 Speed
7.6 Other Rates
7.7 Summary
8 Percents
8.1 What is a Percent
8.2 Word Problems
8.3 Percent Increase and Decrease
8.4 Summary
9 Square Roots
9.1 From Squares to Square Roots
9.2 Square Roots of Non-Square Integers
9.3 Arithmetic with Square Roots
9.4 Summary
10 Angles
10.1 Measuring Angles
10.2 Parallel Lines
10.3 Angles in Polygons
10.4 Summary
11 Perimeter and Area
11.1 Measuring Segments
11.2 Area
11.3 Circles
11.4 Summary
12 Right Triangles and Quadrilaterals
12.1 The Pythagorean Theorem
12.2 Some Specia! Triangles
12.3 Types of Quadrilaterals
12.4 Summary
13 Data and Statistics
13.1 Basic Statistics
13.2 Limits of Basic Statistics
13.3 Tabies, Graphs, and Charts
13.4 Summary
14 Counting
14.1 Counting with Addition and Subtraction
14.2 The Multiplication Principle
14.3 Casework
14.4 Counting Pairs
14.5 Probability
14.6 Summary
15 Problem-Solving Strategies
15.1 Find a Pattern
15.2 Make a List
15.3 Draw a Picture
15.4 Work Backwards
15.5 Summary