AOPS Pre Algebra 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