AOPS Pre Algebra Syllabus

课程大纲 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

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