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Academic Decathlon™
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Mathematics
BASIC GUIDE
United States Academic Decathlon®
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Table of Contents
Introduction . . . . . . . . . . . . 3 Trigonometry. . . . . . . . . . . 33
Algebra . . . . . . . . . . . . . . . . 4 Calculus . . . . . . . . . . . . . . 36
Properties of Real Numbers. . . . . . . . . . . . . . 4
Polynomials . . . . . . . . . . . . . . . . . . . . . . . . 10
Linear Equations . . . . . . . . . . . . . . . . . . . . . 11
Statistics . . . . . . . . . . . . . . 38
Descriptive Statistics . . . . . . . . . . . . . . . . . .38
Quadratic Equations . . . . . . . . . . . . . . . . . . 11
Measures of Central Tendencies. . . . . . . . . . 39
Factoring . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Rational Expressions. . . . . . . . . . . . . . . . . . 15
Linear Inequalities . . . . . . . . . . . . . . . . . . . 17
Inferential Statistics . . . . . . . . . . . . . . . . . . 40
Binomial Experiments. . . . . . . . . . . . . . . . . 41
Linear Equations in Two Variables . . . . . . . . 18
Normal Probability Distributions . . . . . . . . . 42
Parabolas . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Writing Equations of Lines. . . . . . . . . . . . . . 21
Normal as Approximation to Binomial . . . . . 42
Systems of Equations . . . . . . . . . . . . . . . . . 22
Estimates and Sample Sizes . . . . . . . . . . . . 42
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Estimates and Sample Sizes of Proportions . . 43
Complex Numbers . . . . . . . . . . . . . . . . . . . 24
Testing Hypotheses . . . . . . . . . . . . . . . . . . . 43
Geometry. . . . . . . . . . . . . 26
Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
General Testing Procedure . . . . . . . . . . . . . . 43
Testing a Claim about a Mean . . . . . . . . . . . 44
Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Tests of Proportion . . . . . . . . . . . . . . . . . . . 44
Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Similar Triangles . . . . . . . . . . . . . . . . . . . . . 29
Correlation and Regression . . . . . . . . . . . . . 44
Measures for Polygonal Regions. . . . . . . . . . 30
Polyhedrons . . . . . . . . . . . . . . . . . . . . . . . . 31
2
Bibliography. . . . . . . . . . . 46
Mathematics Basic Guide
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Mathematics Basic Guide
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Mathematics Basic Guide
27
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Mathematics Basic Guide
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Mathematics Basic Guide
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Mathematics Basic Guide
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Mathematics Basic Guide
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Mathematics Basic Guide
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45
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Mathematics Basic Guide