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(Ebook PDF) Competition Math for Middle School 1st edition by J Batterson ISBN 978-1441488879 1441488871 full chapters

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Author(s): J. Batterson
ISBN(s): 9781441488879, 1441488871
Edition: Later Printing Used
File Details: PDF, 13.56 MB
Year: 2009
Language: english
SKU: EB-50546662 Category: Tag:

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ISBN 10:1441488871

ISBN 13:978-1441488879

Author: J. Batterson

Written for the gifted math student, the new math coach, the teacher in search of problems and materials to challenge exceptional students, or anyone else interested in advanced mathematical problems. Competition Math contains over 700 examples and problems in the areas of Algebra, Counting, Probability, Number Theory, and Geometry. Examples and full solutions present clear concepts and provide helpful tips and tricks. “I wish I had a book like this when I started my competition career.” – Four-Time National Champion MATHCOUNTS coach Jeff Boyd. “This book is full of juicy questions and ideas that will enable the reader to excel in MATHCOUNTS and AMC competitions. I recommend it to any students who aspire to be great problem solvers.” – Former AHSME Committee Chairman Harold Reiter.
 

Table of Contents:

Introduction

1: Algebra
1.1: Variables and Equations

  • Variables, Consecutive Integers, d=rt, Harmonic Mean, Moles Digging Holes.

1.2: Linear Equations

  • Slope, Intercepts, Slope-Intercept Form, Point-Slope Form, Standard Form, Parallel/Perpendicular Lines, Horizontal and Vertical Lines.

1.3: Systems of Equations

  • Substitution, Elimination, Common Word Problems, Cheating the System.

1.4: Ratios, Proportions, and Percents

  • Ratios, Proportions, Percents, and Percent of Change.

Review 1.1 to 1.4

1.5: Distribution

  • The Distributive Property, Difference of Squares and Perfect Squares, Sum of the Reciprocals.

1.6: Quadratics

  • Perfect Squares, Difference of Squares, Factoring By Grouping, Solving Quadratics by Factoring, The Quadratic Formula, Word Problems, Sum and Product of the Roots.

1.7: Exponents and Radicals

  • Multiplying, Dividing, Raising a Power to a Power, Fractional Exponents, Square Roots.

1.8: Statistics

  • Mean, Median, Mode and Range.

1.9: Sequences and Series

  • Arithmetic Sequences and Series, Geometric Sequences and Series.

1.10: More Substitution

  • Nested Square Roots, Continued Fractions.

Chapter Review

2: Counting
2.1: Basics

  • Simple Counting Techniques.

2.2: Venn Diagrams

  • Two and Three-Set Venn Diagrams.

2.3: Bowling Pins and Handshakes

  • Triangular Number Patterns.

2.4: Counting Outcomes

  • The Fundamental Counting Principle.

2.5: Casework

  • Keeping Organized.

Review 2.1 to 2.5

2.6: Factorials and Permutations

  • Factorials, Permutations, Permutations with Restrictions.

2.7: Combinations

  • Combinations, Paths on a Grid, Beyond Casework, Complementary Counting.

Review 2.1 to 2.7

2.8: Sticks and Stones

  • With and Without Restrictions.

2.9: Pascal’s Triangle

  • Combinations and Pascal’s Triangle.

Chapter Review

3: Probability
3.1: Probability Basics

  • Compound Events, Dependent and Independent, Replacement, Cards.

3.2: Compound Events and Counting

  • Combining Counting Techniques and Compound Probability.

3.3: Casework and Probability

3.4: Probability and Combinations

3.5: Complementary Counting and Probability

Review 3.1 to 3.5

3.6: Geometric Probability

3.7: Expected Value

  • Finding the average outcome.

Chapter Review

4: Number Theory
4.1: Primes and Divisibility

  • Sieve of Eratosthenes, Primes, Divisibility Rules.

4.2: Factors

  • The Fundamental Theorem of Arithmetic, Factor Counting.

4.3: Factor Tricks

  • Product of the Factors, Sum of the Factors, GCF and LCM, Factorials.

Review 2.1 to 2.5

4.4: Different Bases

  • Notation, Basic Arithmetic.

4.5: The Units Digit

  • Addition, Multiplication, Perfect Squares, Exponents.

4.6: Fractions and Decimals

  • Repeating/Terminating, Conversions.

4.7: Modular Arithmetic

Chapter Review

5: Geometry
5.1: Geometry Basics

  • Lines, Angles, Triangles, Polygons, Trapezoids, Parallelograms, Kites.

5.2: Circles

  • Chords, Secants, Tangents, Arcs, Inscribed Angles, Properties, Circumference and Arc Length.

5.3: Pythagorean Theorem

  • Triples, Special Right Triangles, Distance Formula, Algebra and the Pythagorean Theorem.

5.4: Area

  • Formulas, Heron’s Formula, Altitudes, Working Backwards.

5.5: Three-Dimensional Geometry

  • Polyhedra, Faces, Vertices, and Edges, Volume.

5.6: Similarity

  • Right Triangles, Circles, Parallel Lines, Area and Volume Relationships.

Chapter Review

6: Solutions
Algebra

  • Key
  • Solutions

Counting

  • Key
  • Solutions

Probability

  • Key
  • Solutions

Number Theory

  • Key
  • Solutions

Geometry

  • Key
  • Solutions

7: Appendix

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