Contest Math I

Learn the key techniques and train hard for contest math.

Via intriguing problems and competition-style practice, we’ll guide you through your training from start to finish. Improve your speed and accuracy while gaining an appreciation for how fun math can be.

Upon completion, you’ll have perfected your algebra, geometry, probability, and number sense game, and have the tools needed to successfully tackle math competitions at the level of MATHCOUNTS and the AMC8.

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1. 1

Introduction

Do you like solving challenging math puzzles?

1. Algebra

Learn to search for algebraic strategies that minimize the work you need to do.

2. Geometry

Rotate, stretch, combine, and break apart pieces of the figures in these challenges.

3. Combinatorics

Learn casework and counting strategies that can be applied to many areas of math including probability.

4. Number Theory

Explore the relationships between prime and composite numbers and the rules for determining divisibility.

2. 2

Algebra: Equations

Calculate the value of unknowns quickly and efficiently.

1. Included with

Diagnostic: Ratios and Percentages

Check your knowledge of ratios and percentages and identify areas for growth.

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Diagnostic: Simple Equations

Review these essential techniques for keeping equations in balance and isolating variables.

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Sequences and Series

Find the pattern, extend the pattern, and add them all up in these questions about sequences.

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Equations with Ratios

Learn some counter-intuitive tricks for working with ratio equations to avoid making them harder.

3. 3

Algebra: Data

Measure data that is static and in fluctuation.

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Diagnostic: Data

Check your knowledge of data and statistics and identify areas for growth.

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Data Measures

There are many ways to describe the center of a data set. Make sure you know which is which.

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Changing Data Sets

How do modifications to the data sets affect these statistics?

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Determine the Set

Reconstruct the original data from incomplete information.

4. 4

Geometry: Measures

Calculate angle measures, lengths, areas, and volumes.

1. Included with

Diagnostic: Measures

Review your knowledge of geometry and identify areas for growth.

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Diagnostic: Angle Hunting

Finding angles relies on a handful of key ideas; make sure you're familiar with them all.

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Polygon Angle Hunting

Extend your hunt for angles to more complicated, polygonal figures.

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Special Right Triangles

The side ratios in these special right triangles show up again and again on contests!

5. 5

Geometry: Similarity

Stretch, divide, and compare geometric shapes.

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Diagnostic: Similarity

Check your understanding of the key ideas used in similarity problems, and identify areas for growth.

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Scaling

Scale figures in multiple dimensions to answer these questions.

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Exploring Similarity

Leverage your skill with similarity to solve these challenging puzzles.

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Applying Similarity

To solve these problems, look for opportunities to add line segments that will create similar figures.

6. 6

Geometry: Composites

Find familiar shapes in hidden places.

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Diagnostic: Composites

Check your understanding of the fundamental geometric formulas and identify areas for growth.

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Lunes & Leaves

These circle pieces are easiest to work with when they are sliced up.

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Inscribed Figures

Polygons in circle and circles in polygons!

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Ratios Meet Geometry

Connect proportional reasoning from algebra to geometry in order to solve these problems.

7. 7

Combinatorics: Counting

Rearrange, organize, and enumerate the possibilities.

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Diagnostic: Counting

Review these combinatorics problem-solving strategies, and identify areas for growth.

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Venn Diagrams

Use Venn diagrams to think carefully about the properties of sets.

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Branch Diagrams

Learn an essential, organizational technique for counting in many situations.

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Over-Counting

Sometimes the best way to count everything is to count some parts twice and then subtract the extra.

8. 8

Combinatorics: Probability

Develop principles and strategies to calculate probabilities quickly and efficiently.

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Diagnostic: Probability

Review the principles that underlie basic probability, and identify areas for growth.

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Probability by Outcomes

Use the definition of probability to solve these problems by counting.

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PIE and Complements

See what happens when probability intersects with thinking about sets.

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Choosing

Solve these problems that combine counting with probability.

9. 9

Number Theory: Efficiency

Save time on competitions with these techniques for shortening and simplifying problems.

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Diagnostic: Efficiency

Try to solve these problems efficiently, and identify areas for growth in your number theory skills.

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Calculations

Find the fastest (and laziest!) way to solve these problems.

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Exponents

Apply the product and quotient rule to rapidly simplify these exponent questions.

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Roots

Explore a handful of techniques for working with radicals.

10. 10

Number Theory: Factorization

Learn new applications for breaking down numbers into the product of several factors.

1. Included with

Diagnostic: Factorization

Review and apply factorization with these practice problems, and identify areas for growth.

2. Included with

Number of Divisors

What's the best way to determine how many divisors an integer has?

3. Included with