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.

Interactive
quizzes

68

Concepts and
exercises

815+
  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.

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      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.

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      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.

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      Diagnostic: Factorization

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

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      Number of Divisors

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

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      GCD and LCM

      Use the prime factorization of integers to work with greatest common divisor and least common multiple.

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      Factorials

      Work with these gigantic values without calculating them out fully.