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Brilliant

Contest Math I

via Brilliant

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Overview

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.

Syllabus

  • Introduction: Do you like solving challenging math puzzles?
    • Algebra: Learn to search for algebraic strategies that minimize the work you need to do.
    • Geometry: Rotate, stretch, combine, and break apart pieces of the figures in these challenges.
    • Combinatorics: Learn casework and counting strategies that can be applied to many areas of math including probability.
    • Number Theory: Explore the relationships between prime and composite numbers and the rules for determining divisibility.
    • Math Requires Creativity: There are many ways to solve each puzzle! Stretch your mental muscles and come up with a unique approach.
  • Algebra: Equations: Calculate the value of unknowns quickly and efficiently.
    • Diagnostic: Ratios and Percentages: Check your knowledge of ratios and percentages and identify areas for growth.
    • Diagnostic: Simple Equations: Review these essential techniques for keeping equations in balance and isolating variables.
    • Sequences and Series: Find the pattern, extend the pattern, and add them all up in these questions about sequences.
    • Equations with Ratios: Learn some counter-intuitive tricks for working with ratio equations to avoid making them harder.
    • Non-numeric Geometric Ratios: How can you work with ratios when the numerical values are unknown?
    • Equations Practice Quiz 1: Put your knowledge to the test with these equation practice questions.
    • Equations Practice Quiz 2: Put your knowledge to the test with these equation practice questions.
  • Algebra: Data: Measure data that is static and in fluctuation.
    • Diagnostic: Data: Check your knowledge of data and statistics and identify areas for growth.
    • Data Measures: There are many ways to describe the center of a data set. Make sure you know which is which.
    • Changing Data Sets: How do modifications to the data sets affect these statistics?
    • Determine the Set: Reconstruct the original data from incomplete information.
    • Multiple Possibilities: Determine what values satisfy each of these circumstances.
    • Data Practice 1: Put your knowledge to the test with these data practice questions.
    • Data Practice Quiz 2: Put your knowledge to the test with these data practice questions.
  • Geometry: Measures: Calculate angle measures, lengths, areas, and volumes.
    • Diagnostic: Measures: Review your knowledge of geometry and identify areas for growth.
    • Diagnostic: Angle Hunting: Finding angles relies on a handful of key ideas; make sure you're familiar with them all.
    • Polygon Angle Hunting: Extend your hunt for angles to more complicated, polygonal figures.
    • Special Right Triangles: The side ratios in these special right triangles show up again and again on contests!
    • Creating Right Triangles: Add lines to figures to turn tricky puzzles into right triangle problems that you can solve quickly!
    • Measures Practice Quiz 1: Put your knowledge to the test with these geometry practice questions.
    • Measures Practice Quiz 2: Put your knowledge to the test with these geometry practice questions.
  • Geometry: Similarity: Stretch, divide, and compare geometric shapes.
    • Diagnostic: Similarity: Check your understanding of the key ideas used in similarity problems, and identify areas for growth.
    • Scaling: Scale figures in multiple dimensions to answer these questions.
    • Exploring Similarity: Leverage your skill with similarity to solve these challenging puzzles.
    • Applying Similarity: To solve these problems, look for opportunities to add line segments that will create similar figures.
    • Coordinate Geometry: Connect your algebra and geometry skills by putting geometric figures on a coordinate plane.
    • Similarity Practice Quiz 1: Put your knowledge to the test with these similarity practice questions.
    • Similarity Practice Quiz 2: Put your knowledge to the test with these similarity practice questions.
  • Geometry: Composites: Find familiar shapes in hidden places.
    • Diagnostic: Composites: Check your understanding of the fundamental geometric formulas and identify areas for growth.
    • Lunes & Leaves: These circle pieces are easiest to work with when they are sliced up.
    • Inscribed Figures: Polygons in circle and circles in polygons!
    • Ratios Meet Geometry: Connect proportional reasoning from algebra to geometry in order to solve these problems.
    • Working in 3D: Deepen your intuition and extend your thinking into the third dimension.
    • Composites Practice Quiz 1: Put your knowledge to the test with these composite practice questions.
    • Composites Practice Quiz 2: Put your knowledge to the test with these composite practice questions.
  • Combinatorics: Counting: Rearrange, organize, and enumerate the possibilities.
    • Diagnostic: Counting: Review these combinatorics problem-solving strategies, and identify areas for growth.
    • Venn Diagrams: Use Venn diagrams to think carefully about the properties of sets.
    • Branch Diagrams: Learn an essential, organizational technique for counting in many situations.
    • Over-Counting: Sometimes the best way to count everything is to count some parts twice and then subtract the extra.
    • Symmetry: Counting is easiest when you can avoid it; look for ways to shortcut these problems with symmetry.
    • Counting Practice Quiz 1: Put your knowledge to the test with these counting practice questions.
    • Counting Practice Quiz 2: Put your knowledge to the test with these counting practice questions.
  • Combinatorics: Probability: Develop principles and strategies to calculate probabilities quickly and efficiently.
    • Diagnostic: Probability: Review the principles that underlie basic probability, and identify areas for growth.
    • Probability by Outcomes: Use the definition of probability to solve these problems by counting.
    • PIE and Complements: See what happens when probability intersects with thinking about sets.
    • Choosing: Solve these problems that combine counting with probability.
    • Symmetry and Conditional: Symmetry can be just as useful in probability as it is in counting.
    • Probability Practice Quiz 1: Put your knowledge to the test with these probability practice questions.
    • Probability Practice Quiz 2: Put your knowledge to the test with these probability practice questions.
  • Number Theory: Efficiency: Save time on competitions with these techniques for shortening and simplifying problems.
    • Diagnostic: Efficiency: Try to solve these problems efficiently, and identify areas for growth in your number theory skills.
    • Calculations: Find the fastest (and laziest!) way to solve these problems.
    • Exponents: Apply the product and quotient rule to rapidly simplify these exponent questions.
    • Roots: Explore a handful of techniques for working with radicals.
    • What's the Number?: These cryptogram puzzles will put your understanding of arithmetic into practice!
    • Efficiency Practice Quiz 1: Put your knowledge to the test with these arithmetic efficiency practice questions.
    • Efficiency Practice Quiz 2: Put your knowledge to the test with these arithmetic efficiency practice questions.
  • Number Theory: Factorization: Learn new applications for breaking down numbers into the product of several factors.
    • Diagnostic: Factorization: Review and apply factorization with these practice problems, and identify areas for growth.
    • Number of Divisors: What's the best way to determine how many divisors an integer has?
    • GCD and LCM: Use the prime factorization of integers to work with greatest common divisor and least common multiple.
    • Factorials: Work with these gigantic values without calculating them out fully.
    • Cryptograms: Apply divisibility rules and careful thinking to solve these cryptograms.
    • Factorization Practice Quiz 1: Put your knowledge to the test with these factorization practice questions.
    • Factorization Practice Quiz 2: Put your knowledge to the test with these factorization practice questions.

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