Euclid Contest 2024 - Study Guide

2024 Euclid Contest Study Guide

Tip

This contest was written on April 3-4, 2024. Each question is worth 10 marks. Take your time and show your work!

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• Problem 1

  Substitution, Pythagorean theorem, fractions
• Problem 2

  Sequences - arithmetic and geometric
• Problem 3

  Quadratics, sales tax, recursive functions
• Problem 4

  Geometry with perpendiculars, coordinate geometry areas
• Problem 5

  Rectangle area ratios, parabola x-intercepts
• Problem 6

  Counting multiples, set membership (clubs)
• Problem 7

  Circular track meeting problems, trigonometric equations
• Problem 8

  Circle tangent geometry, logarithmic systems
• Problem 9

  Combinatorics - ant walks on number line
• Problem 10

  Geometry - partitioning triangles into equal areas

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Problem 1

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Problem 2

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Problem 3

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Problem 4

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Problem 5

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Problem 6

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Problem 7

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Problem 8

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Problem 9

An ant walks along the -axis taking steps of length 1 (positive or negative direction), starting at , taking steps total, ending at . Let be the number of direction changes.

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Problem 10

Points , , form . Points and lie on . Point lies on and on . Line segments and intersect at and partition into four regions. A pair is a “balancing pair” if the four regions have equal area.

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Key Topics Covered