Confidence Builders: Difficulty Level 1

Confidence Builders (Difficulty Level 1) problems are typically used at the beginning of competition sets. They are accessible to any student with knowledge of the subject area.

Confidence Builders (Difficulty Level 1) Math Competition Problems

The problems on this page are Difficulty Level 1 problems written by Douglas Twitchell. These problems are confidence builders. Most math competitions have a few problems that the average student can solve readily with knowledge of the subject area. Brief (not complete) solutions are shown in green, leaving the reader to work through the logic.

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1.1
In a triangle, the measures of the angles are x, 3x, and 5x. What is the measure of the largest angle?

For a student with basic subject knowledge in geometry, this is a simple algebraic equation. Answer is 100 degrees

1.2
Solve for x if 2x - 5 < 11 and x + 3 < 20

Combining two inequalities with 'and'. The answer is x>8 and x<17.

1.3
If a number is added to one more than that number, and then one less than the original number is subtracted from the sum, the result is 21. What is the original number?

Algebraically, this problem is easy to set up and solve. The biggest challenge is interpreting the wording of the problem. Answer: 19