What the MATHCOUNTS Competition looks like
The MATHCOUNTS Competition Series is a math contest for students in grades 6–8. Students who advance go from school to chapter, then state, then the national competition. The individual score comes from two written rounds:
| Round | Format |
|---|---|
| Sprint | 30 problems in 40 minutes, no calculator |
| Target | 8 problems in 4 pairs, 6 minutes per pair, calculator allowed |
| Team | 10 problems in 20 minutes, solved together |
| Countdown | Head-to-head oral round, up to 45 seconds per problem (used at many competitions) |
The individual score is Sprint + 2 × Target, out of 46. Speed matters in the Sprint Round: 30 problems in 40 minutes is about 80 seconds each. Rules change from year to year, so check the official MATHCOUNTS site for the current format.
How to practice for MATHCOUNTS with Mathyessy
Mathyessy is a free practice site built for this kind of contest. It isn't an official MATHCOUNTS product. Here's what it includes:
- Contest Trainer: an adaptive trainer that moves through three stages of increasing difficulty and adjusts to your answers.
- 122 topic sets across algebra, geometry, counting & probability and number theory.
- 60-second speed rounds for quick, accurate answers under time pressure.
- An 8-question diagnostic that points out which topics to work on.
- A 10-question, 15-minute mini mock exam.
- Mistake review, a daily challenge and a leaderboard.
The app also links to past MATHCOUNTS® chapter and state competition papers that are publicly posted online, so you can practise under real timing.
Plan: take the diagnostic, drill your two weakest topics, do a speed round every day for Sprint pace, and finish each week with a mock exam. Then go through every mistake.
Sample MATHCOUNTS-style practice problems
These are original Mathyessy problems in the style of Sprint and Target questions. They are not official MATHCOUNTS problems.
Six books are arranged in a row. Two specific books must NOT be next to each other. How many arrangements are possible?
Show answer and solution
Answer: 480
All arrangements: 6! = 720. Arrangements with the two books together: glue them into one block, giving 5! × 2 = 240. So 720 − 240 = 480 keep them apart.
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How many positive divisors does 360 have?
Show answer and solution
Answer: 24
360 = 2³ × 3² × 5, so it has (3 + 1)(2 + 1)(1 + 1) = 24 divisors.
More like this: Counting divisors practice
A rhombus has diagonals 10 and 24. Find its perimeter.
Show answer and solution
Answer: 52
The diagonals of a rhombus bisect each other at right angles, so each side is the hypotenuse of a right triangle with legs 10 ÷ 2 = 5 and 24 ÷ 2 = 12. Each side is √(25 + 144) = 13, so the perimeter is 4 × 13 = 52.
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A car drives equal distances at 30 mph and 50 mph. Average speed?
Show answer and solution
Answer: 37.5 mph
Pick a distance of 150 miles each way. Time: 150/30 + 150/50 = 5 + 3 = 8 hours for 300 miles, so 300 ÷ 8 = 37.5 mph. (Formula: 2 × 30 × 50 ÷ 80 = 37.5.)
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How many 3 digit numbers from 100 to 999 have at least one even digit?
Show answer and solution
Answer: 775
Count the opposite: numbers with all odd digits. Each of the three digits has 5 odd choices, giving 5 × 5 × 5 = 125. There are 900 three-digit numbers, so 900 − 125 = 775.
More like this: Complementary counting practice
If xy+3x+4y = 24, what is (x+4)(y+3)?
Show answer and solution
Answer: 36
(x + 4)(y + 3) = xy + 3x + 4y + 12 = 24 + 12 = 36.
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