The MathCounts Competition Series is one of the most popular middle school math contests in the United States.
It focuses on problem-solving speed and accuracy across algebra, geometry, probability, number theory, and counting.
This post contains 8 practice problems with solutions designed for Grades 6–8 students preparing for MathCounts.
➕ Problem 1 — Fractions
What is 3/4 + 5/6 simplified?
Answer:
Find LCM of 12 → \(9/12 + 10/12 = 19/12 = 1\frac{7}{12}\).
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➗ Problem 2 — Speed/Distance
A car travels 120 miles in 2 hours and 30 minutes. What is its average speed in miles per hour?
Answer:
Time = 2.5 hours → \(120 ÷ 2.5 = 48\) mph.
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📐 Problem 3 — Geometry
The area of a rectangle is 84 square units. If the length is 12, what is the width?
Answer:
Width = \(84 ÷ 12 = 7\).
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🎲 Problem 4 — Probability
A fair die is rolled once. What is the probability of rolling a number greater than 4?
Answer:
Favorable = {5,6} → \(2/6 = 1/3\).
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🔢 Problem 5 — Number Theory
What is the least common multiple (LCM) of 18 and 24?
Answer:
Prime factors: \(18 = 2 × 3^2\), \(24 = 2^3 × 3\).
LCM = \(2^3 × 3^2 = 72\).
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📊 Problem 6 — Algebra
If \(2x + 5 = 17\), what is the value of \(x\)?
Answer:
\(2x = 12 → x = 6\).
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📈 Problem 7 — Sequences
What is the 10th term of the arithmetic sequence: 5, 8, 11, 14, …?
Answer:
d = 3 → \(a_n = 5 + (n-1)×3\).
\(a_{10} = 5 + 9×3 = 32\).
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🧮 Problem 8 — Counting
How many different 3-digit numbers can be formed using the digits {1,2,3,4,5} without repetition?
Answer:
\(5×4×3 = 60\).
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✅ Summary of Answers
- 19/12 or 1 7/12
- 48 mph
- 7
- 1/3
- 72
- 6
- 32
- 60
These MathCounts practice problems cover the key areas of the competition: algebra, geometry, number theory, probability, and counting.
Working through such problems improves both speed and accuracy, which are crucial for success in the MathCounts Sprint and Target Rounds.
Follow TheCareergram.com for more practice problems and solutions from MathCounts, AMC, Science Olympiad, and USACO contests.
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