These essential MCQ questions are selected from the most important topics in Math Olympiad examinations 2026. Sections include Number Theory, Algebra, Geometry, Combinatorics and Logical Mathematics for IMO, RMO and school-level Olympiad preparation. For truely unlimited daily MCQ practice, visit Vooo AI Education.
🏆 Math Olympiad
1How many prime numbers are between 1 and 20?
Answer: C — 8
The prime numbers between 1 and 20 are: 2, 3, 5, 7, 11, 13, 17, 19 — a total of 8 primes. Remember: 1 is NOT a prime number as it has only one factor (itself).
The prime numbers between 1 and 20 are: 2, 3, 5, 7, 11, 13, 17, 19 — a total of 8 primes. Remember: 1 is NOT a prime number as it has only one factor (itself).
2What is the sum of first 10 natural numbers?
Answer: C — 55
Sum of first n natural numbers = n(n+1)/2. For n=10: 10×11/2 = 55. This formula is attributed to Gauss who discovered it as a child by pairing numbers: 1+10=11, 2+9=11, etc., giving 5×11=55.
Sum of first n natural numbers = n(n+1)/2. For n=10: 10×11/2 = 55. This formula is attributed to Gauss who discovered it as a child by pairing numbers: 1+10=11, 2+9=11, etc., giving 5×11=55.
3If 2x − 3 = 11, what is x?
Answer: C — 7
2x − 3 = 11 → 2x = 11 + 3 = 14 → x = 14/2 = 7. Always verify: 2(7) − 3 = 14 − 3 = 11 ✓. Linear equations are solved by isolating the variable using inverse operations.
2x − 3 = 11 → 2x = 11 + 3 = 14 → x = 14/2 = 7. Always verify: 2(7) − 3 = 14 − 3 = 11 ✓. Linear equations are solved by isolating the variable using inverse operations.
4A square has perimeter 32 cm. Its area is:
Answer: C — 64 cm²
Perimeter of square = 4 × side. So side = 32/4 = 8 cm. Area = side² = 8² = 64 cm². For any square, if perimeter is P then area = (P/4)².
Perimeter of square = 4 × side. So side = 32/4 = 8 cm. Area = side² = 8² = 64 cm². For any square, if perimeter is P then area = (P/4)².
5The HCF of 24 and 36 is:
Answer: C — 12
Using prime factorisation: 24 = 2³×3 and 36 = 2²×3². HCF = 2²×3 = 12. The HCF (Highest Common Factor) is the largest number that divides both numbers exactly without remainder.
Using prime factorisation: 24 = 2³×3 and 36 = 2²×3². HCF = 2²×3 = 12. The HCF (Highest Common Factor) is the largest number that divides both numbers exactly without remainder.
6How many diagonals does a hexagon have?
Answer: D — 9
Number of diagonals in a polygon = n(n−3)/2, where n = number of sides. For hexagon (n=6): 6(6−3)/2 = 6×3/2 = 9 diagonals. A hexagon has 6 vertices and 6 sides.
Number of diagonals in a polygon = n(n−3)/2, where n = number of sides. For hexagon (n=6): 6(6−3)/2 = 6×3/2 = 9 diagonals. A hexagon has 6 vertices and 6 sides.
7What is 2⁸?
Answer: B — 256
2⁸ = 2×2×2×2×2×2×2×2 = 256. Powers of 2 are fundamental in mathematics and computer science: 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁵=32, 2⁶=64, 2⁷=128, 2⁸=256.
2⁸ = 2×2×2×2×2×2×2×2 = 256. Powers of 2 are fundamental in mathematics and computer science: 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁵=32, 2⁶=64, 2⁷=128, 2⁸=256.
8In how many ways can 3 books be arranged?
Answer: B — 6
The number of arrangements of n distinct objects = n! (n factorial). 3! = 3×2×1 = 6. The 6 arrangements of books A, B, C are: ABC, ACB, BAC, BCA, CAB, CBA.
The number of arrangements of n distinct objects = n! (n factorial). 3! = 3×2×1 = 6. The 6 arrangements of books A, B, C are: ABC, ACB, BAC, BCA, CAB, CBA.
9The value of (a + b)² is:
Answer: C — a² + 2ab + b²
(a + b)² = (a + b)(a + b) = a² + ab + ab + b² = a² + 2ab + b². This is one of the most important algebraic identities. Similarly (a−b)² = a² − 2ab + b².
(a + b)² = (a + b)(a + b) = a² + ab + ab + b² = a² + 2ab + b². This is one of the most important algebraic identities. Similarly (a−b)² = a² − 2ab + b².
10A number is divisible by 9 if:
Answer: B — Sum of digits divisible by 9
Divisibility rule for 9: if the sum of all digits of a number is divisible by 9, then the number itself is divisible by 9. Example: 729 → 7+2+9=18, 18÷9=2 ✓. Same rule applies for divisibility by 3.
Divisibility rule for 9: if the sum of all digits of a number is divisible by 9, then the number itself is divisible by 9. Example: 729 → 7+2+9=18, 18÷9=2 ✓. Same rule applies for divisibility by 3.
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