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MATHEMATICS · GYSO 2027

Sample Questions

Explore selected questions from completed competition papers and become familiar with the level, format, and style of mathematical reasoning expected in each division.

PRACTICE COLLECTION

Choose your division.
Test your reasoning.

Each question has one correct answer. The point label indicates the original difficulty value: easy questions are worth 1 point, medium questions 2 points, and hard questions 3 points.

These are selected questions from completed DMO 2026 papers published with the GYSO 2027 Mathematics syllabus. They are provided for practice and do not reveal a live examination.

01

Numerical foundations

Elementary School

8 selected questions
Question 01Order of operations1 point

Evaluate 7 + 3 × 15 ÷ 5 − 10.

  1. A5
  2. B6
  3. C18
  4. D20
Reveal answer +

B — 6

Question 02Linear equations1 point

The difference of two integers is 3 and their product is 6. What is the sum of their squares?

  1. A18
  2. B21
  3. C54
  4. D108
Reveal answer +

B — 21

Question 03Backward reasoning3 points

A bookshop begins with one box of textbooks. Half the books plus 3 are sold on day one; half the remainder plus 6 on day two; then half of what remains, less 2 books, on day three. If 11 books remain, how many were there at first?

  1. A98
  2. B102
  3. C110
  4. D128
Reveal answer +

B — 102

Question 04Powers1 point

Find the value of 29² − 25² + 11².

  1. A337
  2. B373
  3. C377
  4. D733
Reveal answer +

A — 337

Question 05Number patterns2 points

What is the difference between the sum of the first 2024 positive even numbers and the sum of the first 2024 positive odd numbers?

  1. A0
  2. B1
  3. C1012
  4. D2024
Reveal answer +

D — 2024

Question 06Prime numbers2 points

If a, b, and c are prime numbers and a = 7(b − c), what is a + b + c?

  1. A11
  2. B12
  3. C23
  4. D27
Reveal answer +

B — 12

Question 07Factors1 point

How many positive factors does 2024 have?

  1. A8
  2. B12
  3. C16
  4. D24
Reveal answer +

C — 16

Question 08Counting1 point

A sentence is formed by choosing one of 8 nouns, one of 6 verbs, and one of 3 adjectives. How many different sentences can be formed?

  1. A144
  2. B108
  3. C64
  4. D48
Reveal answer +

A — 144

02

Connected reasoning

Junior High School

8 selected questions
Question 01Equations1 point

How many real solutions does x²⁰²⁴ − x²⁰²¹ = x²⁰²³ − x²⁰²⁰ have?

  1. A0
  2. B1
  3. C2
  4. D3
  5. E4
Reveal answer +

C — 2

Question 02Rational functions1 point

For real p, let q = 4p ÷ (p² + 2p + 4). What is the minimum possible value of q?

  1. A−4
  2. B−2
  3. C−1
  4. D0
  5. E1
Reveal answer +

B — −2

Question 03Quadratic equations1 point

One root of (b + 1)x² + (b − 3)x − (b + 5) = 0 is −2. What is the other root?

  1. A−3
  2. B−1
  3. C0
  4. D1
  5. E2
Reveal answer +

C — 0

Question 04Exponents1 point

Let x be the sum of ten copies of 3¹⁰. What is x ÷ 3⁹?

  1. A3¹⁰
  2. B3¹¹
  3. C30
  4. D900
  5. E3⁹
Reveal answer +

C — 30

Question 05Triangle inequality1 point

Two sides of a triangle are 50 and 60. Which length cannot be the third side?

  1. A120
  2. B100
  3. C85
  4. D70
  5. E65
Reveal answer +

A — 120

Question 06Probability2 points

In a class of 35 students, 22 like art, 19 like music, and 8 like both. What is the probability that a randomly chosen student likes neither activity?

  1. A2/35
  2. B3/35
  3. C4/35
  4. D5/35
  5. E6/35
Reveal answer +

A — 2/35

Question 07Divisibility2 points

What is the greatest integer n for which 44⁴⁴ is divisible by 8ⁿ?

  1. A27
  2. B28
  3. C29
  4. D30
  5. E31
Reveal answer +

C — 29

Question 08Digit reasoning3 points

The six-digit number 14X147Y is divisible by 12. What is the minimum possible value of X + Y?

  1. A1
  2. B4
  3. C7
  4. D10
  5. E13
Reveal answer +

C — 7

03

Olympiad depth

Senior High School

8 selected questions
Question 01Inequalities2 points

For positive a, b, and c, what is the minimum value of a/(b + c) + b/c + c/a?

  1. A1
  2. B2
  3. C2.5
  4. D6
  5. E9
Reveal answer +

C — 2.5

Question 02Integer equations3 points

Let a, b, c, d, and e be natural numbers satisfying abcde = a + b + c + d + e. What is the largest possible value among them?

  1. A1
  2. B2
  3. C3
  4. D5
  5. E9
Reveal answer +

D — 5

Question 03Polynomials2 points

The polynomial x³ − ax² + bx − 2024 has three distinct positive integer roots. What is the greatest possible value of a?

  1. A1012
  2. B1013
  3. C1014
  4. D1015
  5. E2111
Reveal answer +

D — 1015

Question 04Optimisation3 points

A cost model is C(x) = 4x + 100/x + 40 million units for x > 0. What is the minimum cost?

  1. A75 million
  2. B80 million
  3. C90 million
  4. D120 million
  5. E145 million
Reveal answer +

B — 80 million

Question 05Trigonometry2 points

If (1 + tan 1°)(1 + tan 2°) … (1 + tan 45°) = 2ⁿ, find n.

  1. A22
  2. B23
  3. C44
  4. D45
  5. E99
Reveal answer +

B — 23

Question 06Combinatorics2 points

How many 3-element subsets of {1, 2, …, 20} have a sum divisible by 3?

  1. A294
  2. B400
  3. C624
  4. D2280
  5. EOther
Reveal answer +

E — Other

Question 07Exponential equations1 point

Solve 2ˣ⁺¹ = 8ˣ⁻¹.

  1. A0
  2. B2
  3. C1
  4. D3
  5. E4
Reveal answer +

B — 2

Question 08Factorials2 points

How many trailing zeros does 99! have?

  1. A9
  2. B11
  3. C22
  4. D99
  5. E999
Reveal answer +

C — 22

CONTINUE PREPARING

Review the complete Mathematics syllabus.

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