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AMO 2025 Primary 5 (Grade 5)

Question 1

Quadrilateral $ABCD$ is drawn on a $10\times10$ grid of unit squares. What is its area in square units?

Question illustration
  1. 18.5 square units
  2. 17.5 square units
  3. 15.0 square units
  4. 12.5 square units

Question 2

A number machine adds 30 to its input, takes one-fifth of the result, then divides by 3. Its output is 4. What was the input?

Question illustration
  1. 40
  2. 30
  3. 20
  4. 15

Question 3

Two identical squares are placed as shown. One is upright; the other is turned 45° with its top vertex at the centre of the first. Each has area 120 square inches. Find the shaded area in square inches.

Question illustration
  1. 100 square inches
  2. 90 square inches
  3. 80 square inches
  4. 75 square inches

Question 4

Mrs. Smith chooses five of seven math-club students for an event. How many different five-person teams can she choose?

Question illustration
  1. 42
  2. 35
  3. 21
  4. 16

Question 5

Ten numbers have average 12. Replacing one number by 5 changes the average to 10. What was that number originally?

Question illustration
  1. 30
  2. 25
  3. 20
  4. 15

Question 6

A caterpillar moves horizontally or vertically along $A(2,2),B(2,7),C(5,7),D(5,5),E(7,5),F(7,3),G(3,3),H(3,2),A(2,2)$ in that order. How many units does it travel?

Question illustration
  1. 16
  2. 18
  3. 20
  4. 24

Question 7

Sandra has 200 marbles. She uses 1 marble for the first pattern, 3 for the second, 5 for the third, and so on. How many complete steps can she make? The marbles used in earlier steps are not reused.

Question illustration
  1. 16
  2. 14
  3. 12
  4. 11

Question 8

Evaluate $5\times(\frac13+\frac14+\frac15+\frac17+\frac1{20}+\frac1{42})\times20$.

Question illustration
  1. 75
  2. 84
  3. 100
  4. 120

Question 9

An integer $N$ lies between 1 and 100. It leaves remainder 1 when divided by 2 and remainder 5 when divided by 8. What is its largest possible value?

Question illustration
  1. 95
  2. 93
  3. 91
  4. 89