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AMO 2024 Primary 6 (Grade 6)

Question 1

A heart-shaped tangram consists of square ABCD and two semicircles on adjacent sides AB and BC. The marked points on the sides are midpoints. What is the ratio of shaded area to unshaded area?

Question illustration
  1. $\frac{\pi+1}{4}$
  2. $\frac{\pi+1}{3}$
  3. $\frac{2\pi}{3}$
  4. $\frac{3\pi+1}{5}$

Question 2

The Fahrenheit and Celsius scales satisfy $F=\frac95 C+32$. What Celsius temperature corresponds to 86°F?

Question illustration
  1. 27.0°C
  2. 30.0°C
  3. 35.0°C
  4. 36.5°C

Question 3

A sheet of paper is about 0.2 mm thick. If it could be folded in half 20 times, about how thick would the layers be, in metres?

Question illustration
  1. About 10 metres
  2. About 100 metres
  3. About 200 metres
  4. About 500 metres

Question 4

In triangle ABC, $AB=AC$, D lies on AC, $BC=BD$, and $\angle BAC=36^\circ$. Find $\angle DBC$. Clarification: the source omits the name of the 36° angle in its sentence; its diagram and solution identify it as angle BAC.

Question illustration
  1. 45°
  2. 42°
  3. 36°
  4. 30°

Question 5

What is the difference between the median and the mean of $\{2,6,14,26,24,30,20,18,28,32\}$?

Question illustration
  1. 4
  2. 3
  3. 2
  4. 1

Question 6

Lisa draws a ball from ten balls numbered 1 to 10, records its number and replaces it. She repeats this for three draws. Assuming every ball is equally likely on each draw, what is the probability that the three numbers are not all even?

Question illustration
  1. $3/8$
  2. $5/8$
  3. $6/8$
  4. $7/8$

Question 7

Points $A=(3,5)$, $B=(1,1)$ and $C=(4,2)$ form triangle ABC in the coordinate plane. What is its area in square units?

Question illustration
  1. 8.0
  2. 6.5
  3. 5.0
  4. 2.5

Question 8

M is divisible by 16 and N by 27. Let $T=MN$. What is the minimum number of positive factors of T? Clarification: M and N are taken to be positive integers, as intended in the source solution.

Question illustration
  1. 24
  2. 20
  3. 16
  4. 12

Question 9

Which listed number satisfies $5x+2<7x-8$?

Question illustration
  1. -12
  2. 0
  3. 3
  4. 25