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IKMC 2025 - Grades 9-10 - Set 2 - Self-study

Question 1

The left and right parts of a three-part brochure each contain four transparent windows. When both parts are folded onto the middle part, some of its numbers are visible through the windows. What is the sum of the visible numbers when the brochure is folded?

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  1. 7
  2. 9
  3. 12
  4. 14
  5. 15

Question 2

The base of a triangle is extended by 50% and its height is reduced by one third. What is the ratio of the area of the new triangle to the area of the original triangle?
  1. 2:1
  2. 1:1
  3. 1:2
  4. 1:3
  5. 1:4

Question 3

In which of the following hexagons is exactly one third of the area black and half of the area white?
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Question 4

Every year, the third Thursday in March is Kangaroo Day. What is the earliest calendar day that can be a Kangaroo Day?
  1. 14/3
  2. 15/3
  3. 20/3
  4. 21/3
  5. 22/3

Question 5

A recipe needs $1\frac12$ cups of water for 1 cup of rice. Rouven wants to use $1\frac12$ cups of rice. How many cups of water does he need?
  1. 1
  2. $1\frac14$
  3. $1\frac34$
  4. $2\frac14$
  5. $2\frac12$

Question 6

Lisa has four wooden digits with which she can make the number 2025. How many different numbers greater than 2025 can she make using these four digits?

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  1. 3
  2. 6
  3. 8
  4. 9
  5. 11

Question 7

Alex folds a square sheet of paper along its diagonal to form a triangle. He then folds it again so that one shorter side lies on the longer side, producing the smaller triangle AXC shown. What is $\angle CXA$?

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  1. 108°
  2. 112.5°
  3. 120°
  4. 145°
  5. 157.5°

Question 8

The four-digit number $\overline{80ab}$ is missing its last two digits. It is divisible by both 8 and 9. What is the product of the two missing digits?
  1. 6
  2. 16
  3. 20
  4. 24
  5. 48

Question 9

Luka has dogs, rabbits and cats as pets. Eight pets are not dogs, five are not rabbits and seven are not cats. How many pets does Luka have?
  1. 10
  2. 11
  3. 15
  4. 16
  5. 20

Question 10

A circle has centre O and radius 10 cm. A square OPQR is drawn inside it so that Q lies on the circle, as shown. What is the area of the grey triangle PQR?

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  1. 12.5 cm²
  2. 25 cm²
  3. 50 cm²
  4. 75 cm²
  5. 100 cm²

Question 11

An athlete has 2 gold medals and 5 silver medals, numbered in some order from 1 to 7. Each of the six black-and-white photographs shows exactly one gold medal. What is the sum of the numbers on the two gold medals?

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  1. 7
  2. 8
  3. 9
  4. 10
  5. 11

Question 12

Anna is looking at a picture on her smartphone. Its format is 16:9 and it fills the entire screen. When she turns the phone, the picture becomes smaller, as shown. What proportion of the screen does the smaller picture occupy?

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  1. $3/4$
  2. $9/16$
  3. $27/64$
  4. $32/81$
  5. $81/256$

Question 13

Kate and Tom both celebrate their birthday today. Tom notices that $1/19$ of Kate’s age equals $1/17$ of his age. Together they are older than 40 years and younger than 100 years. How old is Kate?
  1. 19
  2. 34
  3. 38
  4. 57
  5. 76

Question 14

Paul shoots at the two targets shown a total of 27 times. He hits the upper-left target on 50% of the shots aimed at it and the bottom-right target on 80% of the shots aimed at it. Altogether 9 shots miss their target. How many times does he hit the upper-left target?

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  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 15

Sara has a bag of 18 balls numbered from 1 to 18. What is the smallest number of balls she must remove to be sure that at least three removed balls bear prime numbers?
  1. 11
  2. 12
  3. 13
  4. 14
  5. 15

Question 16

We place the numbers 1 through 8 in the eight squares shown, one per square, so that consecutive numbers are never in adjacent squares, including diagonal adjacency. Which numbers can be written in the square marked X?

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  1. 1 or 8
  2. 2 or 7
  3. 3 or 6
  4. 4 or 5
  5. 7 or 8

Question 17

N is the largest six-digit number whose digits have product 180. What is the sum of the digits of N?
  1. 21
  2. 22
  3. 23
  4. 24
  5. 25

Question 18

The two small rectangles in the diagram are congruent, and each has area 4. What is the area of rectangle ABCD?

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  1. 10
  2. $8\sqrt3$
  3. 8
  4. 12
  5. $4\sqrt3$

Question 19

The product of three prime numbers is 11 times their sum. What is the maximum possible sum of the three primes?
  1. 14
  2. 17
  3. 21
  4. 25
  5. 26

Question 20

Five bricks form the wall shown. Peter may remove a brick only when no other brick is directly above it. At each turn he chooses uniformly at random among the currently removable bricks and removes one. What is the probability that brick 4 is the third brick removed?

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  1. $1/3$
  2. $1/4$
  3. $1/5$
  4. $1/6$
  5. $1/8$