Math Kangaroo practice test, grades 9–10

10 free Math Kangaroo practice questions at Grades 9–10, with answers. 178 questions in the full bank, covering 15 topics.

Free now

10

Full bank

178

Topics

15

10 free practice questions

Pick an answer to check it. No account needed. These are past competition tasks — the answer is shown with its source paper.

1. Question 1arithmetic

   When the results of the following additions are written in descending order, what sum will be in the middle?

   • A$1 + 2 + 345$
   • B$12 + 3 + 45$
   • C$1 + 23 + 45$
   • D$12 + 34 + 5$
   • E$1 + 234 + 5$
   Show answer and source

   Answer: C

   Source: Math Kangaroo 2020 Level 9-10 Task 1

2. Question 2combinatorics

   Ahmad walks up 8 steps going up either 1 or 2 steps at a time. There is a hole on the 6th step, so he cannot use this step. In how many different ways can Ahmad reach the top step?

   • A6
   • B7
   • C8
   • D9
   • E10
   Show answer and source

   Answer: C

   Source: Math Kangaroo 2021 Level 9-10 Task 12

3. Question 3coordinate geometry

   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?

   • A2:1
   • B1:1
   • C1:2
   • D1:3
   • E1:4
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2025 Level 9-10 Task 2

4. Question 4fractions

   Olga was walking in the park. For half the time, she walked with a speed of $2\text{ km/h}$. For half the distance, she walked with a speed of $3\text{ km/h}$. For the remaining time, she walked with a speed of $4\text{ km/h}$. Which fraction of the time did she walk with $4\text{ km/h}$?

   • A$\frac{1}{14}$
   • B$\frac{1}{12}$
   • C$\frac{1}{7}$
   • D$\frac{1}{5}$
   • E$\frac{1}{4}$
   Show answer and source

   Answer: A

   Source: Math Kangaroo 2024 Level 9-10 Task 28

5. Question 5geometry

   Ally drew 3 triangles on a grid. Exactly 2 of them have the same area, exactly 2 of them are isosceles, and exactly 2 are right-angled triangles. 2 of the triangles are shown. Which could be the third one?

   
   • A
   • B
   • C
   • D
   • E
   Show answer and source

   Answer: D

   Source: Math Kangaroo 2021 Level 9-10 Task 9

6. Question 6logic

   Who is the mother of the daughter of the mother of Lia's daughter?

   • ALia's sister.
   • BLia.
   • CLia's mother.
   • DLia's niece.
   • ELia's aunt.
   Show answer and source

   Answer: D

   Source: Math Kangaroo 2020 Level 9-10 Task 2

7. Question 7number theory

   The figures for the year 2020 are repeated twice each and are different. How many times does this happen since the year 1000 until now?

   • A11
   • B17
   • C20
   • D24
   • E29
   Show answer and source

   Answer: E

   Source: Math Kangaroo 2020 Level 9-10 Task 7

8. Question 8percentages

   There are 5 people to choose from on a ballot paper. After counting 90 % of the votes the intermediate result looks as shown in the table. How many of the 5 people cannot win the election anymore?

   
   • A1
   • B2
   • C3
   • D4
   • E5
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2022 Level 9-10 Task 10

9. Question 9probability

   Five bricks form a wall (see figure). Peter can only remove a brick if there is no other brick directly above it. On each turn, he randomly selects one of the removable bricks with equal probability and removes it. What is the probability that the brick numbered 4 is the third to be removed?

   
   • A$\frac{1}{3}$
   • B$\frac{1}{4}$
   • C$\frac{1}{5}$
   • D$\frac{1}{6}$
   • E$\frac{1}{8}$
   Show answer and source

   Answer: D

   Source: Math Kangaroo 2025 Level 9-10 Task 19

10. Question 10ratios

    Vlado has participated in 31 cross-country races in the last five years. In the first year, he participated in the smallest number of races and he then successively increased the number of races each year. In the fifth year, he participated in three times as many races as in the first year. How many races did he participate in in the fourth year?

    • A6
    • B7
    • C8
    • D9
    • E10
    Show answer and source

    Answer: C

    Source: Math Kangaroo 2024 Level 9-10 Task 20