Math Kangaroo practice test, grades 11–12

10 free Math Kangaroo practice questions at Grades 11–12, with answers. 178 questions in the full bank, covering 17 topics.

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10 free practice questions

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1. Question 1algebra

   Which of the following expressions has the same value as $16^{15} + 16^{15} + 16^{15} + 16^{15}$?

   • A$4^{31}$
   • B$4^{38}$
   • C$4^{60}$
   • D$4^{120}$
   • E$4^{122}$
   Show answer and source

   Answer: A

   Source: Math Kangaroo 2024 Level 11-12 Task 7

2. Question 2arithmetic

   Noah starts with the number 1 and multiplies it with either 6 or 10. He then multiplies the result again by either 6 or 10. He repeats this process several times. Which of the following numbers can he **not** obtain in this way?

   • A$2^{100} \cdot 3^{20} \cdot 5^{80}$
   • B$2^{90} \cdot 3^{30} \cdot 5^{80}$
   • C$2^{90} \cdot 3^{20} \cdot 5^{70}$
   • D$2^{110} \cdot 3^{80} \cdot 5^{30}$
   • E$2^{50} \cdot 5^{50}$
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2024 Level 11-12 Task 9

3. Question 3combinatorics

   23 animals are sitting in the first row of a cinema. Each animal is either a beaver or a kangaroo. Each animal has at least one kangaroo next to it. What is the maximum amount of beavers in the row?

   • A7
   • B8
   • C10
   • D11
   • E12
   Show answer and source

   Answer: D

   Source: Math Kangaroo 2023 Level 11-12 Task 9

4. Question 4coordinate geometry

   How many three-digit natural numbers have the property that when their digits are written in reverse order, the result is a three-digit number which is 99 more than the original number?

   • A8
   • B64
   • C72
   • D80
   • E81
   Show answer and source

   Answer: D

   Source: Math Kangaroo 2021 Level 11-12 Task 13

5. Question 5fractions

   What is the simplified representation of the following fraction? $\frac{7777^2}{5555 \cdot 2222}$

   • A1
   • B$\frac{7}{10}$
   • C$\frac{49}{10}$
   • D$\frac{49}{100}$
   • E49
   Show answer and source

   Answer: C

   Source: Math Kangaroo 2023 Level 11-12 Task 1

6. Question 6functions

   Let $x = \frac{\pi}{4}$. Which of the following numbers is the largest?

   • A$x^4$
   • B$x^2$
   • C$x$
   • D$\sqrt{x}$
   • E$\sqrt[4]{x}$
   Show answer and source

   Answer: E

   Source: Math Kangaroo 2021 Level 11-12 Task 7

7. Question 7geometry

   A tile pattern is made up of a number of identical irregular pentagons. Which of the following tiles fits into the hole in such a way that a closed curve is formed?

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

   Answer: C

   Source: Math Kangaroo 2024 Level 11-12 Task 2

8. Question 8logic

   Three square Martians and three round Jupiterians are sitting at a table as shown. One of the six has the key to the spaceship. Everyone from one planet always tells the truth, and everyone from the other planet always lies. When asked "Does any of your neighbours have the key?" all six answer as shown. Who has the key?

   
   • AA
   • BB
   • CC
   • DD
   • EE
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2025 Level 11-12 Task 19

9. Question 9number theory

   How many positive three-digit numbers are divisible by 13?

   • A68
   • B69
   • C70
   • D76
   • E77
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2022 Level 11-12 Task 2

10. Question 10percentages

    Silvia's favourite chocolate bars are sold in packets. There used to be five bars in each packet. Now there are only four in each packet, but the packets still cost the same. By how many percent has each bar become more expensive?

    • Aby 10%
    • Bby 20%
    • Cby 25%
    • Dby 30%
    • Eby 50%
    Show answer and source

    Answer: C

    Source: Math Kangaroo 2025 Level 11-12 Task 8