Math Kangaroo practice test, grades 5–6

10 free Math Kangaroo practice questions at Grades 5–6, with answers. 152 questions in the full bank, covering 11 topics.

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152

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11

10 free practice questions

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1. Question 1arithmetic

   Eva paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in an anti-clockwise direction?

   
   • A1 and 4
   • B2, 3 and 5
   • C2 and 3
   • D1, 4 and 5
   • E1 and 3
   Show answer and source

   Answer: E

   Source: Math Kangaroo 2022 Level 5-6 Task 2

2. Question 2combinatorics

   Vera has built a tower of cubes. She wants to replace the two cubes with question marks with cubes with numbers. Vera wants the number on each cube to be at least 2 higher than the number on the cube below it. How many ways can she replace the two cubes?

   
   • A3
   • B4
   • C5
   • D6
   • E7
   Show answer and source

   Answer: D

   Source: Math Kangaroo 2025 Level 5-6 Task 10

3. Question 3geometry

   Pia writes a number into each of the 16 little circles (see picture). Numbers in neighbouring circles differ by 1. She writes the number 5 into one of the circles and the number 13 into another one. How many different numbers does Pia write in the 16 circles?

   
   • A9
   • B10
   • C13
   • D14
   • E16
   Show answer and source

   Answer: A

   Source: Math Kangaroo 2024 Level 5-6 Task 9

4. Question 4logic

   Six children were running a race. Ariadne finished third. Bill finished sixth, just behind Ernest. Fatima finished between Ariadne and Ernest. Diana overtook Charles just before the finish line. Who won the race?

   • AAriadne
   • BCharles
   • CDiana
   • DErnest
   • EFatima
   Show answer and source

   Answer: C

   Source: Math Kangaroo 2025 Level 5-6 Task 7

5. Question 5number theory

   Bodil lays these seven cards 4, 69, 113, 9, 51, 5, 67 next to each other, so that the smallest possible 12-digit number which can be made from these cards is formed. What are the last three digits of this number?

   • A699
   • B113
   • C551
   • D967
   • E459
   Show answer and source

   Answer: A

   Source: Math Kangaroo 2022 Level 5-6 Task 7

6. Question 6probability

   Simon has four cups with matching saucers (see picture). He places a randomly chosen cup on each saucer. Which statement is definitely true?

   
   • AIt is certain that none of the 4 cups are on the matching saucer.
   • BIt is certain that exactly one cup is on the matching saucer.
   • CIt is impossible that exactly 2 cups are on the matching saucers.
   • DIt is impossible that exactly 3 cups are on the matching saucers.
   • EIt is impossible that all 4 cups are on the matching saucers.
   Show answer and source

   Answer: D

   Source: Math Kangaroo 2024 Level 5-6 Task 14

7. Question 7ratios

   Carin is going to paint the walls in her room green. The green paint is too dark, so she mixes it with white paint. She tries different mixtures. Which of the following mixtures will give the darkest green colour?

   • A1 part green + 3 parts white
   • B2 parts green + 6 parts white
   • C3 parts green + 9 parts white
   • D4 parts green + 12 parts white
   • EThey will all be equally dark
   Show answer and source

   Answer: E

   Source: Math Kangaroo 2021 Level 5-6 Task 8

8. Question 8solid geometry

   The picture on the right is 45 cm wide, 30 cm high and made up of identical rectangles. What is the area of one such rectangle?

   
   • A24 cm$^2$
   • B27 cm$^2$
   • C30 cm$^2$
   • D33 cm$^2$
   • E36 cm$^2$
   Show answer and source

   Answer: E

   Source: Math Kangaroo 2024 Level 5-6 Task 10

9. Question 9statistics

   The diagram shows 3 hexagons with numbers at their vertices, but some numbers are invisible. The sum of the 6 numbers around each hexagon is 30. What is the number on the vertex marked with a question mark?

   
   • A3
   • B4
   • C5
   • D6
   • E7
   Show answer and source

   Answer: B

   Source: Math Kangaroo 2021 Level 5-6 Task 14

10. Question 10unclassified

    Which of the pieces shown completes the pattern?

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

    Answer: C

    Source: Math Kangaroo 2025 Level 5-6 Task 1