JKJunior Kangaroo Practice

UKMT Junior Kangaroo

Past papers from 2023–2025, grouped by topic. Pick a question to read it, work it out, and reveal the official solution. A math tutor is one click away if you get stuck.

Arithmetic7

Operations, fractions, percentages, rates and everyday calculation.

4. A doctor told Mikael to take a pill every 75 minutes. He took his first pill at 11:05.

3. There are 12 ducks on Old McBride’s farm. Three ducks each lay one egg every day, four ducks each

4. Which of the following fractions is closest to 2?

8. Alisha has four paper strips of the same length.

21. A train has 12 carriages. Each carriage has the same number of compartments. Iliana is travelling in

10. The number 2581953764 is written on a strip of paper. Dilraj cuts the strip twice and gets three

11. My granny bought enough cat food to last her four cats for twelve days. However, on her way home,

Number Theory14

Digits, divisibility, primes, place-value puzzles and integer tricks.

1. Which single digit should be placed in all three of the boxes shown to give a

6. The integer 36 is divisible by its units digit. The integer 38 is not.

13. How many pairs of two-digit positive integers have a difference of 50?

15. In a certain month, the dates of three of the Sundays are prime.

20. For how many three-digit numbers can you subtract 297 and obtain a second three-digit number which

10. Every day Freya writes down the date in her diary and calculates the sum of the digits she writes. For

17. In the sum shown, equal letters represent equal digits and different letters represent

18. The number 100 is multiplied by either 2 or 3. The result then has 1 or 2 added to it. Finally the new

19. In the four-digit number ‘PQRS’, the digits P, Q , R and S are all non-zero and are in increasing order

7. 2025 is a square. How many distinct primes divide exactly into 2025?

12. Each letter in the eight-digit integer ‘ BENJAMIN ’ represents one of the digits 1, 2, 3, 4, 5, 6 or 7.

23. Joey is playing with his calculator. He starts with the number 12 and then multiplies or divides by 2 or

24. The digits of the three-digit integer ‘ XYZ ’ are all different. The sum of the digits of the three-digit

25. Two three-digit integers have all six of their digits distinct. The first digit of the second integer is

Algebra14

Equations, unknowns, ratios, sequences and word problems.

2. The sum of the ages of three children, Ava, Bob and Carlo, is 31.

8. Peter the penguin likes catching fish. On Monday, he realised that if he had caught three times as

22. In the Maths Premier League, teams get 3 points for a win, 1 point for a draw and 0 points for a loss.

23. For a given list of three numbers, the operation “changesum” replaces each number in the list with the

25. Tony had a large number of 1p, 5p, 10p and 20p coins in a bag. He removed some of the coins. The

5. Sophie and Armaan are playing a game. The winner of each game gets 3 points and the loser gets 1

6. Molly and Holly each own a big dog. Molly’s dog and Holly’s dog weigh 80 kg in total. Molly’s dog

7. Every plant in my mum’s window box has either two leaves and one flower or five leaves and no

13. Diego noticed that 20% of 30% of a number was 3 less than 30% of 40% of the same number.

23. Jo, Flo and Mo divided up a sum of money. Jo took £10 plus a quarter of what was then left.

9. There are 30 students in a class. They sit in pairs so that each boy is sitting next to a girl and exactly

13. Tim, Tom and Jim are triplets. Their brother Carl is three years younger.

17. Luigi opened a small restaurant. His friend Giacomo gave him some square tables and some chairs.

21. A rectangular swimming pool of length 20 m is surrounded on all four sides by a path 2 m wide. The

Geometry11

Shapes, areas, perimeters, symmetry and coordinate problems.

5. When she drew two intersecting circles, as shown, Tatiana divided the space

9. Maria has drawn some shapes on iden-

21. The diagram shows a square PQRS with area 120 cm2. Point T is the

9. Elliot drew six squares, each with side-length 1 cm, to make the shape shown.

12. The rectangle PQRS shown is divided into four smaller congruent rectangles.

14. The area of a rectangle is 12 cm2. The lengths of its sides, measured in cm, are integers. Which of

1. Which of the following traffic signs has the greatest number of lines of symmetry?

2. Joseph draws a square with side-length 10 cm. He joins the midpoints of the sides

14. The perimeter of the rectangle PQRS is 30 cm. A new shape is formed by

18. Lily wants to make a large triangle from small triangular tiles. She has already

19. Three vertices of the rectangle PQRS are at P ( 1, 1) , Q ( 7, 4) and R ( 5, 8) .

3D & Spatial9

Cubes, nets, folding, views and other three-dimensional puzzles.

10. Christopher has made a building out of blocks. The grid on the right shows the

12. The diagram shows a wooden cube of side 3 cm with a smaller cube of side 1 cm

24. Emily makes four identical numbered cubes using the net

1. My umbrella has the word KANGAROO written on top, as shown in the diagram.

20. Harvey writes a number on each face of a cube. Then, for each vertex, he

25. Hayden used small cubes of side 1 to build a large cube with side 4. Then he painted three of the

5. The piece of paper shown is folded along the dotted lines to make an open box.

6. Which of the following figures cannot be formed by gluing these two identical

20. A large cube was built from eight equally-sized small cubes,

Counting & Combinatorics8

Counting arrangements, tilings, pigeonhole and configuration problems.

7. What is the largest number of "T" shaped pieces, as shown, that can

18. There are 66 cats in my street. I don’t like 21 of them because they catch mice. Of the rest, 32 have

19. A group of 40 boys and 28 girls stand hand in hand in a circle facing inwards. Exactly 18 of the boys

2. Priya painted each of the nine squares shown black, white or grey.

16. A bag contains 3 green apples, 5 yellow apples, 7 green pears and 2 yellow pears. George takes out

22. In how many ways can three kangaroos be placed

15. Run Ze writes down all the integers with the following properties: the first digit is 1; each of the

16. What is the largest number of shapes of this form

Logic & Reasoning12

Deduction puzzles, truth-tellers, constraints and optimisation.

3. Nico is learning to drive. He knows how to turn right but has not yet

11. In a class election, each of the five candidates got a different number of votes. There were 36 votes

14. A lot of goals were scored in a hockey match I watched recently. In the first half, six goals were scored

16. Alisha wrote an integer in each square of a 4 × 4 grid. Integers in squares with a

17. Ali, Bev and Chaz never tell the truth. Each of them owns exactly one coloured stone that is either red

11. On Abdication Street, there are nine houses in a row. At least one person lives in each house. Any two

15. Mabel wants to colour each of the nine line segments shown in the diagram

24. Four points lie on a straight line. The distances between pairs of points are, in increasing order, 2, 3,

3. Millie’s mother likes her to set the table with a knife on the

4. On the left-hand side of the room, Jia and Lottie are sleeping with their

8. Five squirrels V, W, X, Y and Z are sitting on the line shown below.

22. Kirsten wrote numbers in five of the ten circles arranged around a pentagon, as