Primary maths challenge practice

Primary maths challenge practice paper for Year 5

A free paper in the primary challenge's shape: 25 questions in 45 minutes, the first 20 with five choices and the last 5 written in, for 25 marks. Print it, then check every answer and its working at the end.

See the answersSit a new paper online

Scholar Tests · Sample paper

Primary maths challenge-style paper, Year 5

25 questions · 25 marks · 45 minutes · no negative marking

Name ______________________ Date ____________

Questions 1 to 20

Questions 1 to 20, 1 mark each. Circle the letter of the best answer.

  1. 1.

    What fraction of the big square is shaded?

    1. A13/32
    2. B27/32
    3. C3/4
    4. D7/8
    5. E13/16
  2. 2.

    A frog starts on 2 on a number line and hops forward 3 each time: 2, 5, 8, and so on. Where does it land after 4 hops?

    1. A15
    2. B10
    3. C17
    4. D14
    5. E11
  3. 3.

    The shapes keep repeating in the same way. Which shape is 11th?

    1. A
    2. B
    3. C
    4. D
    5. E
  4. 4.

    1 pear weighs the same as 4 shells. How many shells weigh the same as 5 pears?

    1. A9
    2. B24
    3. C16
    4. D20
    5. E4
  5. 5.

    Theo, Jada and Kai are playing, and one of them has the ball.
    Theo says: "I have the ball."
    Jada says: "Kai does not have the ball."
    Kai says: "Theo does not have the ball."
    Exactly one of them is telling the truth. Who has the ball?

    1. AKai
    2. BIvan
    3. CTheo
    4. DWes
    5. EJada
  6. 6.

    How many triangles of any size are there in this figure?

    1. A6
    2. B7
    3. C3
    4. D2
    5. E5
  7. 7.

    Five cards, each with a shape on it, were put down one at a time. Which card was put down first?

    1. A
    2. B
    3. C
    4. D
    5. E
  8. 8.

    Two prices come to £32, and one is £10 more than the other. What is the cheaper price?

    1. A£16
    2. B£21
    3. C£22
    4. D£11
    5. E£5
  9. 9.

    Dina is older than Uma. Wes is older than Ava. Gus is older than Wes. Ava is older than Dina.
    Who is the youngest?

    1. AAva
    2. BUma
    3. CDina
    4. DWes
    5. EGus
  10. 10.

    Find the missing number marked with the asterisk (*) in the magic square below. (Every row, column and diagonal adds to the same total.)

    1. A16
    2. B17
    3. C19
    4. D11
    5. E18
  11. 11.

    Square tiles are joined edge to edge to make flat shapes. A shape may be turned round to match another, but it may not be flipped over, so a shape and its mirror image count as two different shapes. How many different shapes can be made from five tiles?

    1. A17
    2. B19
    3. C18
    4. D7
    5. E12
  12. 12.

    Lena is faster than Sara. Dina is slower than Lena. Nia is slower than Sara. Jada is faster than Lena.
    Who is the second fastest?

    1. ADina
    2. BJada
    3. CLena
    4. DNia
    5. ESara
  13. 13.

    Lena, Fay, Nia, Milo and Gus are playing, and one of them has the ball.
    Lena says: "Nia does not have the ball."
    Fay says: "Nia has the ball."
    Nia says: "Lena has the ball."
    Milo says: "Gus does not have the ball."
    Gus says: "I do not have the ball."
    Exactly one of them is telling the truth. Who has the ball?

    1. AFay
    2. BNia
    3. CLena
    4. DGus
    5. EMilo
  14. 14.

    Use each of the digits 8, 2, 7, 4, 3 once to make the smallest even 5-digit number. What digit is in the ten thousands place?

    1. A8
    2. B7
    3. C2
    4. D4
    5. E3
  15. 15.

    How many lines of symmetry does this shape have?

    1. A2
    2. B0
    3. C4
    4. D3
    5. E12
  16. 16.

    In a class with 42 children, 19 play chess, 21 play football and 3 do both. How many do neither?

    1. A23 children
    2. B2 children
    3. C5 children
    4. D37 children
    5. E21 children
  17. 17.

    Five cards, each with a shape on it, were put down one at a time. Which card was put down fourth?

    1. A
    2. B
    3. C
    4. D
    5. E
  18. 18.

    What fraction of the big square is shaded?

    1. A3/4
    2. B13/16
    3. C27/32
    4. D7/8
    5. E13/32
  19. 19.

    1 apple weighs the same as 4 cubes. 1 cube weighs the same as 2 blocks. How many blocks weigh the same as 1 apple?

    1. A8
    2. B4
    3. C2
    4. D7
    5. E9
  20. 20.

    The shapes keep repeating in the same way. Which shape is 38th?

    1. A
    2. B
    3. C
    4. D
    5. E

Questions 21 to 25

Questions 21 to 25, 1 mark each. Write your answer on the line.

  1. 21.

    How many squares that have a circle directly to their right are there in the picture?

    Answer: ______________

  2. 22.

    Use each of the digits 3, 4, 9 and 7 once to make two two-digit numbers. What is the largest sum the two numbers can have?

    Answer: ______________

  3. 23.

    A board is ruled into a 7 by 7 grid of small squares. How many squares of any size can be found on it, counting the small ones and every larger square they make up?

    Answer: ______________

  4. 24.

    A smallholding holds only hens and goats. Altogether there are 34 animals and 124 legs. How many hens are there?

    Answer: ______________

  5. 25.

    A straight driveway is 1,895 m long. There is a tree every 5 m along it, including one at each end. How many trees are there?

    Answer: ______________

Answers and working

Questions 1 to 20

  1. 1.E (13/16). The big square has 16 small squares. The shaded part is 13 squares. So 13 out of 16 is shaded: 13/16.
  2. 2.D (14). 4 hops of 3 take the frog 12 along, from 2 to 14.
  3. 3.B. The pattern repeats every 2 shapes. 11 = 2 × 5 + 1, so the 11th shape is the same as the 1st: a star.
  4. 4.D (20). Each pear can be swapped for 4 shells, so 5 pears weigh the same as 5 × 4 = 20 shells.
  5. 5.A (Kai). Try each child as the one with the ball and count the true statements. Only when Kai has it is exactly one statement true.
  6. 6.A (6). Counting size by size, from the smallest up to the biggest, finds 6 triangles.
  7. 7.C. Wherever two cards overlap, the card on top came later. That gives the order heart, circle, triangle, square, star, so the card with the heart was put down first.
  8. 8.D (£11). Take the difference off the total first: £32 − £10 = £22. That is what TWO of the smaller one come to, so the smaller is £11 and the larger is £11 + £10 = £21.
  9. 9.B (Uma). From oldest to youngest, the order is Gus, Wes, Ava, Dina, Uma. So the answer is Uma.
  10. 10.B (17). The magic total is 3 × centre = 33. The diagonal through * gives 33 − 11 − 5 = 17.
  11. 11.C (18). Listing every shape, with turned and flipped copies counted as the rules say, gives 18 shapes.
  12. 12.C (Lena). The clues do not fix the whole order, but in every order they allow, Lena is in that place.
  13. 13.D (Gus). Try each child as the one with the ball and count the true statements. Only when Gus has it is exactly one statement true.
  14. 14.C (2). The smallest even number from those digits is 23478. Its ten thousands digit is 2.
  15. 15.C (4). Only the folds that make both halves match count, so this shape has 4 lines of symmetry.
  16. 16.C (5 children). 19 + 21 − 3 = 37 do at least one, and the other 5 of the 42 do neither. So the answer is 5 children.
  17. 17.E. Wherever two cards overlap, the card on top came later. That gives the order circle, triangle, square, heart, star, so the card with the heart was put down fourth.
  18. 18.B (13/16). The big square has 16 small squares. The shaded part is 13 squares. So 13 out of 16 is shaded: 13/16.
  19. 19.A (8). 1 apple weighs the same as 4 cubes, and each cube is 2 blocks, so the answer is 4 × 2 = 8.
  20. 20.B. The pattern repeats every 4 shapes. 38 = 4 × 9 + 2, so the 38th shape is the same as the 2nd: a star.

Questions 21 to 25

  1. 21.4. Going row by row and ticking each one that fits, there are 4 squares that have a circle directly to their right.
  2. 22.167. The tens digits count ten times as much, so the two biggest digits, 9 and 7, go in the tens places: 94 + 73 = 167.
  3. 23.140. Take the sizes one at a time: a square of side k can sit in (7 − k + 1) × (7 − k + 1) positions. Adding those up from k = 1 to 7 gives 140, which on a square grid is just 1² + 2² + … + 7².
  4. 24.6. If all 34 had two legs there would be 68 legs, but there are 124 — 56 extra. Each goat adds two extra legs, so there are 28 goats and 6 hens. The answer is 6.
  5. 25.380. 1,895 ÷ 5 = 379, so there are 379 gaps. Something stands at both ends, so there is one more tree than gaps: 379 + 1 = 380.

Written by Scholar Tests in the primary maths challenge's published shape. Not a past paper; we are not connected with the Mathematical Association.

Sit a new paper online

Every online paper is new, timed like the real thing, and marked the moment it ends, 1 mark a question. For the last five, type a whole number.

  • Year 5

    25 questions · 45 minutes

    Number puzzles, patterns, logic and shape, the hardest last. No calculator.

Questions parents ask

Is this paper right for Year 5?
Yes. The primary challenge is for children aged 9 to 11, and this paper keeps to puzzles a Year 5 child can reach, with the last five harder.
How is it marked?
Every right answer is worth 1 mark, so the paper is out of 25. Nothing is taken off for a wrong answer, so it is worth answering every question.
How do the last five questions work?
Questions 21 to 25 have no choices. Work out the answer and write it on the line. Online, type a whole number.
Are these real past papers?
No. We write our own questions in the challenge's published shape. Past papers belong to the Mathematical Association, and we are not connected with it.

Papers for other years

Year 6 paper

The other maths challenges

Junior Maths ChallengeIntermediate Maths Challenge