Junior maths challenge practice

Junior maths challenge practice paper for Year 8

A free paper in the junior challenge's shape: 25 questions in 60 minutes, five choices each, for 135 marks. Print it, then check every answer and its working at the end.

See the answersSit a new paper online

Scholar Tests · Sample paper

Junior maths challenge-style paper, Year 8

25 questions · 135 marks · 60 minutes · no negative marking

Name ______________________ Date ____________

Questions 1 to 15

Questions 1 to 15, 5 marks each. Circle the letter of the best answer.

  1. 1.

    In a class, 9 children play tennis, 11 play chess and 6 do both. Everyone does at least one of the two. How many children are there?

    1. A20 children
    2. B8 children
    3. C26 children
    4. D11 children
    5. E14 children
  2. 2.

    Pia is faster than Eli. Eli is faster than Dina. Wes is faster than Zoe. Zoe is faster than Pia.
    Who is the slowest?

    1. AWes
    2. BZoe
    3. CPia
    4. DEli
    5. EDina
  3. 3.

    Two whole numbers add to 22 and multiply to 120. What is the larger number?

    1. A11
    2. B120
    3. C10
    4. D22
    5. E12
  4. 4.

    In the triangle below, what is the size of the angle marked x?

    1. A25°
    2. B115°
    3. C65°
    4. D110°
    5. E245°
  5. 5.

    Ruby rolls a die 16 times and gets: 2, 3, 2, 6, 4, 2, 1, 5, 2, 1, 2, 3, 1, 3, 3, 3. From these results, what is the experimental probability of rolling a 1?

    1. A3/16
    2. B1/2
    3. C1/8
    4. D3/13
    5. E1/6
  6. 6.

    Find the value of x.
    5x + 11 = 2x + 35

    1. A9
    2. B24
    3. C8
    4. D10
    5. E7
  7. 7.

    Three consecutive prime numbers add up to 131. (Consecutive primes come straight after one another, with no other prime between them.) What is the smallest of them?

    1. A47
    2. B37
    3. C44
    4. D43
    5. E41
  8. 8.

    A box holds 20 cards numbered 1 to 20. Cards 1 to 3 are yellow, 4 to 15 are purple and 16 to 20 are orange. One card is taken out without looking. What is the chance that it is yellow and its number is a square number?

    1. A3/20
    2. B1/5
    3. C1/20
    4. D7/20
    5. E1/3
  9. 9.

    Ava, Dina, Hana, Ben and Omar are playing, and one of them has the ball.
    Ava says: "Hana has the ball."
    Dina says: "Ben does not have the ball."
    Hana says: "Ava has the ball."
    Ben says: "Ava has the ball."
    Omar says: "Ava does not have the ball."
    Exactly one of them is telling the truth. Who has the ball?

    1. ABen
    2. BAva
    3. CDina
    4. DOmar
    5. EHana
  10. 10.

    240 ÷ 10 is the same as which of these?

    1. A(200 ÷ 10) × (40 ÷ 10)
    2. B(200 ÷ 10) + (40 ÷ 10)
    3. C(200 ÷ 10) − (40 ÷ 10)
    4. D(240 ÷ 1) + (240 ÷ 9)
    5. E(10 ÷ 200) + (10 ÷ 40)
  11. 11.

    When a number is multiplied by 5, the answer is the same as multiplying that number by 3 and then adding 10. What is the number?

    1. A3
    2. B7
    3. C5
    4. D2
    5. E1
  12. 12.

    How many lines of symmetry does this shape have?

    1. A4
    2. B3
    3. C6
    4. D2
    5. E1
  13. 13.

    Each of these three numbers has one digit hidden by a question mark: 5?2, 58?, 45?. The average of the three numbers is 544. What is the sum of the three hidden digits?

    1. A19
    2. B100
    3. C10
    4. D1
    5. E13
  14. 14.

    A coach has 6 cricket balls and 21 tennis balls. She makes the largest number of equal groups she can, with the same number of each kind in every group and none left over. How many cricket balls and tennis balls are in each group altogether?

    1. A27
    2. B2
    3. C9
    4. D7
    5. E3
  15. 15.

    A rectangle is made from 12 square tiles, with none left over. A square counts as a rectangle, and a rectangle that is only turned on its side is still the same rectangle. How many different rectangles can be made?

    1. A3
    2. B4
    3. C2
    4. D5
    5. E6

Questions 16 to 25

Questions 16 to 25, 6 marks each. Circle the letter of the best answer.

  1. 16.

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

    1. AHana
    2. BZoe
    3. CKai
    4. DGus
    5. ENia
  2. 17.

    How many whole numbers from 1 to 120 can be divided exactly by 4 or by 6, or both?

    1. A50
    2. B45
    3. C30
    4. D10
    5. E40
  3. 18.

    The seats along one row of a hall are numbered 9, 10, 11 and so on up to 23. What do all the seat numbers add up to?

    1. A16
    2. B480
    3. C240
    4. D224
    5. E32
  4. 19.

    In the triangle below, what is the size of the angle marked x?

    1. A109°
    2. B103°
    3. C45°
    4. D251°
    5. E71°
  5. 20.

    A palindrome is a number that reads the same forwards and backwards, such as 373. How many 5-digit palindromes are there?

    1. A1000
    2. B900
    3. C90
    4. D9000
    5. E90000
  6. 21.

    Identical cubes are joined face to face to make solid shapes. Turning a shape round in the hand does not make a new one, but a shape and its mirror image count as two different shapes. How many different shapes can be made from four cubes?

    1. A2
    2. B5
    3. C7
    4. D8
    5. E9
  7. 22.

    How many factors does 90 have?

    1. A6
    2. B12
    3. C13
    4. D10
    5. E3
  8. 23.

    836 ÷ 19 is the same as which of these?

    1. A(760 ÷ 19) + (76 ÷ 19)
    2. B(760 ÷ 19) × (76 ÷ 19)
    3. C(836 ÷ 1) + (836 ÷ 18)
    4. D(760 ÷ 19) − (76 ÷ 19)
    5. E(19 ÷ 760) + (19 ÷ 76)
  9. 24.

    What is the value of 1/(1 × 2) + 1/(2 × 3) + 1/(3 × 4) + ... + 1/(7 × 8)?

    1. A7/8
    2. B1/56
    3. C1/8
    4. D8/9
    5. E6/7
  10. 25.

    I have a bag of marbles. There are more than 19 and fewer than 31. When I share them out, I find they leave 3 left over when grouped in 4s, and leave 0 left over when grouped in 9s, and leave 0 left over when grouped in 3s.   How many marbles are there?

    1. A30
    2. B26
    3. C27
    4. D31
    5. E28

Answers and working

Questions 1 to 15

  1. 1.E (14 children). 9 + 11 counts the 6 who do both twice, so take them off once: 9 + 11 − 6. So the answer is 14 children.
  2. 2.E (Dina). From fastest to slowest, the order is Wes, Zoe, Pia, Eli, Dina. So the answer is Dina.
  3. 3.E (12). Only 10 and 12 multiply to 120 and add to 22. The larger is 12: 12.
  4. 4.B (115°). An outside angle equals the two far inside angles: 70° + 45° = 115°.
  5. 5.A (3/16). 3 of the 16 rolls were a 1, and 3/16 in simplest form is 3/16. So the answer is 3/16.
  6. 6.C (8). Take 2x from both sides: 3x + 11 = 35. Take off 11: 3x = 24. Divide by 3: x = 8.
  7. 7.E (41). The primes 41, 43, 47 come one after another and add up to 131. The smallest is 41.
  8. 8.C (1/20). Of the yellow ones, 1 to 3, the ones whose number is a square number: 1. That is 1 of the 20: 1/20.
  9. 9.A (Ben). Try each child as the one with the ball and count the true statements. Only when Ben has it is exactly one statement true.
  10. 10.B ((200 ÷ 10) + (40 ÷ 10)). 240 = 200 + 40, so 240 ÷ 10 = (200 ÷ 10) + (40 ÷ 10), which is 24.
  11. 11.C (5). Multiplying by 5 rather than by 3 adds 5 − 3 = 2 lots of the number. Those 2 lots come to 10, so the number is 10 ÷ 2 = 5.
  12. 12.E (1). Only the folds that make both halves match count, so this shape has 1 line of symmetry.
  13. 13.A (19). The total is 3 × 544 = 1632. The visible parts make 1532, so the hidden digits are worth 100. Whatever way they fit, the digits add to 19.
  14. 14.C (9). With 3 groups, each has 6 ÷ 3 = 2 and 21 ÷ 3 = 7, so 9 altogether.
  15. 15.A (3). Listing the rectangles with the smaller side first, 3 of them have an area of 12.

Questions 16 to 25

  1. 16.A (Hana). Try each child as the one with the ball and count the true statements. Only when Hana has it is exactly one statement true.
  2. 17.E (40). 30 divide by 4 and 20 divide by 6, but 10 of them divide by both (they are multiples of 12). 30 + 20 − 10 = 40.
  3. 18.C (240). There are (23 − 9) ÷ 1 + 1 = 15 numbers, and the first and last add to 9 + 23 = 32. Writing the run out backwards underneath itself makes 15 pairs of 32, so the total is 15 × 32 ÷ 2 = 240.
  4. 19.A (109°). An outside angle equals the two far inside angles: 77° + 32° = 109°.
  5. 20.B (900). The back half copies the front half, so only the first three digits are chosen. The first cannot be 0, giving 9 ways, and each other free digit has 10: 9 × 10 × 10 = 900.
  6. 21.D (8). Listing every shape, with turned and flipped copies counted as the rules say, gives 8 shapes.
  7. 22.B (12). The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90: 12 of them.
  8. 23.A ((760 ÷ 19) + (76 ÷ 19)). 836 = 760 + 76, so 836 ÷ 19 = (760 ÷ 19) + (76 ÷ 19), which is 44.
  9. 24.A (7/8). Most of the fractions cancel, and what is left is 7/8.
  10. 25.C (27). Checking every number from 20 to 30 against all 3 clues, only 27 fits every one.

Written by Scholar Tests in the junior maths challenge's published shape. Not a past paper; we are not connected with the UK Mathematics Trust.

Sit a new paper online

Every online paper is new, timed like the real thing, and marked the moment it ends, 5 marks for each of the first 15 and 6 for the rest.

  • Year 8

    25 questions · 60 minutes

    Logic, number puzzles, counting and shape, the hardest last. No calculator.

Questions parents ask

Is this paper right for Year 8?
Yes. This is the top year for the junior challenge, and this paper leans on the harder number and counting puzzles.
How is it marked?
Questions 1 to 15 are worth 5 marks each and 16 to 25 are worth 6, so the paper is out of 135. Nothing is taken off for a wrong answer, so it is worth answering every question.
Can my child use a calculator?
No. The challenge allows no calculator or measuring instruments, only rough paper. Practise the same way.
Are these real past papers?
No. We write our own questions in the challenge's published shape. Past papers belong to the UK Mathematics Trust, and we are not connected with it.

Papers for other years

Year 6 paperYear 7 paper

The other maths challenges

Primary Maths ChallengeIntermediate Maths Challenge