Junior maths challenge practice

Junior maths challenge practice paper for Year 6

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 6

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.

    A rectangle is made from 48 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. A4
    2. B6
    3. C10
    4. D5
    5. E9
  2. 2.

    What fraction of the big square is shaded?

    1. A3/8
    2. B1/3
    3. C1/2
    4. D1/8
    5. E1/4
  3. 3.

    How many lines of symmetry does this shape have?

    1. A6
    2. B0
    3. C10
    4. D5
    5. E4
  4. 4.

    Uma is older than Carlos. Eli is older than Omar. Ivan is older than Uma. Omar is older than Ivan.
    Who is the oldest?

    1. AEli
    2. BUma
    3. COmar
    4. DCarlos
    5. EIvan
  5. 5.

    Find the missing number: 20 × 4 = 4 × 14 + ?

    1. A120
    2. B24
    3. C10
    4. D84
    5. E6
  6. 6.

    Each of these three numbers has one digit hidden by a question mark: 3?7, 6?6, 9?2. The average of the three numbers is 645. What is the sum of the three hidden digits?

    1. A12
    2. B120
    3. C2
    4. D15
    5. E5
  7. 7.

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

    1. ARaj
    2. BDina
    3. CSara
    4. DTheo
    5. EGus
  8. 8.

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

    1. A11
    2. B13
    3. C15
    4. D14
    5. E12
  9. 9.

    A floor is tiled with a 6 by 6 grid of small square tiles. How many squares of any size can be found on it, counting the small ones and every larger square they make up?

    1. A36
    2. B441
    3. C49
    4. D21
    5. E91
  10. 10.

    Use each of the digits 6, 5, 1 and 7 once. What is the smallest number you can make?

    1. A6517
    2. B1568
    3. C6571
    4. D1567
    5. E6157
  11. 11.

    1 ball weighs the same as 2 shells. 1 shell weighs the same as 4 marbles. How many marbles weigh the same as 2 balls?

    1. A4
    2. B8
    3. C15
    4. D9
    5. E16
  12. 12.

    In the drawing below, the two lines marked with arrows are parallel. What is the size of the angle marked x?

    1. A88°
    2. B140°
    3. C92°
    4. D268°
    5. E128°
  13. 13.

    At 7:45 pm two machines start a cycle in the factory together. After that, the first starts a cycle every 12 minutes and the second every 15 minutes. At what time will they next start a cycle together?

    1. A8:12 pm
    2. B8:00 pm
    3. C7:48 pm
    4. D8:45 pm
    5. E8:44 pm
  14. 14.

    Two whole numbers multiply together to make 676, and one of them is 4 times the other. What is the smaller number?

    1. A14
    2. B52
    3. C13
    4. D135
    5. E169
  15. 15.

    In a Year 6 group, 33 students play chess, 29 take art classes and 9 do both. Everyone does at least one of the two. How many students are there?

    1. A44 students
    2. B62 students
    3. C71 students
    4. D33 students
    5. E53 students

Questions 16 to 25

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

  1. 16.

    Use each of the digits 0, 8, 7, 6, 9 once to make the smallest multiple of 5 5-digit number. What digit is in the thousands place?

    1. A6
    2. B9
    3. C0
    4. D8
    5. E7
  2. 17.

    Priya rolls a die 20 times and gets: 4, 1, 6, 2, 2, 5, 6, 3, 2, 5, 4, 1, 5, 4, 5, 1, 5, 5, 1, 2. From these results, what is the experimental probability of rolling an even number?

    1. A9/11
    2. B2/5
    3. C11/20
    4. D1/2
    5. E9/20
  3. 18.

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

    1. ATheo
    2. BHana
    3. CGus
    4. DAva
    5. EBen
  4. 19.

    How many more factors does 36 have than 69?

    1. A4
    2. B3
    3. C13
    4. D5
    5. E9
  5. 20.

    18 ÷ 9 × 5 is the same as which of these?

    1. A18 × 9 ÷ 5
    2. B18 ÷ (9 × 5)
    3. C9 ÷ 18 × 5
    4. D(18 + 5) ÷ 9
    5. E18 × 5 ÷ 9
  6. 21.

    What is the highest common factor of 105, 135?

    1. A945
    2. B105
    3. C15
    4. D5
    5. E240
  7. 22.

    Two whole numbers add to 31 and multiply to 238. What is the larger number?

    1. A17
    2. B30
    3. C14
    4. D31
    5. E238
  8. 23.

    Find the value of x.
    11x + 20 = 7x + 44

    1. A24
    2. B7
    3. C5
    4. D16
    5. E6
  9. 24.

    A tub holds 18 balls numbered 1 to 18. Balls 1 to 7 are white, 8 to 13 are black and 14 to 18 are grey. One ball is taken out without looking. What is the chance that it is not white and its number is not a factor of 60?

    1. A1/9
    2. B4/9
    3. C11/18
    4. D5/9
    5. E1/2
  10. 25.

    What fraction of the big square is shaded?

    1. A1/8
    2. B3/13
    3. C5/16
    4. D1/4
    5. E3/16

Answers and working

Questions 1 to 15

  1. 1.D (5). Listing the rectangles with the smaller side first, 5 of them have an area of 48.
  2. 2.E (1/4). The big square has 4 small squares. The shaded part is 1 squares. So 1 out of 4 is shaded: 1/4.
  3. 3.D (5). Only the folds that make both halves match count, so this shape has 5 lines of symmetry.
  4. 4.A (Eli). From oldest to youngest, the order is Eli, Omar, Ivan, Uma, Carlos. So the answer is Eli.
  5. 5.B (24). 20 lots of 4 is 6 lots more than 14 lots of 4, so the missing number is 6 × 4 = 24.
  6. 6.A (12). The total is 3 × 645 = 1935. The visible parts make 1815, so the hidden digits are worth 120. Whatever way they fit, the digits add to 12.
  7. 7.D (Theo). Try each child as the one with the ball and count the true statements. Only when Theo has it is exactly one statement true.
  8. 8.B (13). The magic total is 3 × centre = 33. The diagonal through * gives 33 − 11 − 9 = 13.
  9. 9.E (91). Take the sizes one at a time: a square of side k can sit in (6 − k + 1) × (6 − k + 1) positions. Adding those up from k = 1 to 6 gives 91, which on a square grid is just 1² + 2² + … + 6².
  10. 10.D (1567). The smallest number you can make from 6, 5, 1 and 7 is 1567.
  11. 11.E (16). 2 balls weigh the same as 4 shells, and each shell is 4 marbles, so the answer is 4 × 4 = 16.
  12. 12.A (88°). The top triangle's angle at E is 180° − 40° − 52°, and x is vertically opposite it: 88°.
  13. 13.D (8:45 pm). The smallest number that both 12 and 15 divide into is 60. So they meet again 60 minutes after 7:45 pm, which is 8:45 pm.
  14. 14.C (13). Call the smaller number n. The larger is 4n, so the two multiply to 4 × n × n = 676. That makes n × n = 676 ÷ 4 = 169, so n = 13 and the larger number is 52.
  15. 15.E (53 students). 33 + 29 counts the 9 who do both twice, so take them off once: 33 + 29 − 9. So the answer is 53 students.

Questions 16 to 25

  1. 16.E (7). The smallest multiple of 5 number from those digits is 67890. Its thousands digit is 7.
  2. 17.E (9/20). 9 of the 20 rolls were an even number, and 9/20 in simplest form is 9/20. So the answer is 9/20.
  3. 18.A (Theo). Try each child as the one with the ball and count the true statements. Only when Theo has it is exactly one statement true.
  4. 19.D (5). 36 has 9 factors and 69 has 4, so 36 has 5 more.
  5. 20.E (18 × 5 ÷ 9). 18 ÷ 9 × 5 = 10, and so does 18 × 5 ÷ 9.
  6. 21.C (15). 105 = 3 × 5 × 7, 135 = 3 × 3 × 3 × 5. The primes they all share multiply to 15.
  7. 22.A (17). Only 14 and 17 multiply to 238 and add to 31. The larger is 17: 17.
  8. 23.E (6). Take 7x from both sides: 4x + 20 = 44. Take off 20: 4x = 24. Divide by 4: x = 6.
  9. 24.B (4/9). Leaving out the white ones and every one whose number is a factor of 60 leaves 8 of the 18: 8/18 = 4/9.
  10. 25.E (3/16). The big square has 16 small squares. The shaded part is 1 whole squares and 4 halves, which is 3 squares. So 3 out of 16 is shaded: 3/16.

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 6

    25 questions · 60 minutes

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

Questions parents ask

Is this paper right for Year 6?
It is pitched a little below the real challenge, which is set for Years 7 and 8, so a confident Year 6 child can try the format first.
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 7 paperYear 8 paper

The other maths challenges

Primary Maths ChallengeIntermediate Maths Challenge