Junior maths challenge practice

Junior maths challenge practice paper for Year 7

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 7

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.

    Each of these three numbers has one digit hidden by a question mark: 54?, 69?, 96?. The average of the three numbers is 734. What is the sum of the three hidden digits?

    1. A12
    2. B13
    3. C3
    4. D14
    5. E1
  2. 2.

    At 8:30 pm two machines start a cycle in the factory together. After that, the first starts a cycle every 4 minutes and the second every 14 minutes. At what time will they next start a cycle together?

    1. A8:32 pm
    2. B8:58 pm
    3. C8:44 pm
    4. D8:59 pm
    5. E8:48 pm
  3. 3.

    Milo is heavier than Carlos. Hana is heavier than Milo. Pia is heavier than Hana. Carlos is heavier than Theo.
    Who is the heaviest?

    1. AMilo
    2. BTheo
    3. CHana
    4. DPia
    5. ECarlos
  4. 4.

    Three consecutive prime numbers add up to 97. (Consecutive primes come straight after one another, with no other prime between them.) What is the largest of them?

    1. A31
    2. B41
    3. C37
    4. D32
    5. E29
  5. 5.

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

    1. A130°
    2. B105°
    3. C50°
    4. D125°
    5. E230°
  6. 6.

    Find the value of x.
    4x − 15 = 2x − 7

    1. A8
    2. B3
    3. C4
    4. D5
    5. E6
  7. 7.

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

    1. A23
    2. B20
    3. C21
    4. D22
    5. E19
  8. 8.

    A rectangle is made from 30 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. B5
    3. C7
    4. D4
    5. E8
  9. 9.

    A board is ruled into a 3 by 3 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?

    1. A9
    2. B14
    3. C16
    4. D6
    5. E36
  10. 10.

    In a youth group with 35 members, 6 swim in a squad, 23 sing in the choir and 4 do both. How many do neither?

    1. A6 members
    2. B29 members
    3. C12 members
    4. D10 members
    5. E2 members
  11. 11.

    Wes, Raj, Lena, Fay and Eli are playing, and one of them has the ball.
    Wes says: "Fay does not have the ball."
    Raj says: "Wes has the ball."
    Lena says: "Wes has the ball."
    Fay says: "Wes does not have the ball."
    Eli says: "I have the ball."
    Exactly one of them is telling the truth. Who has the ball?

    1. AEli
    2. BWes
    3. CFay
    4. DLena
    5. ERaj
  12. 12.

    33 ÷ 3 × 7 is the same as which of these?

    1. A(33 + 7) ÷ 3
    2. B33 × 3 ÷ 7
    3. C33 × 7 ÷ 3
    4. D3 ÷ 33 × 7
    5. E33 ÷ (3 × 7)
  13. 13.

    A jar holds 12 counters numbered 1 to 12. Counters 1 to 6 are pink, 7 to 9 are brown and 10 to 12 are silver. One counter is taken out without looking. What is the chance that it is silver and its number is a factor of 40?

    1. A1/4
    2. B1/2
    3. C1/3
    4. D3/4
    5. E1/12
  14. 14.

    What fraction of the big square is shaded?

    1. A7/8
    2. B29/32
    3. C7/16
    4. D13/16
    5. E15/16
  15. 15.

    Two whole numbers multiply together to make 1372, and one of them is 7 times the other. What is the smaller number?

    1. A172
    2. B17
    3. C14
    4. D196
    5. E98

Questions 16 to 25

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

  1. 16.

    Ethan rolls a die 15 times and gets: 3, 6, 5, 1, 4, 6, 4, 3, 1, 1, 5, 5, 1, 5, 4. From these results, what is the experimental probability of rolling a number greater than 4?

    1. A1/3
    2. B3/5
    3. C7/15
    4. D2/3
    5. E2/5
  2. 17.

    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. B12
    3. C19
    4. D7
    5. E18
  3. 18.

    196 ÷ 7 is the same as which of these?

    1. A(140 ÷ 7) − (56 ÷ 7)
    2. B(140 ÷ 7) + (56 ÷ 7)
    3. C(7 ÷ 140) + (7 ÷ 56)
    4. D(140 ÷ 7) × (56 ÷ 7)
    5. E(196 ÷ 6) + (196 ÷ 1)
  4. 19.

    How many lines of symmetry does this shape have?

    1. A0
    2. B3
    3. C2
    4. D7
    5. E1
  5. 20.

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

    1. ARaj
    2. BUma
    3. CHana
    4. DCarlos
    5. EIvan
  6. 21.

    Use each of the digits 4, 3, 5, 9, 0 once to make the largest odd 5-digit number. What digit is in the thousands place?

    1. A3
    2. B0
    3. C9
    4. D5
    5. E4
  7. 22.

    Four consecutive prime numbers add up to 420. What is the largest of them?

    1. A101
    2. B105
    3. C113
    4. D109
    5. E107
  8. 23.

    Three different whole numbers multiply to 780 and add to 29. What is the largest of the three numbers?

    1. A390
    2. B13
    3. C16
    4. D10
    5. E6
  9. 24.

    What is the highest common factor of 25, 30?

    1. A150
    2. B55
    3. C5
    4. D25
    5. E4
  10. 25.

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

    1. A102°
    2. B132°
    3. C54°
    4. D126°
    5. E48°

Answers and working

Questions 1 to 15

  1. 1.A (12). The total is 3 × 734 = 2202. The visible parts make 2190, so the hidden digits are worth 12. Whatever way they fit, the digits add to 12.
  2. 2.B (8:58 pm). The smallest number that both 4 and 14 divide into is 28. So they meet again 28 minutes after 8:30 pm, which is 8:58 pm.
  3. 3.D (Pia). From heaviest to lightest, the order is Pia, Hana, Milo, Carlos, Theo. So the answer is Pia.
  4. 4.C (37). The primes 29, 31, 37 come one after another and add up to 97. The largest is 37.
  5. 5.C (50°). 180° − 55° − 75° = 50°.
  6. 6.C (4). Take 2x from both sides: 2x − 15 = -7. Add 15: 2x = 8. Divide by 2: x = 4.
  7. 7.C (21). The magic total is 3 × centre = 57. The diagonal through * gives 57 − 19 − 17 = 21.
  8. 8.D (4). Listing the rectangles with the smaller side first, 4 of them have an area of 30.
  9. 9.B (14). Take the sizes one at a time: a square of side k can sit in (3 − k + 1) × (3 − k + 1) positions. Adding those up from k = 1 to 3 gives 14, which on a square grid is just 1² + 2² + … + 3².
  10. 10.D (10 members). 6 + 23 − 4 = 25 do at least one, and the other 10 of the 35 do neither. So the answer is 10 members.
  11. 11.C (Fay). Try each child as the one with the ball and count the true statements. Only when Fay has it is exactly one statement true.
  12. 12.C (33 × 7 ÷ 3). 33 ÷ 3 × 7 = 77, and so does 33 × 7 ÷ 3.
  13. 13.E (1/12). Of the silver ones, 10 to 12, the ones whose number is a factor of 40: 10. That is 1 of the 12: 1/12.
  14. 14.A (7/8). The big square has 16 small squares. The shaded part is 14 squares. So 14 out of 16 is shaded: 7/8.
  15. 15.C (14). Call the smaller number n. The larger is 7n, so the two multiply to 7 × n × n = 1372. That makes n × n = 1372 ÷ 7 = 196, so n = 14 and the larger number is 98.

Questions 16 to 25

  1. 16.E (2/5). 6 of the 15 rolls were a number greater than 4, and 6/15 in simplest form is 2/5. So the answer is 2/5.
  2. 17.E (18). Listing every shape, with turned and flipped copies counted as the rules say, gives 18 shapes.
  3. 18.B ((140 ÷ 7) + (56 ÷ 7)). 196 = 140 + 56, so 196 ÷ 7 = (140 ÷ 7) + (56 ÷ 7), which is 28.
  4. 19.E (1). Only the folds that make both halves match count, so this shape has 1 line of symmetry.
  5. 20.D (Carlos). Try each child as the one with the ball and count the true statements. Only when Carlos has it is exactly one statement true.
  6. 21.D (5). The largest odd number from those digits is 95403. Its thousands digit is 5.
  7. 22.D (109). The primes 101, 103, 107, 109 come one after another and add up to 420. The largest is 109.
  8. 23.B (13). Only 6, 10 and 13 multiply to 780 and add to 29. The largest is 13: 13.
  9. 24.C (5). 25 = 5 × 5, 30 = 2 × 3 × 5. The primes they all share multiply to 5.
  10. 25.C (54°). The angle at D equals the angle at A (alternate angles), 48°, so x = 180° − 48° − 78° = 54°.

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 7

    25 questions · 60 minutes

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

Questions parents ask

Is this paper right for Year 7?
Yes. The junior challenge is set for Year 8 and below, and most Year 7 children who sit it find the last ten questions hard. That is how it is meant to be.
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 8 paper

The other maths challenges

Primary Maths ChallengeIntermediate Maths Challenge