Maths competition practice

Maths competition practice paper for Years 7 and 8

A free paper in the shape of the Kangaroo Math Competition's Cadet level (Form 1 and 2 in Malaysia): 30 questions in 75 minutes, five choices each, for 120 points. Print it, then check every answer and its working at the end.

See the answersSit a new paper online

Scholar Tests · Sample paper

Maths competition paper, Years 7 and 8

30 questions · 120 points · 75 minutes · no negative marking

Name ______________________ Date ____________

Questions 1 to 10

Questions 1 to 10, 3 points each. Circle the letter of the best answer.

  1. 1.

    What is the total of all the whole numbers from 11 to 19, counting both ends?

    1. A15
    2. B120
    3. C270
    4. D30
    5. E135
  2. 2.

    76 ÷ 4 is the same as which of these?

    1. A(40 ÷ 4) − (36 ÷ 4)
    2. B(40 ÷ 4) × (36 ÷ 4)
    3. C(4 ÷ 40) + (4 ÷ 36)
    4. D(76 ÷ 1) + (76 ÷ 3)
    5. E(40 ÷ 4) + (36 ÷ 4)
  3. 3.

    What is the value of (1 + 1/2) × (1 + 1/3) × ... × (1 + 1/6)?

    1. A7
    2. B4
    3. C3
    4. D7/2
    5. E7/6
  4. 4.

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

    1. A8
    2. B3
    3. C2
    4. D9
    5. E5
  5. 5.

    Sara is heavier than Raj. Nia is heavier than Ava. Raj is heavier than Nia. Ava is heavier than Zoe.
    Who is the lightest?

    1. ARaj
    2. BNia
    3. CZoe
    4. DSara
    5. EAva
  6. 6.

    How many lines of symmetry does this shape have?

    1. A3
    2. B1
    3. C2
    4. D0
    5. E4
  7. 7.

    Start at 132 and count back in steps of 3. What is the first number you reach that is less than 113?

    1. A111
    2. B114
    3. C108
    4. D117
    5. E112
  8. 8.

    Each of these three numbers has one digit hidden by a question mark: 15?, 21?, 72?. The average of the three numbers is 366. What is the sum of the three hidden digits?

    1. A18
    2. B15
    3. C5
    4. D7
    5. E19
  9. 9.

    In a youth group with 21 members, 11 swim in a squad, 8 have a dog and 3 do both. How many do neither?

    1. A10 members
    2. B5 members
    3. C2 members
    4. D13 members
    5. E16 members
  10. 10.

    A rectangle is made from 18 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. B3
    3. C5
    4. D2
    5. E6

Questions 11 to 20

Questions 11 to 20, 4 points each. Circle the letter of the best answer.

  1. 11.

    In the drawing below, B, C and D lie on a straight line, and the sides with a tick are equal. What is the size of the angle marked x?

    1. A57°
    2. B33°
    3. C114°
    4. D48°
    5. E66°
  2. 12.

    Find the value of x.
    7x − 16 = 4x + 5

    1. A8
    2. B6
    3. C9
    4. D7
    5. E21
  3. 13.

    A bag holds 2 blue, 5 white and 2 orange marbles. Two marbles are taken out, one after the other, without putting the first back. What is the probability that the first is blue and the second is orange?

    1. A4/81
    2. B1/4
    3. C1/18
    4. D1/36
    5. E17/36
  4. 14.

    Three consecutive prime numbers add up to 59. What is the largest of them?

    1. A17
    2. B20
    3. C23
    4. D19
    5. E29
  5. 15.

    I have a bag of beads. There are more than 19 and fewer than 31. When I share them out, I find they leave 5 left over when grouped in 6s, and leave 2 left over when grouped in 3s, and leave 4 left over when grouped in 5s.   How many beads are there?

    1. A29
    2. B28
    3. C31
    4. D23
    5. E30
  6. 16.

    How many whole numbers from 1 to 250 can be divided exactly by 12 or by 18, or both?

    1. A33
    2. B21
    3. C6
    4. D27
    5. E32
  7. 17.

    What is the value of 1³ + 2³ + 3³ + ... + 6³?

    1. A91
    2. B441
    3. C21
    4. D216
    5. E225
  8. 18.

    What is the value of 3636 × 87 − 8787 × 36?

    1. A101
    2. B3132
    3. C5151
    4. D316332
    5. E0
  9. 19.

    A coach has 65 apples and 78 oranges. 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 groups does she make?

    1. A11
    2. B143
    3. C65
    4. D13
    5. E390
  10. 20.

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

    1. ARaj
    2. BHana
    3. CEli
    4. DOmar
    5. ETheo

Questions 21 to 30

Questions 21 to 30, 5 points each. Circle the letter of the best answer.

  1. 21.

    Two whole numbers multiply together to make 81, and one of them is 9 times the other. What is the smaller number?

    1. A8
    2. B6
    3. C27
    4. D9
    5. E3
  2. 22.

    A tub holds 19 balls numbered 1 to 19. Balls 1 to 12 are white, 13 to 15 are black and 16 to 19 are grey. One ball is taken out without looking. What is the chance that it is not grey and its number is not a multiple of 3?

    1. A15/19
    2. B9/19
    3. C13/19
    4. D11/19
    5. E10/19
  3. 23.

    A solid box is built from 42 identical cubes, with none left over and no gaps. A box that is only turned on its side is still the same box. How many different boxes can be built?

    1. A27
    2. B8
    3. C5
    4. D6
    5. E4
  4. 24.

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

    1. A5
    2. B10
    3. C4
    4. D15
    5. E14
  5. 25.

    How many factors does 90 have?

    1. A12
    2. B6
    3. C10
    4. D13
    5. E3
  6. 26.

    The drawing shows an arrowhead shape ABDC. What is the size of the angle marked x?

    1. A140°
    2. B155°
    3. C101°
    4. D115°
    5. E75°
  7. 27.

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

    1. AIvan
    2. BOmar
    3. CDina
    4. DRaj
    5. EYara
  8. 28.

    Each of these three numbers has one digit hidden by a question mark: 2?7, 6?6, 7?7. The average of the three numbers is 540. What is the sum of the three hidden digits?

    1. A9
    2. B100
    3. C10
    4. D1
    5. E3
  9. 29.

    Two whole numbers add to 46 and multiply to 513. What is the difference between them?

    1. A8
    2. B46
    3. C27
    4. D512
    5. E44
  10. 30.

    A palindrome is a number that reads the same forwards and backwards, such as 373. How many palindromes are there between 700 and 900?

    1. A30
    2. B20
    3. C2
    4. D18
    5. E200

Answers and working

Questions 1 to 10

  1. 1.E (135). There are (19 − 11) ÷ 1 + 1 = 9 numbers, and the first and last add to 11 + 19 = 30. Writing the run out backwards underneath itself makes 9 pairs of 30, so the total is 9 × 30 ÷ 2 = 135.
  2. 2.E ((40 ÷ 4) + (36 ÷ 4)). 76 = 40 + 36, so 76 ÷ 4 = (40 ÷ 4) + (36 ÷ 4), which is 19.
  3. 3.D (7/2). Most of the fractions cancel, and what is left is 7/2.
  4. 4.D (9). Counting size by size, from the smallest up to the biggest, finds 9 triangles.
  5. 5.C (Zoe). From heaviest to lightest, the order is Sara, Raj, Nia, Ava, Zoe. So the answer is Zoe.
  6. 6.B (1). Only the folds that make both halves match count, so this shape has 1 line of symmetry.
  7. 7.A (111). 6 steps of 3 take 132 down to 114, which is not below 113. One more step gives 111.
  8. 8.A (18). The total is 3 × 366 = 1098. The visible parts make 1080, so the hidden digits are worth 18. Whatever way they fit, the digits add to 18.
  9. 9.B (5 members). 11 + 8 − 3 = 16 do at least one, and the other 5 of the 21 do neither. So the answer is 5 members.
  10. 10.B (3). Listing the rectangles with the smaller side first, 3 of them have an area of 18.

Questions 11 to 20

  1. 11.B (33°). Angle ACB = 66°, so angle ACD = 114°, and the second triangle's equal angles are 33° each. The angle marked x is 33°.
  2. 12.D (7). Take 4x from both sides: 3x − 16 = 5. Add 16: 3x = 21. Divide by 3: x = 7.
  3. 13.C (1/18). The first draw is 2/9, and with one marble out the second is 2/8, so the chance is 2/9 × 2/8. So the answer is 1/18.
  4. 14.C (23). The primes 17, 19, 23 come one after another and add up to 59. The largest is 23.
  5. 15.A (29). Checking every number from 20 to 30 against all 3 clues, only 29 fits every one.
  6. 16.D (27). 20 divide by 12 and 13 divide by 18, but 6 of them divide by both (they are multiples of 36). 20 + 13 − 6 = 27.
  7. 17.B (441). The numbers 1 to 6 add to 21, and the cubes add to 21² = 441.
  8. 18.E (0). 3636 is 36 × 101, and 8787 is 87 × 101. 36 × 101 × 87 − 87 × 101 × 36: both parts are 36 × 87 × 101, so they cancel to 0. The value is 0.
  9. 19.D (13). The highest common factor of 65 and 78 is 13, so she makes 13 groups.
  10. 20.C (Eli). Try each child as the one with the ball and count the true statements. Only when Eli has it is exactly one statement true.

Questions 21 to 30

  1. 21.E (3). Call the smaller number n. The larger is 9n, so the two multiply to 9 × n × n = 81. That makes n × n = 81 ÷ 9 = 9, so n = 3 and the larger number is 27.
  2. 22.E (10/19). Leaving out the grey ones and every one whose number is a multiple of 3 leaves 10 of the 19: 10/19.
  3. 23.C (5). Listing the boxes with the three numbers going up, 5 of them multiply to 42.
  4. 24.D (15). Counting size by size, from the smallest up to the biggest, finds 15 triangles.
  5. 25.A (12). The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90: 12 of them.
  6. 26.E (75°). The four inside angles add to 360°: x = 360° − 220° − 39° − 26° = 75°.
  7. 27.B (Omar). Try each child as the one with the ball and count the true statements. Only when Omar has it are exactly 4 statements true.
  8. 28.C (10). The total is 3 × 540 = 1620. The visible parts make 1520, so the hidden digits are worth 100. Whatever way they fit, the digits add to 10.
  9. 29.A (8). Only 19 and 27 multiply to 513 and add to 46. The difference is 27 − 19 = 8: 8.
  10. 30.B (20). The last digit has to copy the first, so only the first two digits are chosen. The first can be 7 up to 8, which is 2 ways, and the middle digit is free with 10 ways: 2 × 10 = 20.

Written by Scholar Tests in the Kangaroo Math Competition's published shape. Not a past paper. We are not connected with Kangourou sans Frontières, Kangaroo Math Malaysia or any national organiser of the competition.

Sit a new paper online

Every online paper is new, timed like the real thing, and marked the moment it ends: 3, 4 or 5 points a question, with nothing taken off for a wrong answer.

  • Cadet (Years 7 and 8)

    30 questions · 75 minutes

    Logic, patterns, counting and picture puzzles, the hardest last. No calculator.

Questions parents ask

Is this paper right for Years 7 and 8?
Yes. It is the Cadet level, which the competition sets for Years 7 and 8 (Form 1 and 2 in Malaysia). A child in the younger year will find more of the last questions hard. That is how it is meant to be.
How is it marked?
Questions 1 to 10 are worth 3 points each, 11 to 20 are worth 4 and the last 10 are worth 5, so the paper is out of 120. Our marking takes nothing off for a wrong answer; check your own country's rules, as some take a quarter of the points off.
Can my child use a calculator?
No. The competition allows no calculator, only rough paper. Practise the same way.
Is it free?
The printed papers are free, with every answer. Online, a free account includes 3 practice tests. The maths competition pack (RM99 for 6 months) opens unlimited tests and shows the right answer and the working for every question.
Are these real past papers?
No. We write our own questions in the competition's published shape. Past papers belong to the organisers. We are not connected with Kangourou sans Frontières, Kangaroo Math Malaysia or any national organiser of the competition.

Papers for other years

Years 1 and 2Years 3 and 4Years 5 and 6Years 9 and 10Years 11 and 12