Maths competition practice

Maths competition practice paper for Years 9 and 10

A free paper in the shape of the Kangaroo Math Competition's Junior level (Form 3 and 4 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 9 and 10

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.

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

    1. ASara
    2. BIvan
    3. CFay
    4. DHana
    5. EOmar
  2. 2.

    Zoe rolls a die 13 times and gets: 4, 1, 3, 2, 6, 2, 5, 5, 2, 3, 3, 6, 2. From these results, what is the experimental probability of rolling a 1?

    1. A12/13
    2. B2/13
    3. C1/6
    4. D1/13
    5. E1/12
  3. 3.

    A competition has 10 teams in one pool. Every team plays every other team in its pool once. How many games are played altogether?

    1. A44
    2. B43
    3. C90
    4. D46
    5. E45
  4. 4.

    How many positive whole numbers divide exactly into 14?

    1. A5
    2. B4
    3. C1
    4. D2
    5. E3
  5. 5.

    A tub holds 19 balls numbered 1 to 19. Balls 1 to 7 are white, 8 to 13 are black and 14 to 19 are grey. One ball is taken out without looking. What is the chance that it is black and its number is odd?

    1. A10/19
    2. B1/2
    3. C6/19
    4. D16/19
    5. E3/19
  6. 6.

    What is the lowest common multiple of 4, 6, 10?

    1. A60
    2. B240
    3. C12
    4. D2
    5. E10
  7. 7.

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

    1. A145°
    2. B100°
    3. C15°
    4. D215°
    5. E35°
  8. 8.

    A right-angled triangle has a longest side of 17 cm and another side of 8 cm. What is its area, in square centimetres?

    1. A68
    2. B120
    3. C59
    4. D61
    5. E60
  9. 9.

    The mean of 9 numbers is 30. One of the numbers is taken away, and the mean of the 8 numbers left is 32. What number was taken away?

    1. A15
    2. B2
    3. C12
    4. D14
    5. E13
  10. 10.

    How many numbers are in the list 13, 21, 29, …, 229, where each number is 8 more than the one before?

    1. A28
    2. B30
    3. C26
    4. D27
    5. E29

Questions 11 to 20

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

  1. 11.

    How many numbers are in the list 13, 18, 23, …, 528, where each number is 5 more than the one before?

    1. A105
    2. B106
    3. C103
    4. D102
    5. E104
  2. 12.

    What is the value of 1³ + 2³ + 3³ + ... + 9³?

    1. A45
    2. B2025
    3. C1296
    4. D729
    5. E285
  3. 13.

    9 points are marked on a circle. How many triangles have all 3 of their corners at these points?

    1. A36
    2. B85
    3. C504
    4. D83
    5. E84
  4. 14.

    How many factors does 100 have?

    1. A2
    2. B5
    3. C10
    4. D9
    5. E7
  5. 15.

    How many three-digit whole numbers have digits that add up to 7?

    1. A15
    2. B28
    3. C26
    4. D27
    5. E29
  6. 16.

    Two whole numbers add to 8 and multiply to 15. What is the larger number?

    1. A5
    2. B3
    3. C4
    4. D15
    5. E8
  7. 17.

    The equation x2 − 6x + 8 = 0 has two whole-number solutions. What is the sum of the squares of its two solutions?

    1. A28
    2. B20
    3. C6
    4. D52
    5. E36
  8. 18.

    How many positive whole numbers divide exactly into 450?

    1. A18
    2. B16
    3. C8
    4. D4
    5. E19
  9. 19.

    A town's streets form a grid of square blocks. Ana walks from one corner of a rectangle 4 blocks wide and 3 blocks high to the opposite corner, always walking east or north along the streets. How many different routes can she take?

    1. A12
    2. B7
    3. C36
    4. D35
    5. E34
  10. 20.

    What is the last digit of 71571?

    1. A2
    2. B7
    3. C3
    4. D1
    5. E9

Questions 21 to 30

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

  1. 21.

    If 2x = 4x − 5, what is the value of x?

    1. A5
    2. B12
    3. C9
    4. D10
    5. E11
  2. 22.

    Four consecutive prime numbers add up to 556. What is the difference between the middle two?

    1. A6
    2. B18
    3. C10
    4. D276
    5. E2
  3. 23.

    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. A8
    2. B7
    3. C9
    4. D5
    5. E2
  4. 24.

    The mean of 23 numbers is 34. One of the numbers is taken away, and the mean of the 22 numbers left is 35.5. What number was taken away?

    1. A1
    2. B2
    3. C3
    4. D4
    5. E0
  5. 25.

    420 ÷ 15 is the same as which of these?

    1. A(15 ÷ 300) + (15 ÷ 120)
    2. B(300 ÷ 15) × (120 ÷ 15)
    3. C(420 ÷ 11) + (420 ÷ 4)
    4. D(300 ÷ 15) + (120 ÷ 15)
    5. E(300 ÷ 15) − (120 ÷ 15)
  6. 26.

    Find the value of x.
    11x + 8 = 7x + 32

    1. A24
    2. B6
    3. C10
    4. D7
    5. E5
  7. 27.

    In a class with 33 children, 13 have a dog, 19 play netball and 11 do both. How many do neither?

    1. A1 child
    2. B20 children
    3. C21 children
    4. D12 children
    5. E14 children
  8. 28.

    The number 536! means 1 × 2 × 3 × … × 536. How many zeros are at the end of 536! when it is written out in full?

    1. A131
    2. B132
    3. C107
    4. D53
    5. E133
  9. 29.

    What is the number formed by the last two digits of 7123?

    1. A61
    2. B43
    3. C44
    4. D49
    5. E42
  10. 30.

    A right-angled triangle has a longest side of 15 cm and another side of 9 cm. What is its area, in square centimetres?

    1. A54
    2. B108
    3. C90
    4. D55
    5. E53

Answers and working

Questions 1 to 10

  1. 1.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.
  2. 2.D (1/13). 1 of the 13 rolls was a 1, and 1/13 in simplest form is 1/13. So the answer is 1/13.
  3. 3.E (45). In one pool there are 10 × 9 ÷ 2 = 45 pairs of teams. That is 45 games.
  4. 4.B (4). 14 = 21 × 71. A divisor takes each prime to any power from 0 up, so there are 2 × 2 = 4 divisors.
  5. 5.E (3/19). Of the black ones, 8 to 13, the ones whose number is odd: 9, 11 and 13. That is 3 of the 19: 3/19.
  6. 6.A (60). 4 = 2 × 2, 6 = 2 × 3, 10 = 2 × 5. Taking the most of each prime gives 60.
  7. 7.A (145°). An outside angle equals the two far inside angles: 80° + 65° = 145°.
  8. 8.E (60). By Pythagoras, the third side is √(172 − 82) = 15 cm. The area is half of 8 × 15, which is 60.
  9. 9.D (14). The 9 numbers add up to 9 × 30 = 270. The 8 left add up to 8 × 32 = 256. The number taken away is the difference, 14.
  10. 10.A (28). From 13 to 229 is 216, which is 27 steps of 8. The list has one more number than steps: 28.

Questions 11 to 20

  1. 11.E (104). From 13 to 528 is 515, which is 103 steps of 5. The list has one more number than steps: 104.
  2. 12.B (2025). The numbers 1 to 9 add to 45, and the cubes add to 45² = 2025.
  3. 13.E (84). Any 3 of the points make exactly one triangle, so count the ways to choose 3 of the 9: 84.
  4. 14.D (9). The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100: 9 of them.
  5. 15.B (28). Fix the first digit, then count the ways the other digits can make up the rest of 7. Adding the cases gives 28.
  6. 16.A (5). Only 3 and 5 multiply to 15 and add to 8. The larger is 5: 5.
  7. 17.B (20). The solutions add to 6 and multiply to 8. The sum of the squares is 62 − 2 × 8 = 20.
  8. 18.A (18). 450 = 21 × 32 × 52. A divisor takes each prime to any power from 0 up, so there are 2 × 3 × 3 = 18 divisors.
  9. 19.D (35). Every route is 7 blocks long, 4 of them east. Choosing which 4 are east gives 35 routes.
  10. 20.C (3). The last digit of the powers of 7 repeat in a cycle. Find the cycle, then find where the power 1571 falls in it: the answer is 3.

Questions 21 to 30

  1. 21.D (10). 2 = 21 and 4 = 22, so 1x = 2(x − 5). That gives 10 = 1x, so x = 10.
  2. 22.E (2). The primes 131, 137, 139, 149 come one after another and add up to 556. The middle two, 137 and 139, are 2 apart.
  3. 23.A (8). Listing every shape, with turned and flipped copies counted as the rules say, gives 8 shapes.
  4. 24.A (1). The 23 numbers add up to 23 × 34 = 782. The 22 left add up to 22 × 35.5 = 781. The number taken away is the difference, 1.
  5. 25.D ((300 ÷ 15) + (120 ÷ 15)). 420 = 300 + 120, so 420 ÷ 15 = (300 ÷ 15) + (120 ÷ 15), which is 28.
  6. 26.B (6). Take 7x from both sides: 4x + 8 = 32. Take off 8: 4x = 24. Divide by 4: x = 6.
  7. 27.D (12 children). 13 + 19 − 11 = 21 do at least one, and the other 12 of the 33 do neither. So the answer is 12 children.
  8. 28.B (132). Each zero at the end comes from a 10 = 2 × 5, and there are far more 2s than 5s, so count the 5s. There are 107 multiples of 5, 21 multiples of 25, 4 multiples of 125, so 536! ends in 132 zeros.
  9. 29.B (43). The last two digits of the powers of 7 repeat in a cycle. Find the cycle, then find where the power 123 falls in it: the answer is 43.
  10. 30.A (54). By Pythagoras, the third side is √(152 − 92) = 12 cm. The area is half of 9 × 12, which is 54.

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.

  • Junior (Years 9 and 10)

    30 questions · 75 minutes

    Number theory, algebra, counting and geometry puzzles, the hardest last. No calculator.

Questions parents ask

Is this paper right for Years 9 and 10?
Yes. It is the Junior level, which the competition sets for Years 9 and 10 (Form 3 and 4 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 7 and 8Years 11 and 12