Maths competition practice

Maths competition practice paper for Years 3 and 4

A free paper in the shape of the Kangaroo Math Competition's Ecolier level (Standard 3 and 4 in Malaysia): 24 questions in 75 minutes, five choices each, for 96 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 3 and 4

24 questions · 96 points · 75 minutes · no negative marking

Name ______________________ Date ____________

Questions 1 to 8

Questions 1 to 8, 3 points each. Circle the letter of the best answer.

  1. 1.

    A league has 13 players. Every one of them plays one game against every other one. How many games are there altogether?

    1. A79
    2. B78
    3. C169
    4. D91
    5. E156
  2. 2.

    The shapes keep repeating in the same way. Which shape is 19th?

    1. A
    2. B
    3. C
    4. D
    5. E
  3. 3.

    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. B22
    3. C19
    4. D21
    5. E20
  4. 4.

    Each of these three numbers has one digit hidden by a question mark: 30?, 2?3, 6?4. The average of the three numbers is 415. What is the sum of the three hidden digits?

    1. A10
    2. B8
    3. C138
    4. D7
    5. E21
  5. 5.

    Use each of the digits 7, 8 and 2 once. What is the smallest number you can make?

    1. A728
    2. B279
    3. C278
    4. D872
    5. E782
  6. 6.

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

    1. AGus
    2. BKai
    3. CMilo
    4. DWes
    5. EIvan
  7. 7.

    How many shaded triangles are there in the picture?

    1. A2
    2. B1
    3. C3
    4. D7
    5. E4
  8. 8.

    What fraction of the big square is shaded?

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

Questions 9 to 16

Questions 9 to 16, 4 points each. Circle the letter of the best answer.

  1. 9.

    A smallholding holds only hens and goats. Altogether there are 29 animals and 68 legs. How many hens are there?

    1. A39
    2. B24
    3. C17
    4. D34
    5. E5
  2. 10.

    Use each of the digits 0, 8, 9 and 2 once. What is the smallest odd number you can make? A number cannot start with 0.

    1. A289
    2. B8029
    3. C8902
    4. D2089
    5. E8092
  3. 11.

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

    1. AFay
    2. BUma
    3. CIvan
    4. DSara
    5. ECarlos
  4. 12.

    Hana is slower than Raj. Hana is slower than Gus. Kai is faster than Yara. Gus is slower than Yara.
    Who is the slowest?

    1. AKai
    2. BHana
    3. CRaj
    4. DYara
    5. EGus
  5. 13.

    The shapes keep repeating in the same way. How many squares are there in the first 16 shapes?

    1. A6
    2. B5
    3. C8
    4. D4
    5. E7
  6. 14.

    2 pears weigh the same as 3 balls. 1 ball weighs the same as 2 shells. How many shells weigh the same as 4 pears?

    1. A8
    2. B6
    3. C13
    4. D11
    5. E12
  7. 15.

    A straight cycle path is 2,000 m long. There is a bollard every 8 m along it, including one at each end. How many bollards are there?

    1. A261
    2. B252
    3. C250
    4. D251
    5. E222
  8. 16.

    Five cards, each with a shape on it, were put down one at a time. Which card was put down second?

    1. A
    2. B
    3. C
    4. D
    5. E

Questions 17 to 24

Questions 17 to 24, 5 points each. Circle the letter of the best answer.

  1. 17.

    Five cards, each with a shape on it, were put down one at a time. Which card was put down third?

    1. A
    2. B
    3. C
    4. D
    5. E
  2. 18.

    A frog starts on 12 on a number line and hops forward 3 each time: 12, 15, 18, and so on. Which of these numbers does it land on?

    1. A62
    2. B61
    3. C60
    4. D58
    5. E59
  3. 19.

    A window is made of a 5 by 5 grid of small square panes. How many squares of any size can be found on it, counting the small ones and every larger square they make up?

    1. A225
    2. B25
    3. C36
    4. D55
    5. E15
  4. 20.

    What fraction of the big square is shaded?

    1. A3/4
    2. B7/8
    3. C11/16
    4. D11/32
    5. E5/8
  5. 21.

    How many triangles that have a square directly to their right are there in the picture?

    1. A3
    2. B4
    3. C2
    4. D5
    5. E9
  6. 22.

    Two numbers add to 52, and one is 18 more than the other. What is the larger number?

    1. A17
    2. B35
    3. C26
    4. D34
    5. E9
  7. 23.

    1 apple and 1 block together weigh the same as 8 plums. 1 apple weighs the same as 6 plums. How many plums weigh the same as 3 blocks?

    1. A24
    2. B18
    3. C6
    4. D2
    5. E11
  8. 24.

    Fay is slower than Omar. Sara is faster than Omar. Dina is slower than Fay. Omar is faster than Ava.
    Who is the second fastest?

    1. ADina
    2. BAva
    3. CSara
    4. DFay
    5. EOmar

Answers and working

Questions 1 to 8

  1. 1.B (78). Each of the 13 meets 12 others, which counts 13 × 12 = 156 — but that counts every pair twice, so halve it to get 78.
  2. 2.C. The pattern repeats every 3 shapes. 19 = 3 × 6 + 1, so the 19th shape is the same as the 1st: a triangle.
  3. 3.D (21). The magic total is 3 × centre = 57. The diagonal through * gives 57 − 19 − 17 = 21.
  4. 4.E (21). The total is 3 × 415 = 1245. The visible parts make 1107, so the hidden digits are worth 138. Whatever way they fit, the digits add to 21.
  5. 5.C (278). The smallest number you can make from 7, 8 and 2 is 278.
  6. 6.C (Milo). Try each child as the one with the ball and count the true statements. Only when Milo has it is exactly one statement true.
  7. 7.C (3). Going row by row and ticking each one that fits, there are 3 shaded triangles.
  8. 8.C (1/4). The big square has 4 small squares. The shaded part is 1 squares. So 1 out of 4 is shaded: 1/4.

Questions 9 to 16

  1. 9.B (24). If all 29 had two legs there would be 58 legs, but there are 68 — 10 extra. Each goat adds two extra legs, so there are 5 goats and 24 hens. The answer is 24.
  2. 10.D (2089). The smallest odd number you can make from 0, 8, 9 and 2 is 2089.
  3. 11.B (Uma). Try each child as the one with the ball and count the true statements. Only when Uma has it is exactly one statement true.
  4. 12.B (Hana). The clues do not fix the whole order, but in every order they allow, Hana is in that place.
  5. 13.A (6). Each repeat of 3 shapes has 1 square. 16 shapes make 5 whole repeats (5) and 1 more shapes, which hold 1. So there are 6.
  6. 14.E (12). 4 pears weigh the same as 6 balls, and each ball is 2 shells, so the answer is 6 × 2 = 12.
  7. 15.D (251). 2,000 ÷ 8 = 250, so there are 250 gaps. Something stands at both ends, so there is one more bollard than gaps: 250 + 1 = 251.
  8. 16.C. Wherever two cards overlap, the card on top came later. That gives the order star, circle, triangle, square, heart, so the card with the circle was put down second.

Questions 17 to 24

  1. 17.E. Wherever two cards overlap, the card on top came later. That gives the order triangle, square, circle, star, heart, so the card with the circle was put down third.
  2. 18.C (60). The frog lands on 12 plus a whole number of 3s. 60 − 12 = 48 = 16 × 3, so it lands on 60. None of the others is a whole number of hops from 12.
  3. 19.D (55). Take the sizes one at a time: a square of side k can sit in (5 − k + 1) × (5 − k + 1) positions. Adding those up from k = 1 to 5 gives 55, which on a square grid is just 1² + 2² + … + 5².
  4. 20.C (11/16). The big square has 16 small squares. The shaded part is 8 whole squares and 6 halves, which is 11 squares. So 11 out of 16 is shaded: 11/16.
  5. 21.A (3). Going row by row and ticking each one that fits, there are 3 triangles that have a square directly to their right.
  6. 22.B (35). Take the difference off the total first: 52 − 18 = 34. That is what TWO of the smaller one come to, so the smaller is 17 and the larger is 17 + 18 = 35.
  7. 23.C (6). Take the apple off: 8 − 6 = 2, so one block weighs the same as 2 plums, and 3 blocks weigh the same as 6 plums.
  8. 24.E (Omar). The clues do not fix the whole order, but in every order they allow, Omar is in that place.

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.

  • Ecolier (Years 3 and 4)

    24 questions · 75 minutes

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

Questions parents ask

Is this paper right for Years 3 and 4?
Yes. It is the Ecolier level, which the competition sets for Years 3 and 4 (Standard 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 8 are worth 3 points each, 9 to 16 are worth 4 and the last 8 are worth 5, so the paper is out of 96. 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 5 and 6Years 7 and 8Years 9 and 10Years 11 and 12