Maths competition practice

Maths competition practice paper for Years 5 and 6

A free paper in the shape of the Kangaroo Math Competition's Benjamin level (Standard 5 and 6 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 5 and 6

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.

    At 7:15 pm two trams leave the terminus together. After that, the first leaves every 8 minutes and the second every 12 minutes. At what time will they next leave together?

    1. A7:35 pm
    2. B7:39 pm
    3. C7:40 pm
    4. D7:27 pm
    5. E7:19 pm
  2. 2.

    Square tiles are joined edge to edge to make flat shapes. A shape that matches another when it is turned round or flipped over is not a new shape. How many different shapes can be made from four tiles?

    1. A12
    2. B7
    3. C2
    4. D4
    5. E5
  3. 3.

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

    1. AIvan
    2. BLena
    3. CHana
    4. DEli
    5. EGus
  4. 4.

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

    1. A5
    2. B3
    3. C6
    4. D4
    5. E2
  5. 5.

    Use each of the digits 2, 9 and 6 once. What is the smallest number you can make?

    1. A962
    2. B270
    3. C269
    4. D926
    5. E296
  6. 6.

    How many pairs of different whole numbers from 1 to 16 add up to 24?

    1. A5
    2. B11
    3. C4
    4. D3
    5. E8
  7. 7.

    What is the total of all the whole numbers from 9 to 15, counting both ends?

    1. A72
    2. B12
    3. C24
    4. D84
    5. E168
  8. 8.

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

    1. A120°
    2. B135°
    3. C105°
    4. D60°
    5. E240°
  9. 9.

    12 ÷ 4 × 6 is the same as which of these?

    1. A12 × 4 ÷ 6
    2. B4 ÷ 12 × 6
    3. C12 ÷ (4 × 6)
    4. D(12 + 6) ÷ 4
    5. E12 × 6 ÷ 4
  10. 10.

    A bar of chocolate is scored 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. A6
    2. B9
    3. C16
    4. D36
    5. E14

Questions 11 to 20

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

  1. 11.

    Dina, Hana, Zoe, Ivan and Pia are playing, and one of them has the ball.
    Dina says: "Hana has the ball."
    Hana says: "Dina has the ball."
    Zoe says: "Dina has the ball."
    Ivan says: "Dina does not have the ball."
    Pia says: "Zoe does not have the ball."
    Exactly one of them is telling the truth. Who has the ball?

    1. AHana
    2. BIvan
    3. CDina
    4. DZoe
    5. EPia
  2. 12.

    What fraction of the big square is shaded?

    1. A7/9
    2. B7/16
    3. C1/2
    4. D7/32
    5. E3/8
  3. 13.

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

    1. A10
    2. B4
    3. C15
    4. D14
    5. E5
  4. 14.

    Milo is younger than Gus. Milo is younger than Pia. Dina is older than Milo. Hana is older than Dina.
    Who is the youngest?

    1. APia
    2. BDina
    3. CHana
    4. DGus
    5. EMilo
  5. 15.

    A league has 14 players. Every one of them plays one game against every other one. How many games are there altogether?

    1. A196
    2. B90
    3. C91
    4. D105
    5. E182
  6. 16.

    How many lines of symmetry does this shape have?

    1. A3
    2. B2
    3. C7
    4. D0
    5. E1
  7. 17.

    Use each of the digits 8, 6, 3, 2, 0 once to make the smallest even 5-digit number. What digit is in the tens place?

    1. A3
    2. B2
    3. C6
    4. D8
    5. E0
  8. 18.

    2 blocks weigh the same as 3 pears. 1 pear weighs the same as 2 plums. How many plums weigh the same as 6 blocks?

    1. A12
    2. B13
    3. C19
    4. D9
    5. E18
  9. 19.

    When a number is multiplied by 4, the answer is the same as multiplying that number by 2 and then adding 32. What is the number?

    1. A19
    2. B8
    3. C5
    4. D16
    5. E15
  10. 20.

    A smallholding holds only hens and goats. Altogether there are 41 animals and 102 legs. How many hens are there?

    1. A31
    2. B26
    3. C10
    4. D51
    5. E61

Questions 21 to 30

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

  1. 21.

    Estimate 331 + 176 + 422 by rounding each number to the nearest ten.

    1. A929
    2. B928
    3. C920
    4. D950
    5. E930
  2. 22.

    What fraction of the big square is shaded?

    1. A3/5
    2. B3/8
    3. C1/2
    4. D5/16
    5. E7/16
  3. 23.

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

    1. A78°
    2. B170°
    3. C124°
    4. D134°
    5. E107°
  4. 24.

    A palindrome is a number that reads the same forwards and backwards, such as 373. How many 6-digit palindromes are there?

    1. A900000
    2. B90
    3. C900
    4. D9000
    5. E1000
  5. 25.

    Square tiles are joined edge to edge to make flat shapes. A shape that matches another when it is turned round or flipped over is not a new shape. How many different shapes can be made from five tiles?

    1. A5
    2. B11
    3. C13
    4. D12
    5. E18
  6. 26.

    A shop had some jars of honey. On Monday it sold 0.6 of the jars. On Tuesday it sold 7/8 of the jars that were left. On Wednesday it sold 1/3 of the jars still on the shelf. It then had 40 jars left. How many jars did it have at first?

    1. A1200
    2. B160
    3. C800
    4. D60
    5. E480
  7. 27.

    At a holiday camp with 46 children, 27 play chess and 30 play tennis. Everyone does at least one of the two. How many do both?

    1. A57 children
    2. B16 children
    3. C3 children
    4. D11 children
    5. E19 children
  8. 28.

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

    1. A22
    2. B21
    3. C19
    4. D23
    5. E25
  9. 29.

    Use each of the digits 8, 1, 7, 5, 0 once to make the smallest even 5-digit number. What digit is in the thousands place?

    1. A8
    2. B7
    3. C1
    4. D0
    5. E5
  10. 30.

    Ethan stacks cans in a triangle. The top row has 1 can, the row below it has 2, the next has 3, and so on down to 40 cans in the bottom row. How many cans are in the whole stack?

    1. A861
    2. B780
    3. C820
    4. D1600
    5. E1640

Answers and working

Questions 1 to 10

  1. 1.B (7:39 pm). The smallest number that both 8 and 12 divide into is 24. So they meet again 24 minutes after 7:15 pm, which is 7:39 pm.
  2. 2.E (5). Listing every shape, with turned and flipped copies counted as the rules say, gives 5 shapes.
  3. 3.D (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.
  4. 4.D (4). Counting size by size, from the smallest up to the biggest, finds 4 triangles.
  5. 5.C (269). The smallest number you can make from 2, 9 and 6 is 269.
  6. 6.C (4). Work up from the smallest number a pair could start with. It cannot be below 8, because its partner would then be more than 16, and it cannot be above 11, because after that the pairs repeat the other way round. That gives 8 + 16, 9 + 15, 10 + 14, 11 + 13 — 4 pairs.
  7. 7.D (84). There are (15 − 9) ÷ 1 + 1 = 7 numbers, and the first and last add to 9 + 15 = 24. Writing the run out backwards underneath itself makes 7 pairs of 24, so the total is 7 × 24 ÷ 2 = 84.
  8. 8.D (60°). 180° − 45° − 75° = 60°.
  9. 9.E (12 × 6 ÷ 4). 12 ÷ 4 × 6 = 18, and so does 12 × 6 ÷ 4.
  10. 10.E (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.

Questions 11 to 20

  1. 11.D (Zoe). Try each child as the one with the ball and count the true statements. Only when Zoe has it is exactly one statement true.
  2. 12.B (7/16). The big square has 16 small squares. The shaded part is 7 squares. So 7 out of 16 is shaded: 7/16.
  3. 13.C (15). Counting size by size, from the smallest up to the biggest, finds 15 triangles.
  4. 14.E (Milo). The clues do not fix the whole order, but in every order they allow, Milo is in that place.
  5. 15.C (91). Each of the 14 meets 13 others, which counts 14 × 13 = 182 — but that counts every pair twice, so halve it to get 91.
  6. 16.E (1). Only the folds that make both halves match count, so this shape has 1 line of symmetry.
  7. 17.C (6). The smallest even number from those digits is 20368. Its tens digit is 6.
  8. 18.E (18). 6 blocks weigh the same as 9 pears, and each pear is 2 plums, so the answer is 9 × 2 = 18.
  9. 19.D (16). Multiplying by 4 rather than by 2 adds 4 − 2 = 2 lots of the number. Those 2 lots come to 32, so the number is 32 ÷ 2 = 16.
  10. 20.A (31). If all 41 had two legs there would be 82 legs, but there are 102 — 20 extra. Each goat adds two extra legs, so there are 10 goats and 31 hens. The answer is 31.

Questions 21 to 30

  1. 21.E (930). Round each number to the nearest ten: 330 + 180 + 420 = 930.
  2. 22.B (3/8). The big square has 16 small squares. The shaded part is 4 whole squares and 4 halves, which is 6 squares. So 6 out of 16 is shaded: 3/8.
  3. 23.A (78°). The four inside angles add to 360°: x = 360° − 226° − 27° − 29° = 78°.
  4. 24.C (900). The back half copies the front half, so only the first three digits are chosen. The first cannot be 0, giving 9 ways, and each other free digit has 10: 9 × 10 × 10 = 900.
  5. 25.D (12). Listing every shape, with turned and flipped copies counted as the rules say, gives 12 shapes.
  6. 26.A (1200). Working back from 40 through the 3 shares gives 1200 at the start. So the answer is 1200.
  7. 27.D (11 children). 27 + 30 = 57 is 11 more than the 46 children, because those 11 were counted in both groups. So the answer is 11 children.
  8. 28.A (22). The magic total is 3 × centre = 57. The diagonal through * gives 57 − 19 − 16 = 22.
  9. 29.D (0). The smallest even number from those digits is 10578. Its thousands digit is 0.
  10. 30.C (820). This is 1 + 2 + 3 + … + 40. Pairing the rows from both ends gives 40 pairs of 41, which counts every row twice — so halve it: 40 × 41 ÷ 2 = 820.

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.

  • Benjamin (Years 5 and 6)

    30 questions · 75 minutes

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

Questions parents ask

Is this paper right for Years 5 and 6?
Yes. It is the Benjamin level, which the competition sets for Years 5 and 6 (Standard 5 and 6 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 7 and 8Years 9 and 10Years 11 and 12