Scholar Tests · Sample paper
Primary maths challenge-style paper, Year 6
25 questions · 25 marks · 45 minutes · no negative marking
Name ______________________ Date ____________
Questions 1 to 20
Questions 1 to 20, 1 mark each. Circle the letter of the best answer.
- 1.
What fraction of the big square is shaded?
- A1/4
- B3/16
- C3/32
- D3/13
- E1/8
- 2.
A frog starts on 3 on a number line and hops forward 3 each time: 3, 6, 9, and so on. Where does it land after 3 hops?
- A13
- B11
- C12
- D15
- E9
- 3.
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?
- A5
- B4
- C7
- D2
- E12
- 4.
Five cards, each with a shape on it, were put down one at a time. Which card was put down first?
- A
- B
- C
- D
- E
- 5.
The shapes keep repeating in the same way. Which shape is 13th?
- A
- B
- C
- D
- E
- 6.
1 marble weighs the same as 2 pears. How many pears weigh the same as 5 marbles?
- A2
- B7
- C12
- D10
- E8
- 7.
Gus is older than Yara. Yara is older than Raj. Raj is older than Fay. Sara is older than Gus.
Who is the oldest?- AGus
- BYara
- CSara
- DFay
- ERaj
- 8.
How many triangles of any size are there in this figure?
- A4
- B5
- C7
- D3
- E6
- 9.
Zoe, Ivan and Yara are playing, and one of them has the ball.
Zoe says: "Ivan has the ball."
Ivan says: "Yara has the ball."
Yara says: "I have the ball."
Exactly one of them is telling the truth. Who has the ball?- AAva
- BOmar
- CIvan
- DYara
- EZoe
- 10.
Each of these three numbers has one digit hidden by a question mark: 46?, 1?4, 3?9. The average of the three numbers is 313. What is the sum of the three hidden digits?
- A7
- B6
- C66
- D0
- E12
- 11.
How many lines of symmetry does this shape have?
- A1
- B4
- C2
- D3
- E0
- 12.
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?
- A7
- B18
- C12
- D19
- E17
- 13.
Use each of the digits 0, 3, 8 and 4 once. What is the smallest number you can make? A number cannot start with 0.
- A3804
- B3048
- C3840
- D3084
- E348
- 14.
Find the missing number marked with the asterisk (*) in the magic square below. (Every row, column and diagonal adds to the same total.)
- A18
- B21
- C17
- D15
- E19
- 15.
702 ÷ 13 is the same as which of these?
- A(650 ÷ 13) − (52 ÷ 13)
- B(13 ÷ 650) + (13 ÷ 52)
- C(702 ÷ 9) + (702 ÷ 4)
- D(650 ÷ 13) × (52 ÷ 13)
- E(650 ÷ 13) + (52 ÷ 13)
- 16.
A floor is tiled with a 3 by 5 grid of small square tiles. How many squares of any size can be found on it, counting the small ones and every larger square they make up?
- A90
- B6
- C24
- D15
- E26
- 17.
In a Year 6 group with 32 students, 12 play tennis and 23 play football. Everyone does at least one of the two. How many do both?
- A35 students
- B20 students
- C9 students
- D11 students
- E3 students
- 18.
Two whole numbers multiply together to make 1352, and one of them is 8 times the other. What is the larger number?
- A107
- B150
- C104
- D169
- E13
- 19.
At 2:30 pm two buses leave the same stop together. After that, the first leaves every 16 minutes and the second every 12 minutes. At what time will they next leave together?
- A3:17 pm
- B2:46 pm
- C2:34 pm
- D2:58 pm
- E3:18 pm
- 20.
In the triangle below, what is the size of the angle marked x?
- A141°
- B281°
- C79°
- D101°
- E140°
Questions 21 to 25
Questions 21 to 25, 1 mark each. Write your answer on the line.
- 21.
The seats along one row of a hall are numbered 36, 37, 38 and so on up to 52. What do all the seat numbers add up to?
Answer: ______________
- 22.
A smallholding holds only hens and goats. Altogether there are 31 animals and 70 legs. How many hens are there?
Answer: ______________
- 23.
How many pairs of different whole numbers from 1 to 18 add up to 28?
Answer: ______________
- 24.
A palindrome is a number that reads the same forwards and backwards, such as 373. How many 5-digit palindromes are there?
Answer: ______________
- 25.
A tank held some litres of water. On the first day 3/5 of the water was used. On the second day 3/8 of the water that was left was used. On the third day 50% of what remained was used. On the fourth day 80% of the rest was used. There were 22 litres left. How many litres were used on the second day?
Answer: ______________
Answers and working
Questions 1 to 20
- 1.B (3/16). The big square has 16 small squares. The shaded part is 3 squares. So 3 out of 16 is shaded: 3/16.
- 2.C (12). 3 hops of 3 take the frog 9 along, from 3 to 12.
- 3.A (5). Listing every shape, with turned and flipped copies counted as the rules say, gives 5 shapes.
- 4.B. Wherever two cards overlap, the card on top came later. That gives the order triangle, star, square, circle, heart, so the card with the triangle was put down first.
- 5.D. The pattern repeats every 3 shapes. 13 = 3 × 4 + 1, so the 13th shape is the same as the 1st: a star.
- 6.D (10). Each marble can be swapped for 2 pears, so 5 marbles weigh the same as 5 × 2 = 10 pears.
- 7.C (Sara). From oldest to youngest, the order is Sara, Gus, Yara, Raj, Fay. So the answer is Sara.
- 8.E (6). Counting size by size, from the smallest up to the biggest, finds 6 triangles.
- 9.C (Ivan). Try each child as the one with the ball and count the true statements. Only when Ivan has it is exactly one statement true.
- 10.E (12). The total is 3 × 313 = 939. The visible parts make 873, so the hidden digits are worth 66. Whatever way they fit, the digits add to 12.
- 11.E (0). Only the folds that make both halves match count, so this shape has 0 lines of symmetry.
- 12.B (18). Listing every shape, with turned and flipped copies counted as the rules say, gives 18 shapes.
- 13.B (3048). The smallest number you can make from 0, 3, 8 and 4 is 3048.
- 14.A (18). The magic total is 3 × centre = 45. The diagonal through * gives 45 − 15 − 12 = 18.
- 15.E ((650 ÷ 13) + (52 ÷ 13)). 702 = 650 + 52, so 702 ÷ 13 = (650 ÷ 13) + (52 ÷ 13), which is 54.
- 16.E (26). Take the sizes one at a time: a square of side k can sit in (3 − k + 1) × (5 − k + 1) positions. Adding those up from k = 1 to 3 gives 26.
- 17.E (3 students). 12 + 23 = 35 is 3 more than the 32 students, because those 3 were counted in both groups. So the answer is 3 students.
- 18.C (104). Call the smaller number n. The larger is 8n, so the two multiply to 8 × n × n = 1352. That makes n × n = 1352 ÷ 8 = 169, so n = 13 and the larger number is 104.
- 19.E (3:18 pm). The smallest number that both 16 and 12 divide into is 48. So they meet again 48 minutes after 2:30 pm, which is 3:18 pm.
- 20.D (101°). 180° − 39° − 40° = 101°.
Questions 21 to 25
- 21.748. There are (52 − 36) ÷ 1 + 1 = 17 numbers, and the first and last add to 36 + 52 = 88. Writing the run out backwards underneath itself makes 17 pairs of 88, so the total is 17 × 88 ÷ 2 = 748.
- 22.27. If all 31 had two legs there would be 62 legs, but there are 70 — 8 extra. Each goat adds two extra legs, so there are 4 goats and 27 hens. The answer is 27.
- 23.4. Work up from the smallest number a pair could start with. It cannot be below 10, because its partner would then be more than 18, and it cannot be above 13, because after that the pairs repeat the other way round. That gives 10 + 18, 11 + 17, 12 + 16, 13 + 15 — 4 pairs.
- 24.900. 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.
- 25.132. Working back from 22 gives 352 before share 2 and 220 after it, so share 2 is 132. So the answer is 132.
Written by Scholar Tests in the primary maths challenge's published shape. Not a past paper; we are not connected with the Mathematical Association.