Sutton Boys' Second Stage Maths Mock Paper 9

Preparation for the Sutton Boys' Second Stage Examination, sat for admission to Wilson's School, Sutton Grammar School and Wallington County Grammar School. This is an original mock paper written by Revision Library. It is not a past paper and it is not an official specimen.

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Time allowed: 50 minutes
Total marks: 40
Questions: 22
Level: Hard

You have 50 minutes for this paper. There are 22 questions and 40 marks altogether. The number of marks is printed beside each question.
Show your working. Several questions carry marks for method, so a sensible method still earns credit even when the final answer is wrong.
Write your answers in the spaces provided in this booklet. There is no separate answer sheet.
You may not use a calculator. Use the space beside each question for rough work.
Diagrams are described in words and are not drawn to size. Always work from the measurements you are given, never by measuring.
The questions are not in order of difficulty. If one is holding you up, leave it and come back to it at the end.

Mathematics

Answer every question. Write each answer clearly in the space provided.

12 marks
Two whole numbers add up to 96. The difference between the same two numbers is 14.
Work out the product of the two numbers.
Answer:
21 mark
Here are four numbers written in different ways.
0.7 3/5 65 per cent 2/3
Write them in order, starting with the smallest.
Answer:
33 marks
A rectangle has an area of 160 square centimetres. Its length is 6 cm longer than its width, and both measurements are whole numbers of centimetres.
Work out the perimeter of the rectangle. Give your answer in centimetres. The rectangle is not drawn to size.
Answer:
42 marks
A pictogram shows how many trees were planted in four parks last winter. Each complete tree symbol stands for 8 trees, and part symbols stand for the matching fraction of 8.
Ashwood Park: four and a half symbols. Beechfield Park: three symbols. Cedar Rise: five and a quarter symbols. Dell End: two and three quarter symbols.
How many trees were planted altogether?
Answer:
51 mark
A wall is 3.6 m long. A shelf fixed to it is 145 cm long.
How much shorter than the wall is the shelf? Give your answer in centimetres.
Answer:
62 marks
Two fifths of the seats in a theatre are in the stalls.
Of the seats that are not in the stalls, three quarters are in the circle and the rest are in the balcony.
What fraction of all the seats in the theatre are in the balcony? Give your answer in its simplest form.
Answer:
71 mark
Eight identical hardback books have a total mass of 2.96 kg.
What is the mass of one book? Give your answer in kilograms.
Answer:
83 marks
In a sequence, every term from the third onwards is found by adding together the two terms immediately before it.
The fourth term is 19 and the fifth term is 31.
What is the first term?
Answer:
92 marks
The three angles inside a triangle are in the ratio 2 : 3 : 5.
Work out the size of the largest angle. Give your answer in degrees. The triangle is not drawn to size.
Answer:
101 mark
A fair coin is flipped and at the same time a fair six-sided dice is rolled.
What is the probability of getting a head on the coin and a six on the dice? Give your answer as a fraction.
Answer:
113 marks
A weather station recorded the rainfall for each of the first six months of the year, in millimetres.
January 82, February 55, March 68, April 47, May 39, June 27.
How much greater than the mean monthly rainfall was the rainfall in January? Give your answer in millimetres.
Answer:
122 marks
A cinema screen has 14 rows of seats and every row holds 22 seats. At one showing, 45 of the seats are empty.
Each ticket sold costs 7 pounds 50 pence.
How much money does the cinema take for that showing? Give your answer in pounds.
Answer:
131 mark
A straight nature trail is 1.25 km long. Wooden markers are placed along it every 250 m, with one marker at each end of the trail.
How many markers are there?
Answer:
143 marks
A box holds 30 raffle tickets, numbered 1 to 30 with no number repeated. One ticket is drawn at random.
What is the probability that the number on the drawn ticket is a multiple of 3 but is not a multiple of 5? Give your answer as a fraction in its simplest form.
Answer:
152 marks
Last year 250 pupils entered a national maths challenge.
This year the number of pupils entering fell by 12 per cent.
How many pupils entered the challenge this year?
Answer:
161 mark
A cuboid box has a square base with sides of 4 cm. Its volume is 112 cubic centimetres.
How tall is the box? Give your answer in centimetres. The box is not drawn to size.
Answer:
172 marks
A designer makes patterns from square tiles. Pattern 1 uses 5 tiles, pattern 2 uses 9 tiles and pattern 3 uses 13 tiles. The patterns carry on growing in the same way.
Which pattern uses exactly 61 tiles?
Answer:
181 mark
A bar chart shows how many goals a hockey team scored in each of its last six matches. The bars read 2, 0, 3, 1, 4 and 2 goals.
What is the median number of goals?
Answer:
193 marks
Hannah, Isaac and Jade club together to buy one present.
Hannah pays one third of the cost and Isaac pays two fifths of the cost. Jade pays the remaining 12 pounds.
What is the total cost of the present? Give your answer in pounds.
Answer:
201 mark
A whole number is a multiple of 6 and also a multiple of 8. The number lies between 100 and 130.
What is the number?
Answer:
212 marks
A recipe says that a joint of meat should be roasted for 35 minutes for every kilogram, plus an extra 20 minutes.
A joint has a mass of 2.4 kg.
For how long should it be roasted? Give your answer in hours and minutes.
Answer:
221 mark
A parallelogram has two shorter sides of 7 cm each and two longer sides that are equal to each other. Its perimeter is 46 cm.
How long is each of the longer sides? Give your answer in centimetres. The shape is not drawn to size.
Answer:

Answers, mark scheme and worked explanations

12 marks
2255
- 1 mark for identifying the two numbers as 55 and 41.
- 1 mark for a product of 2255.
If the two numbers were equal they would each be 48. The difference of 14 means one is 7 above that middle and the other is 7 below it.
So the numbers are 48 + 7 = 55 and 48 - 7 = 41. Check: 55 + 41 = 96 and 55 - 41 = 14.
The product is 55 x 41 = 55 x 40 + 55 = 2200 + 55 = 2255.
Always test a pair against both facts. A pair such as 55 and 41 must add to 96 and differ by 14, and only one pair does both.
21 mark
3/5, 65 per cent, 2/3, 0.7
- 1 mark for the complete order 3/5, 65 per cent, 2/3, 0.7. An order that is only partly right scores nothing.
Turn all four into decimals so they can be compared fairly.
3/5 = 0.6, 65 per cent = 0.65, 2/3 = 0.666..., and 0.7 is already a decimal.
In order: 0.6, 0.65, 0.666..., 0.7, which is 3/5, 65 per cent, 2/3, 0.7.
The two closest are 65 per cent and 2/3. Two thirds is 66.7 per cent, so it is the larger of the pair.
33 marks
52 cm
- 1 mark for testing pairs of numbers that multiply to give 160.
- 1 mark for a width of 10 cm and a length of 16 cm.
- 1 mark for a perimeter of 52 cm.
List pairs of whole numbers that multiply to 160: 1 and 160, 2 and 80, 4 and 40, 5 and 32, 8 and 20, 10 and 16.
Now look for the pair that differs by 6. The pair 8 and 20 differs by 12, and 10 and 16 differs by 6.
So the width is 10 cm and the length is 16 cm.
Perimeter = 2 x (10 + 16) = 52 cm.
Answering 160 or 26 means giving the area again, or giving only half the perimeter.
42 marks
124
- 1 mark for at least three of the four park totals correct from 36, 24, 42 and 22.
- 1 mark for 124 trees.
Each symbol is 8 trees, so half a symbol is 4 trees and a quarter of a symbol is 2 trees.
Ashwood: 4 x 8 + 4 = 36. Beechfield: 3 x 8 = 24. Cedar Rise: 5 x 8 + 2 = 42. Dell End: 2 x 8 + 6 = 22.
36 + 24 = 60, and 42 + 22 = 64, so the total is 60 + 64 = 124 trees.
Counting the symbols instead of the trees gives 15 and a half, which is the answer to a different question.
51 mark
215 cm
Change both lengths to the same unit: 3.6 m is 360 cm.
360 - 145 = 215 cm.
62 marks
3/20
- 1 mark for three fifths of the seats being outside the stalls.
- 1 mark for 3/20.
If two fifths are in the stalls, three fifths are not.
The balcony is the quarter of those seats that is not in the circle, so the balcony is 1/4 of 3/5.
1/4 x 3/5 = 3/20.
Check with a real number: if the theatre had 200 seats, 80 are stalls, 90 are circle and 30 are balcony, and 30 out of 200 is 3/20.
Answering 1/4 gives the fraction of the non-stalls seats, not of the whole theatre.
71 mark
0.37 kg
Divide 2.96 by 8. Halving three times is quick: 2.96, 1.48, 0.74, 0.37.
So one book has a mass of 0.37 kg, which is 370 g.
83 marks
5
- 1 mark for a third term of 12.
- 1 mark for a second term of 7.
- 1 mark for a first term of 5.
The fifth term is the third term plus the fourth term, so 31 = third term + 19, which makes the third term 12.
The fourth term is the second plus the third, so 19 = second term + 12, which makes the second term 7.
The third term is the first plus the second, so 12 = first term + 7, which makes the first term 5.
Check forwards: 5, 7, 12, 19, 31.
Subtracting in the wrong direction, for example doing 19 - 31, is what usually goes wrong on this kind of question.
92 marks
90 degrees
- 1 mark for one part being 18 degrees.
- 1 mark for 90 degrees.
The angles of a triangle add to 180 degrees, and the ratio has 2 + 3 + 5 = 10 parts.
One part is 180 / 10 = 18 degrees.
The largest angle is 5 parts: 5 x 18 = 90 degrees, so the triangle is right-angled.
Check: 36 + 54 + 90 = 180. Taking 5 as the answer gives the number of parts, not the angle.
101 mark
1/12
- Accept 1/12 only. 1/2 and 1/6 each describe only one of the two events.
There are 2 results for the coin and 6 for the dice, so there are 2 x 6 = 12 equally likely combinations.
Only one of them is a head with a six, so the probability is 1/12.
Adding 1/2 and 1/6 to get 2/3 treats the two events as alternatives instead of as things that both have to happen.
113 marks
29 mm
- 1 mark for a total of 318 mm.
- 1 mark for a mean of 53 mm.
- 1 mark for 29 mm.
Add the six months: 82 + 55 = 137, 137 + 68 = 205, 205 + 47 = 252, 252 + 39 = 291, and 291 + 27 = 318 mm.
The mean is 318 / 6 = 53 mm.
January had 82 mm, so it was 82 - 53 = 29 mm above the mean.
Dividing by 5 rather than 6 gives 63.6 and comes from counting the gaps between months instead of the months themselves.
122 marks
1972.50
- 1 mark for 263 tickets sold.
- 1 mark for 1972 pounds 50 pence.
The screen has 14 x 22 = 308 seats.
45 are empty, so 308 - 45 = 263 tickets were sold.
263 x 7.50: 263 x 7 = 1841 and half of 263 is 131.50, so the total is 1841 + 131.50 = 1972.50 pounds.
Charging for all 308 seats gives 2310 pounds and forgets the empty seats.
131 mark
6
1.25 km is 1250 m, and 1250 / 250 = 5, so there are 5 gaps between markers.
A line of 5 gaps needs 6 markers, because there is one at the start as well as one at the end of every gap.
Answering 5 counts the gaps rather than the markers. Sketching a short line with markers on it makes this clear.
143 marks
4/15
- 1 mark for 10 multiples of 3 between 1 and 30.
- 1 mark for removing 15 and 30 to leave 8 successful tickets.
- 1 mark for 4/15.
The multiples of 3 from 1 to 30 are 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30. That is 10 tickets.
Two of those are also multiples of 5: 15 and 30. The question says the number must not be a multiple of 5, so cross those two out.
That leaves 8 tickets out of 30, so the probability is 8/30.
Divide both numbers by 2: 8/30 = 4/15.
Forgetting to remove 15 and 30 gives 1/3, and it is the single most likely wrong answer here.
152 marks
220
- 1 mark for a fall of 30 pupils.
- 1 mark for 220 pupils.
10 per cent of 250 is 25, and 1 per cent is 2.5, so 12 per cent is 25 + 5 = 30 pupils.
250 - 30 = 220 pupils entered this year.
You could also work out 88 per cent of 250 straight away, which is the same 220.
Adding the 30 rather than subtracting it gives 280 and misses the word fell.
161 mark
7 cm
The base has area 4 x 4 = 16 square centimetres.
Volume is the base area multiplied by the height, so the height is 112 / 16 = 7 cm.
Check: 4 x 4 x 7 = 112.
172 marks
15
- 1 mark for seeing that each pattern adds 4 tiles, so 61 - 5 = 56 extra tiles are needed.
- 1 mark for pattern 15.
Each new pattern adds 4 more tiles than the one before.
Getting from pattern 1 to the pattern with 61 tiles means adding 61 - 5 = 56 tiles.
56 / 4 = 14 extra steps, so it is 14 patterns after pattern 1, which is pattern 15.
Check: pattern 15 uses 5 + 14 x 4 = 5 + 56 = 61 tiles.
Working out 61 / 4 and answering 15 by luck is not the same method, and the same shortcut fails on the next question of this type.
181 mark
2
Put the values in order: 0, 1, 2, 2, 3, 4.
There are six values, so there is no single middle one. Take the two middle values, the third and fourth, which are 2 and 2.
The median is halfway between them, which is 2.
Reading the middle of the list as written down, without sorting it first, gives 3 and is wrong.
193 marks
45
- 1 mark for Hannah and Isaac paying 11/15 of the cost between them.
- 1 mark for Jade's 12 pounds being 4/15 of the cost.
- 1 mark for 45 pounds.
Put the two fractions over a common denominator of 15: one third is 5/15 and two fifths is 6/15.
Together Hannah and Isaac pay 5/15 + 6/15 = 11/15 of the cost.
Jade pays the rest, which is 15/15 - 11/15 = 4/15, and that is 12 pounds.
So 1/15 of the cost is 12 / 4 = 3 pounds, and the whole present costs 15 x 3 = 45 pounds.
Check: Hannah pays 15 pounds, Isaac pays 18 pounds and Jade pays 12 pounds, which adds to 45.
201 mark
120
A number that is a multiple of both 6 and 8 must be a multiple of 24, the smallest number both divide into.
The multiples of 24 are 24, 48, 72, 96, 120, 144 and so on.
Only 120 lies between 100 and 130.
Multiplying 6 by 8 to get 48 and looking for multiples of 48 misses 120 entirely, because 48 is not the smallest common multiple.
212 marks
1 hour 44 minutes
- 1 mark for 84 minutes of roasting time for the 2.4 kg.
- 1 mark for 1 hour 44 minutes.
35 minutes per kilogram for 2.4 kg is 35 x 2.4. Work it in parts: 35 x 2 = 70 and 35 x 0.4 = 14, so 70 + 14 = 84 minutes.
Add the extra 20 minutes: 84 + 20 = 104 minutes.
104 minutes is 1 hour and 44 minutes, because 104 - 60 = 44.
Adding the 20 minutes for each kilogram instead of once gives 132 minutes and misreads the recipe.
221 mark
16 cm
The two shorter sides use up 2 x 7 = 14 cm of the perimeter.
That leaves 46 - 14 = 32 cm for the two longer sides.
Each longer side is 32 / 2 = 16 cm.

Sutton Boys' Second Stage Examination, Second Stage, Mathematics (written). Written by Revision Library on 2026-08-28, independent check pending.

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