Sutton Boys' Second Stage Maths Mock Paper 6

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: Strong candidate

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.

11 mark
Work out the value of 7 + 6 x (15 - 8) / 3.
Take care to use the correct order of operations.
Answer:
22 marks
A printing machine produces 1250 leaflets every hour that it is running.
It is switched on at 08:30 and switched off at 13:00. During that time it is stopped for one break of 30 minutes.
How many leaflets does the machine produce?
Answer:
31 mark
A sponsored walk raised 640 pounds in total.
35 per cent of that money was raised by Year 6.
How much money did Year 6 raise? Give your answer in pounds.
Answer:
42 marks
In triangle PQR the angle at P is 36 degrees. The angle at Q is exactly twice the size of the angle at R.
Work out the size of the angle at Q. Give your answer in degrees.
The triangle is not drawn to size.
Answer:
53 marks
A cricket club has recorded how many wickets each of its bowlers took last season. The results are shown in a table with two columns, headed Wickets taken and Number of bowlers.
0 wickets: 4 bowlers. 1 wicket: 6 bowlers. 2 wickets: 5 bowlers. 3 wickets: 3 bowlers. 4 wickets: 2 bowlers.
Work out the mean number of wickets per bowler. Give your answer as a decimal.
Answer:
62 marks
A bag holds 5 red counters, 3 blue counters and 4 yellow counters.
Ravi takes one counter out without looking and it is yellow. He does not put it back.
He now takes a second counter out without looking. What is the probability that this counter is also yellow? Give your answer as a fraction in its simplest form.
Answer:
72 marks
A pancake recipe uses 350 ml of milk to serve 4 people.
Aisha makes enough pancakes for 10 people. She starts with a full 1 litre bottle of milk.
How much milk is left in the bottle? Give your answer in millilitres.
Answer:
82 marks
Tom thinks of a number. He adds 9 to it, then multiplies the result by 3, then subtracts 14.
His final answer is 55.
What number did Tom think of?
Answer:
93 marks
In a football squad the ratio of defenders to midfielders is 4 : 3.
Three more midfielders then join the squad, and no other players join or leave. The ratio of defenders to midfielders is now 1 : 1.
How many defenders are in the squad?
Answer:
101 mark
Pencils are sold only in boxes of 24. A school needs at least 500 pencils.
What is the smallest number of boxes the school must buy?
Answer:
113 marks
A rectangular lawn measures 15 m by 8 m. A gravel path exactly 1 m wide runs all the way round the inside edge of the lawn, so that grass is left in the middle.
Work out the ratio of the area of the gravel path to the area of the grass. Give your answer in its simplest form.
The lawn is not drawn to size.
Answer:
122 marks
Leo spends two fifths of his savings on a bicycle. He then spends one third of what is left on a helmet.
He has 72 pounds left after both purchases.
How much money did Leo have saved at the start? Give your answer in pounds.
Answer:
131 mark
A bar chart shows how many books were borrowed from a school library on each day of one week. The bars reach these values:
Monday 24, Tuesday 31, Wednesday 18, Thursday 27, Friday 35.
How many books were borrowed altogether that week?
Answer:
141 mark
Priya has a piece of ribbon 2.4 m long. She cuts off a piece 85 cm long for a parcel.
How much ribbon is left? Give your answer in centimetres.
Answer:
151 mark
Four angles meet at a single point and together fill the whole turn. Three of the four angles are equal to each other and the fourth angle is 132 degrees.
Work out the size of one of the three equal angles. Give your answer in degrees.
Answer:
161 mark
A pack of 12 cards is numbered 1 to 12, one number on each card. Kwame turns over one card without looking.
What is the probability that the number on the card is a factor of 12? Give your answer as a fraction in its simplest form.
Answer:
172 marks
A club hires a coach for a day trip at a fixed cost of 276 pounds. 24 members sign up and agree to share that cost equally between them.
On the morning of the trip 4 of the members do not turn up. The members who do travel share the whole 276 pounds equally instead.
How much more does each travelling member pay than they had expected? Give your answer in pounds.
Answer:
181 mark
Here are the first four terms of a sequence.
4, 11, 18, 25, ...
What is the tenth term of this sequence?
Answer:
192 marks
A supermarket used to sell rice in bags weighing 750 g.
It now sells the same rice in larger bags weighing 900 g, and the price of a bag has not changed.
By what percentage has the weight of a bag increased?
Answer:
202 marks
A netball team has played 6 matches so far this season and has scored a mean of 24 points per match.
The team wants its mean to be 25 points per match after 7 matches.
How many points must the team score in its seventh match?
Answer:
213 marks
A cyclist rides at a steady speed of 15 km per hour throughout her journey.
She sets off at 09:45 and rides 24 km. She then rests for 20 minutes before riding a further 9 km.
At what time does she finish? Give your answer using the 24-hour clock.
Answer:
222 marks
A rectangle has a perimeter of 54 cm. Its length is exactly twice its width.
Work out the area of the rectangle. Give your answer in square centimetres.
The rectangle is not drawn to size.
Answer:

Answers, mark scheme and worked explanations

11 mark
21
Brackets first: 15 - 8 = 7.
Then multiplication and division, working from left to right: 6 x 7 = 42, and 42 / 3 = 14.
Addition last: 7 + 14 = 21.
Adding the 7 and the 6 first would give 13 x 7 / 3, which is not 21. The order of operations is what makes this question work.
22 marks
5000
- 1 mark for working out that the machine actually runs for 4 hours (4 hours 30 minutes less the 30 minute break).
- 1 mark for 5000 leaflets.
From 08:30 to 13:00 is 4 hours and 30 minutes.
Take off the 30 minute break: the machine is actually printing for 4 hours.
4 x 1250 = 5000 leaflets.
Forgetting the break gives 5625, which is the answer this question is built to catch.
31 mark
224
10 per cent of 640 is 64, so 30 per cent is 3 x 64 = 192.
5 per cent is half of 64, which is 32.
192 + 32 = 224 pounds.
42 marks
96 degrees
- 1 mark for finding that the angles at Q and R add up to 144 degrees.
- 1 mark for 96 degrees. Allow this mark if the candidate has correctly found the angle at R as 48 degrees and doubled it.
The three angles of a triangle add up to 180 degrees, so Q and R together are 180 - 36 = 144 degrees.
Q is twice R, so those 144 degrees split into three equal parts: one part for R and two parts for Q.
144 / 3 = 48, so the angle at R is 48 degrees and the angle at Q is 2 x 48 = 96 degrees.
Check: 36 + 96 + 48 = 180. Splitting 144 into two equal halves of 72 is the tempting wrong move.
53 marks
1.65
- 1 mark for a total of 20 bowlers.
- 1 mark for a total of 33 wickets.
- 1 mark for 1.65.
First find how many bowlers there are: 4 + 6 + 5 + 3 + 2 = 20.
Now find the wickets. Multiply each number of wickets by how many bowlers took that many: 0 x 4 = 0, 1 x 6 = 6, 2 x 5 = 10, 3 x 3 = 9, 4 x 2 = 8.
0 + 6 + 10 + 9 + 8 = 33 wickets altogether.
The mean is 33 / 20 = 1.65 wickets per bowler.
The trap is dividing by 5 because the table has five rows. That gives 6.6, which is more wickets than any bowler actually took.
62 marks
3/11
- 1 mark for realising that 11 counters are left and 3 of them are yellow.
- 1 mark for 3/11.
At the start there are 5 + 3 + 4 = 12 counters, 4 of them yellow.
One yellow counter has already been taken out and kept, so 11 counters are left and only 3 of them are yellow.
The probability is 3/11, which will not simplify because 11 is prime.
Answering 4/12 or 1/3 means forgetting that the first counter was removed and that it was a yellow one.
72 marks
125 ml
- 1 mark for 875 ml of milk being needed for 10 people.
- 1 mark for 125 ml left.
10 people is two and a half times 4 people, so the milk needed is 350 x 2.5 = 875 ml.
You can also work out one serving first: 350 / 4 = 87.5 ml each, and 87.5 x 10 = 875 ml.
A 1 litre bottle holds 1000 ml, so 1000 - 875 = 125 ml is left.
Answering 875 is answering a question that was not asked.
82 marks
14
- 1 mark for undoing the last two steps correctly to reach 23.
- 1 mark for 14.
Work backwards, undoing each step in the opposite order.
Undo the subtraction: 55 + 14 = 69.
Undo the multiplication: 69 / 3 = 23.
Undo the addition: 23 - 9 = 14.
Check forwards: 14 + 9 = 23, 23 x 3 = 69, 69 - 14 = 55.
93 marks
12
- 1 mark for seeing that the number of defenders never changes, so the extra midfielders must close the gap of one part.
- 1 mark for one part being 3 players.
- 1 mark for 12 defenders.
Think of the squad as parts: 4 parts of defenders and 3 parts of midfielders, where every part is the same size.
The defenders do not change. Once the ratio is 1 : 1 the midfielders must be 4 parts too, so the 3 new midfielders are exactly one part.
So one part is 3 players.
Defenders are 4 parts: 4 x 3 = 12.
Check: 12 defenders and 9 midfielders is 4 : 3, and 12 and 12 is 1 : 1. Answering 3 gives the size of one part, not the number of defenders.
101 mark
21
20 boxes hold 20 x 24 = 480 pencils, which is not enough.
21 boxes hold 21 x 24 = 504 pencils, which is enough.
So the school must buy 21 boxes. You cannot buy part of a box, so rounding 500 / 24 down to 20 leaves the school short.
113 marks
7 : 13
- 1 mark for the inner rectangle of grass measuring 13 m by 6 m.
- 1 mark for a path area of 42 square metres and a grass area of 78 square metres.
- 1 mark for 7 : 13 in its simplest form.
The whole lawn has area 15 x 8 = 120 square metres.
The path is 1 m wide on every side, so it takes 1 m off each end of the length and 1 m off each side of the width. The grass in the middle is 15 - 2 = 13 m by 8 - 2 = 6 m.
The grass area is 13 x 6 = 78 square metres, so the path area is 120 - 78 = 42 square metres.
The ratio is 42 : 78. Both numbers divide by 6, giving 7 : 13.
Taking only 1 m off each measurement, giving 14 m by 7 m, is the usual slip. The path runs round both sides.
122 marks
180
- 1 mark for showing that 2/5 of the original savings is what remains at the end.
- 1 mark for 180 pounds.
After the bicycle, three fifths of the savings are left.
The helmet takes one third of that, so two thirds of the three fifths survive: 2/3 x 3/5 = 6/15 = 2/5 of the original savings.
So 2/5 of the savings is 72 pounds, which means one fifth is 36 pounds and the whole savings is 5 x 36 = 180 pounds.
Check: 2/5 of 180 is 72 on the bicycle, leaving 108. One third of 108 is 36 on the helmet, leaving 72.
131 mark
135
Add the five bars: 24 + 31 = 55, and 18 + 27 = 45, and 55 + 45 = 100.
Then 100 + 35 = 135 books.
141 mark
155 cm
Change to the same units first: 2.4 m is 240 cm.
240 - 85 = 155 cm.
Subtracting before converting, and writing 2.4 - 0.85, works too but the answer must then be turned back into centimetres.
151 mark
76 degrees
Angles at a point add up to 360 degrees.
360 - 132 = 228 degrees shared between the three equal angles.
228 / 3 = 76 degrees each.
161 mark
1/2
- Accept 1/2 or one half. 6/12 is correct but not in its simplest form, so it scores nothing.
The factors of 12 are 1, 2, 3, 4, 6 and 12. That is 6 of the 12 cards.
6 out of 12 simplifies to 1/2.
Do not confuse factors with multiples: the only multiples of 12 on the cards would be 12 itself.
172 marks
2.30
- 1 mark for both shares: 11 pounds 50 pence each for 24 members and 13 pounds 80 pence each for 20 members.
- 1 mark for 2 pounds 30 pence.
Expected share: 276 / 24 = 11.50 pounds each.
Actual share: only 20 members travel, so 276 / 20 = 13.80 pounds each.
The extra is 13.80 - 11.50 = 2.30 pounds.
The cost of the coach never changes, so working out a share of the cost of the 4 missing members is the wrong route.
181 mark
67
The sequence goes up by 7 each time.
Getting from the first term to the tenth term means adding 7 nine times, not ten times: 9 x 7 = 63.
4 + 63 = 67.
192 marks
20 per cent
- 1 mark for an increase of 150 g.
- 1 mark for 20 per cent.
The extra weight is 900 - 750 = 150 g.
An increase is always measured against the amount you started with, so compare the 150 g with the old weight of 750 g.
750 / 5 = 150, so the increase is one fifth, which is 20 per cent.
Comparing the 150 g with the new 900 g instead gives about 17 per cent and answers a different question.
202 marks
31
- 1 mark for 144 points scored so far, or for 175 points needed in total.
- 1 mark for 31 points.
Points scored so far: 6 x 24 = 144.
Points needed after 7 matches: 7 x 25 = 175.
175 - 144 = 31 points in the seventh match.
Answering 25 forgets that the six earlier matches have to be pulled up as well. Each of them is one point below the target, so six extra points are needed on top of 25.
213 marks
12:17
- 1 mark for the first ride taking 1 hour 36 minutes.
- 1 mark for the second ride taking 36 minutes.
- 1 mark for 12:17.
At 15 km per hour she covers 15 km in 60 minutes, so she covers 1 km in 4 minutes.
24 km therefore takes 24 x 4 = 96 minutes, which is 1 hour 36 minutes. From 09:45 that brings her to 11:21.
The rest of 20 minutes takes her to 11:41.
9 km takes 9 x 4 = 36 minutes, so she finishes at 11:41 plus 36 minutes, which is 12:17.
Writing 1.6 hours as 1 hour 6 minutes instead of 1 hour 36 minutes is the classic error here.
222 marks
162 cm2
- 1 mark for a width of 9 cm and a length of 18 cm.
- 1 mark for 162 square centimetres.
The perimeter is two lengths plus two widths, so one length plus one width is 54 / 2 = 27 cm.
The length is twice the width, so 27 cm is made of three equal parts: 27 / 3 = 9.
The width is 9 cm and the length is 2 x 9 = 18 cm.
Area = 18 x 9 = 162 square centimetres.
Dividing 54 by 3 straight away gives 18, which happens to be the length, but only by luck. Halving the perimeter first is the reliable route.

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

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