Sutton Boys' Second Stage Maths Mock Paper 7

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
A lorry is loaded with 36 crates of soup. Every crate holds 48 tins.
How many tins of soup are on the lorry altogether?
Answer:
22 marks
Triangle KLM is isosceles. The sides KL and KM are equal in length.
The angle at L measures 71 degrees.
Work out the size of the angle at K. Give your answer in degrees. The triangle is not drawn to size.
Answer:
32 marks
A season ticket cost 240 pounds last year. This year its price rose by 15 per cent.
Next year the price will rise by a further 10 per cent of this year's price.
What will the season ticket cost next year? Give your answer in pounds.
Answer:
41 mark
A jug holds 2.25 litres of apple juice. Each cup holds 180 ml.
How many full cups can be poured from the jug?
Answer:
53 marks
A sports centre has 300 members. A table lists how many of them take part in each activity. Every member takes part in exactly one activity.
Swimming 96 members, Badminton 72 members, Climbing 54 members, Gym: the rest of the members.
What percentage of the members use the gym?
Answer:
62 marks
Ella has written down a three-digit whole number. All four of these statements about it are true.
It is greater than 700 and less than 800. It is a multiple of 5. Its three digits add up to 12. Its tens digit is an odd number.
What is Ella's number?
Answer:
72 marks
A spinner has five equal sections numbered 1, 2, 3, 4 and 5. Nadia spins it twice and adds her two numbers together.
What is the probability that her total is 9 or more? Give your answer as a fraction in its simplest form.
Answer:
81 mark
The first five numbers in a counting pattern are 3, 8, 13, 18 and 23.
The pattern carries on in the same way. What is the first number in the pattern that is greater than 60?
Answer:
92 marks
A picture mount is made from a rectangular piece of card measuring 30 cm by 20 cm. A rectangular hole measuring 24 cm by 14 cm is cut from the middle of it.
Work out the area of the card that is left. Give your answer in square centimetres.
The mount is not drawn to size.
Answer:
102 marks
Three friends share a bag of marbles in the ratio 5 : 3 : 2.
The friend with the largest share receives 24 more marbles than the friend with the smallest share.
How many marbles were in the bag altogether?
Answer:
113 marks
A train leaves Ashford at 13:20 and travels 180 km to Colton, arriving at 15:50.
It waits at Colton for 15 minutes and then travels a further 60 km to its final stop at the same average speed as before.
At what time does the train reach its final stop? Give your answer using the 24-hour clock.
Answer:
121 mark
A theatre has 468 seats, arranged in rows that each hold 18 seats.
How many rows of seats are there?
Answer:
132 marks
Nine children recorded how many minutes they read one evening.
25, 40, 15, 30, 20, 55, 20, 35, 45
Work out the difference between the median and the mode of these times.
Answer:
142 marks
A fish tank is a cuboid measuring 60 cm long, 30 cm wide and 40 cm deep. It is filled with water to a depth of 25 cm.
How many litres of water are in the tank? Use 1000 cubic centimetres = 1 litre.
The tank is not drawn to size.
Answer:
151 mark
A box contains 20 chocolates. 8 of them are milk chocolate and 7 are dark chocolate. The rest are white chocolate.
One chocolate is taken from the box at random. What is the probability that it is white chocolate? Give your answer as a fraction in its simplest form.
Answer:
162 marks
A jug holds three quarters of a litre of lemonade. The lemonade is shared equally between 6 glasses.
What fraction of a litre goes into each glass? Give your answer in its simplest form.
Answer:
173 marks
A stall sells cakes at 1 pound 80 pence each, or in packs of 5 for 8 pounds.
Ben needs at least 13 cakes and wants to spend as little money as possible. He may buy any mixture of packs and single cakes.
How much does Ben spend? Give your answer in pounds.
Answer:
181 mark
A film begins at 19:35 and lasts for 2 hours and 48 minutes.
At what time does the film finish? Give your answer using the 24-hour clock.
Answer:
192 marks
In a certain sequence, every term after the first is found by doubling the term before it and then subtracting 3.
The fourth term of the sequence is 27.
What is the first term?
Answer:
202 marks
A pie chart shows how the 240 pupils in a school travel there each morning. Every pupil is counted once.
The sector for walking is exactly one quarter of the whole circle. The sector for cycling has an angle of 54 degrees at the centre.
How many more pupils walk than cycle?
Answer:
211 mark
Three of the four angles inside a quadrilateral measure 85 degrees, 97 degrees and 122 degrees.
Work out the size of the fourth angle. Give your answer in degrees. The quadrilateral is not drawn to size.
Answer:
222 marks
A school has 600 pupils. 45 per cent of them are in Key Stage 3.
One fifth of the Key Stage 3 pupils play in a school team.
How many pupils play in a school team?
Answer:

Answers, mark scheme and worked explanations

11 mark
1728
Split the 48 into 50 - 2 to make the multiplication easier.
36 x 50 = 1800 and 36 x 2 = 72.
1800 - 72 = 1728 tins.
22 marks
38 degrees
- 1 mark for identifying the angle at M as 71 degrees as well.
- 1 mark for 38 degrees.
In an isosceles triangle the two angles opposite the equal sides are equal. KL and KM are equal, so the angles at M and at L are equal.
That makes the angle at M 71 degrees too.
The angles of a triangle add to 180 degrees, so the angle at K is 180 - 71 - 71 = 38 degrees.
Assuming the equal angles sit at K and L instead would give 180 - 142 in the wrong place. Always match the equal angles to the equal sides.
32 marks
303.60
- 1 mark for this year's price of 276 pounds.
- 1 mark for 303 pounds 60 pence.
15 per cent of 240 is 24 + 12 = 36 pounds, so this year the ticket costs 240 + 36 = 276 pounds.
10 per cent of 276 is 27.60 pounds, so next year it costs 276 + 27.60 = 303.60 pounds.
Adding 25 per cent to 240 in one go gives 300 pounds. That is wrong because the second rise is taken from the bigger 276 pound price, not from 240.
41 mark
12
2.25 litres is 2250 ml.
2250 / 180 = 12.5, so twelve cups can be filled completely and half a cup is left over.
The question asks for full cups, so the answer is 12. Rounding up to 13 would mean pouring a cup that is only half full.
53 marks
26 per cent
- 1 mark for 222 members in the three activities that are listed.
- 1 mark for 78 gym members.
- 1 mark for 26 per cent.
The gym figure is not printed, so it has to be worked out first.
96 + 72 + 54 = 222 members are accounted for.
300 - 222 = 78 members use the gym.
78 out of 300 as a percentage: 78 / 300 = 0.26, which is 26 per cent. You can also note that 1 per cent of 300 is 3, and 78 / 3 = 26.
Reading 78 as the answer misses the last step, and dividing by 222 rather than 300 compares the gym with the wrong total.
62 marks
750
- 1 mark for narrowing the number down to the form 7 _ 0 or 7 _ 5 using the range and the multiple of 5.
- 1 mark for 750.
Between 700 and 800 the hundreds digit must be 7.
A multiple of 5 ends in 0 or 5, so the number is 7 _ 0 or 7 _ 5.
The digits add to 12, so the other two digits add to 5. If the units digit is 0 the tens digit is 5; if the units digit is 5 the tens digit is 0.
The tens digit must be odd, and 0 is even, so the answer is 750.
Check: 750 is between 700 and 800, ends in 0, has digits 7 + 5 + 0 = 12, and its tens digit 5 is odd.
72 marks
3/25
- 1 mark for 25 equally likely pairs of spins.
- 1 mark for 3/25, or for correctly listing the three successful pairs.
The first spin has 5 possible results and so does the second, so there are 5 x 5 = 25 equally likely pairs.
A total of 9 or more needs a 9 or a 10. The pairs that work are 4 then 5, 5 then 4, and 5 then 5.
That is 3 pairs out of 25, so the probability is 3/25. It will not simplify.
Forgetting that 4 then 5 and 5 then 4 are two different outcomes gives 2/25 and loses the second mark.
81 mark
63
The pattern goes up in fives, and every number ends in 3 or 8.
Counting on from 23: 28, 33, 38, 43, 48, 53, 58, 63.
58 is not greater than 60, so the first one past 60 is 63.
92 marks
264 cm2
- 1 mark for both areas: 600 square centimetres for the whole card and 336 square centimetres for the hole.
- 1 mark for 264 square centimetres.
Whole card: 30 x 20 = 600 square centimetres.
Hole: 24 x 14 = 336 square centimetres.
Card left: 600 - 336 = 264 square centimetres.
The border is not the same width all round, so there is no shortcut here: the subtraction is the method.
102 marks
80
- 1 mark for one share being 8 marbles, from a difference of 3 shares being 24.
- 1 mark for 80 marbles.
The largest share is 5 parts and the smallest is 2 parts, so the difference is 3 parts.
3 parts = 24 marbles, so 1 part = 8 marbles.
The bag holds 5 + 3 + 2 = 10 parts, which is 10 x 8 = 80 marbles.
Check: the three shares are 40, 24 and 16, and 40 - 16 = 24. Dividing 24 by 5 or by 10 is the usual slip.
113 marks
16:55
- 1 mark for an average speed of 72 km per hour, or for 180 km taking 150 minutes.
- 1 mark for the second leg taking 50 minutes.
- 1 mark for 16:55.
From 13:20 to 15:50 is 2 hours 30 minutes, which is 150 minutes for 180 km.
That is 180 / 150 = 1.2 km every minute, or 72 km per hour.
60 km at 1.2 km per minute takes 60 / 1.2 = 50 minutes.
The train leaves Colton at 15:50 + 15 minutes = 16:05, and arrives 50 minutes later at 16:55.
Forgetting the 15 minute wait gives 16:40, and it is the commonest mistake on a question like this.
121 mark
26
Divide 468 by 18. Doubling both numbers makes it easier: 936 / 36, or halve both to get 234 / 9 = 26.
Check: 18 x 26 = 18 x 25 + 18 = 450 + 18 = 468.
132 marks
10
- 1 mark for a median of 30 minutes and a mode of 20 minutes.
- 1 mark for a difference of 10 minutes.
Put the times in order first: 15, 20, 20, 25, 30, 35, 40, 45, 55.
There are nine values, so the median is the fifth one, which is 30.
The mode is the value that appears most often, which is 20 because it appears twice and every other value appears once.
30 - 20 = 10 minutes.
Finding the median without ordering the list first is what goes wrong here: the middle number as written down is 20, not 30.
142 marks
45 litres
- 1 mark for a water volume of 45000 cubic centimetres.
- 1 mark for 45 litres.
Only the water is being measured, so use the depth of the water, 25 cm, and not the depth of the tank.
Volume of water = 60 x 30 x 25. 60 x 30 = 1800, and 1800 x 25 = 45000 cubic centimetres.
45000 / 1000 = 45 litres.
Using 40 cm gives 72 litres, which is how much the tank would hold if it were full to the brim.
151 mark
1/4
- Accept 1/4 or one quarter. 5/20 is correct but not in its simplest form, so it scores nothing.
White chocolates: 20 - 8 - 7 = 5.
5 out of 20 is 5/20, which simplifies by dividing both numbers by 5 to give 1/4.
162 marks
1/8
- 1 mark for a correct method, such as 3/4 divided by 6 or 3/24.
- 1 mark for 1/8.
Dividing by 6 means each glass gets one sixth of three quarters: 3/4 / 6 = 3/24.
3/24 simplifies to 1/8 by dividing both numbers by 3.
Another route: three quarters is six eighths, and sharing six eighths between six glasses gives one eighth each.
Multiplying by 6 instead of dividing gives 4 and a half litres, which is more than the jug holds.
173 marks
21.40
- 1 mark for choosing two packs of five plus three single cakes.
- 1 mark for 16 pounds for the packs and 5 pounds 40 pence for the singles.
- 1 mark for 21 pounds 40 pence.
A pack of 5 costs 8 pounds, which is 1 pound 60 pence a cake, so packs are better value than singles.
Two packs give 10 cakes for 16 pounds. The remaining 3 cakes cost 3 x 1.80 = 5.40 pounds.
Total: 16 + 5.40 = 21.40 pounds.
It is worth checking the alternative. Three packs give 15 cakes for 24 pounds, which is more than 21.40, and 13 single cakes cost 23.40 pounds. So 21.40 is the cheapest.
Buying only single cakes without comparing the pack price is the mistake this question is testing.
181 mark
22:23
Add the whole hours first: 19:35 plus 2 hours is 21:35.
Then add the 48 minutes. 25 minutes takes you to 22:00, and the other 23 minutes takes you to 22:23.
192 marks
6
- 1 mark for working backwards correctly to the third and second terms, 15 and 9.
- 1 mark for 6.
Work backwards, undoing each rule: add 3, then halve.
From the fourth term 27: 27 + 3 = 30, and 30 / 2 = 15, so the third term is 15.
From 15: 15 + 3 = 18, and 18 / 2 = 9, so the second term is 9.
From 9: 9 + 3 = 12, and 12 / 2 = 6, so the first term is 6.
Check forwards: 6, 9, 15, 27. Undoing in the wrong order, halving before adding 3, gives the wrong chain.
202 marks
24
- 1 mark for 60 pupils walking and 36 pupils cycling.
- 1 mark for 24.
A quarter of the circle means a quarter of the pupils: 240 / 4 = 60 pupils walk.
The whole circle is 360 degrees, so 54 degrees is 54 / 360 of the pupils. That is 15 per cent, and 15 per cent of 240 is 36 pupils.
Another way: each degree stands for 240 / 360 = two thirds of a pupil, and 54 x 2/3 = 36.
60 - 36 = 24 more pupils walk than cycle.
Treating 54 as a number of pupils rather than a number of degrees is the error the question is looking for.
211 mark
56 degrees
The four angles inside any quadrilateral add up to 360 degrees.
85 + 97 + 122 = 304.
360 - 304 = 56 degrees. Using 180 instead of 360 is the trap: that rule belongs to triangles.
222 marks
54
- 1 mark for 270 pupils in Key Stage 3.
- 1 mark for 54 pupils.
45 per cent of 600: 10 per cent is 60, so 40 per cent is 240, and 5 per cent is 30. 240 + 30 = 270 pupils.
One fifth of 270 is 270 / 5 = 54 pupils.
Taking one fifth of all 600 pupils gives 120, which counts pupils from every year group instead of only Key Stage 3.

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

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