Sutton Boys' Second Stage Maths Mock Paper 8

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.

11 mark
A farm collects 1464 eggs one morning and packs them into trays. Each tray holds exactly 12 eggs and every tray is filled.
How many trays does the farm fill?
Answer:
22 marks
Three eighths of the spaces in a car park are taken. There are 145 empty spaces.
How many spaces does the car park have altogether?
Answer:
33 marks
A rectangle measures 36 cm long and 15 cm wide. A straight cut, parallel to the two shorter sides, divides it into two smaller rectangles.
The areas of the two smaller rectangles are in the ratio 4 : 5.
Work out the perimeter of the smaller of the two rectangles. Give your answer in centimetres. The diagram is not drawn to size.
Answer:
41 mark
A recipe uses 0.35 kg of flour. Rasheed follows the recipe 6 times over.
How much flour does he use altogether? Give your answer in grams.
Answer:
52 marks
A spinner is coloured green, red and blue only. When it is spun, the probability that it lands on green is 1/4.
The probability that it lands on red is twice the probability that it lands on blue.
What is the probability that the spinner lands on red? Give your answer as a fraction in its simplest form.
Answer:
62 marks
A two-way table shows how many pupils in Year 5 and Year 6 chose each of three lunchtime clubs. Every pupil chose exactly one club.
Year 5: chess 14, drama 21, coding 25. Year 6: chess 18, drama 14, coding 28.
What percentage of the pupils who chose drama are in Year 6?
Answer:
71 mark
The numbers in a sequence go up by the same amount every time.
The third term is 17 and the seventh term is 41.
What is the first term?
Answer:
83 marks
A school orders 26 boxes of exercise books. Each box holds 40 books.
The first 20 boxes cost 34 pounds each. Every box after the first 20 costs 5 pounds less than that.
The school also pays a delivery charge of 45 pounds. What is the total cost of the order? Give your answer in pounds.
Answer:
91 mark
A regular polygon has 9 sides, all the same length. Its perimeter is 61.2 cm.
How long is one side? Give your answer in centimetres.
Answer:
102 marks
A jar of mixed nuts contains cashews, almonds and peanuts in the ratio 2 : 3 : 7.
There are 84 peanuts in the jar.
How many nuts are in the jar altogether?
Answer:
113 marks
Six children were measured. Five of their heights were 142 cm, 156 cm, 149 cm, 138 cm and 151 cm.
The mean height of all six children is exactly 148 cm.
How much taller than the mean is the sixth child? Give your answer in centimetres.
Answer:
121 mark
A whole number is rounded to the nearest 10 and the result is 4570.
What is the largest whole number it could have been?
Answer:
132 marks
A pond is losing water through a small leak at a steady rate. At 08:00 it holds 3200 litres and at 12:00 it holds 2960 litres.
If the leak carries on at the same rate, how much water will the pond hold at 20:00 on the same day? Give your answer in litres.
Answer:
142 marks
A square and a rectangle have exactly the same perimeter as each other. The rectangle measures 18 cm by 6 cm.
Work out the area of the square. Give your answer in square centimetres. The shapes are not drawn to size.
Answer:
151 mark
One lap of a running track is 0.375 of a kilometre.
Write 0.375 as a fraction in its simplest form.
Answer:
163 marks
A bag holds 24 sweets. One third of them are lemon, one quarter of them are orange and the rest are strawberry.
Priya takes one sweet at random and eats it. It is a strawberry sweet. She then takes a second sweet at random from the bag.
What is the probability that the second sweet is also strawberry? Give your answer as a fraction in its simplest form.
Answer:
172 marks
Ana has three times as much money as Ben.
If Ana gives Ben 18 pounds, the two of them will have exactly the same amount as each other.
How much money does Ana have now? Give your answer in pounds.
Answer:
181 mark
A line graph shows the temperature inside a greenhouse, measured every two hours from 06:00 to 16:00. The points on the graph are at 9, 13, 18, 21, 19 and 14 degrees Celsius.
What is the range of these temperatures? Give your answer in degrees Celsius.
Answer:
192 marks
A shop buys a chair from a supplier for 45 pounds and later sells it for 63 pounds.
Work out the shop's profit as a percentage of the price it paid.
Answer:
201 mark
Squares are built in a straight row from matchsticks, each new square sharing one matchstick with the square before it.
One square uses 4 matchsticks, two squares use 7 matchsticks and three squares use 10 matchsticks.
How many matchsticks are needed for 20 squares?
Answer:
213 marks
An empty water butt holds 60 litres when full. A tap fills it at 4 litres a minute.
After 9 minutes the tap is turned down and from then on it delivers 3 litres a minute.
How long does the water butt take to fill altogether? Give your answer in minutes.
Answer:
221 mark
A cube has a total surface area of 150 square centimetres.
How long is one edge of the cube? Give your answer in centimetres.
Answer:

Answers, mark scheme and worked explanations

11 mark
122
Divide 1464 by 12. Halving twice and dividing by 3 is one neat route, or divide by 4 then by 3.
1464 / 4 = 366, and 366 / 3 = 122.
Check: 122 x 12 = 1464.
22 marks
232
- 1 mark for recognising that the 145 empty spaces are five eighths of the car park.
- 1 mark for 232 spaces.
If three eighths are taken then five eighths are empty, so 145 spaces is five eighths of the total.
One eighth is 145 / 5 = 29 spaces.
The whole car park is 8 x 29 = 232 spaces.
Check: three eighths of 232 is 87 taken, and 232 - 87 = 145 empty. Treating 145 as three eighths gives 386 and is the mistake to avoid.
33 marks
62 cm
- 1 mark for splitting the 36 cm length in the ratio 4 : 5.
- 1 mark for the smaller rectangle measuring 16 cm by 15 cm.
- 1 mark for a perimeter of 62 cm.
Both smaller rectangles are still 15 cm wide, because the cut runs parallel to the short sides. Their areas therefore depend only on how the 36 cm length is shared.
So the 36 cm splits in the ratio 4 : 5. That is 9 parts, and 36 / 9 = 4 cm per part.
The smaller piece is 4 x 4 = 16 cm long, and the larger piece is 5 x 4 = 20 cm long.
The smaller rectangle is 16 cm by 15 cm, so its perimeter is 2 x (16 + 15) = 62 cm.
Check the areas: 16 x 15 = 240 and 20 x 15 = 300, and 240 : 300 does simplify to 4 : 5.
Giving the area 240 instead of the perimeter is the tempting slip, because the ratio was about areas.
41 mark
2100 g
0.35 x 6 = 2.1 kg.
There are 1000 g in a kilogram, so 2.1 kg = 2100 g.
Leaving the answer as 2.1 ignores the unit the question asked for.
52 marks
1/2
- 1 mark for red and blue together having a probability of 3/4.
- 1 mark for 1/2.
All the probabilities have to add up to 1, so red and blue together come to 1 - 1/4 = 3/4.
Red is twice blue, so split that 3/4 into three equal shares: one share for blue and two for red.
One share is 3/4 divided by 3, which is 1/4. So blue is 1/4 and red is 2 x 1/4 = 1/2.
Check: 1/4 green + 1/2 red + 1/4 blue = 1.
Splitting the 3/4 equally into 3/8 and 3/8 ignores the word twice.
62 marks
40 per cent
- 1 mark for 35 pupils choosing drama altogether.
- 1 mark for 40 per cent.
The question asks about the drama column only, so ignore chess and coding.
Drama was chosen by 21 + 14 = 35 pupils, and 14 of them are in Year 6.
14 out of 35: divide both by 7 to get 2/5, which is 40 per cent.
Comparing 14 with all 120 pupils in the table gives about 12 per cent and answers a different question.
71 mark
5
From the third term to the seventh term is four steps, and the numbers rise by 41 - 17 = 24 over those four steps.
So each step is 24 / 4 = 6.
The first term is two steps before the third term: 17 - 6 - 6 = 5.
Dividing 24 by 5 because there are five terms from the third to the seventh is the mistake: count the gaps, not the terms.
83 marks
899
- 1 mark for 20 boxes at 34 pounds costing 680 pounds.
- 1 mark for the remaining 6 boxes at 29 pounds costing 174 pounds.
- 1 mark for a total of 899 pounds including delivery.
The first 20 boxes cost 20 x 34 = 680 pounds.
There are 26 - 20 = 6 boxes left, each at 34 - 5 = 29 pounds. 6 x 29 = 174 pounds.
680 + 174 = 854 pounds for the books, and 854 + 45 = 899 pounds altogether.
The 40 books in each box are not needed at all. A hard paper will often give you a number you do not have to use, and spotting that quickly saves time.
Charging all 26 boxes at 29 pounds gives 754 and misreads the offer.
91 mark
6.8 cm
In a regular polygon every side is the same, so divide the perimeter by the number of sides.
61.2 / 9 = 6.8 cm.
Check: 9 x 6.8 = 61.2.
102 marks
144
- 1 mark for one part being 12 nuts.
- 1 mark for 144 nuts.
The peanuts are 7 parts, and 7 parts = 84 nuts, so one part is 84 / 7 = 12 nuts.
The whole jar is 2 + 3 + 7 = 12 parts, so it holds 12 x 12 = 144 nuts.
Check: 24 cashews, 36 almonds and 84 peanuts add to 144.
Dividing 84 by 12 instead of by 7 confuses the peanut share with the total number of parts.
113 marks
4 cm
- 1 mark for a total height of 888 cm for all six children.
- 1 mark for the sixth child measuring 152 cm.
- 1 mark for 4 cm.
If the mean of six heights is 148 cm, the six heights add up to 6 x 148 = 888 cm.
The five heights given add up to 142 + 156 + 149 + 138 + 151. Taking them in pairs: 142 + 156 = 298 and 149 + 151 = 300, so with 138 the total is 736 cm.
The sixth child is 888 - 736 = 152 cm tall.
The question asks how much taller than the mean that is: 152 - 148 = 4 cm.
Stopping at 152 answers a question that was not asked, and it is the answer most candidates will write down.
121 mark
4574
Numbers from 4565 up to 4574 all round to 4570.
4575 would round up to 4580, so it is too big.
The largest possibility is therefore 4574. Answering 4579 forgets that 4575 and above round the other way.
132 marks
2480 litres
- 1 mark for a leak rate of 60 litres per hour.
- 1 mark for 2480 litres.
Between 08:00 and 12:00 is 4 hours, and the pond loses 3200 - 2960 = 240 litres.
That is 240 / 4 = 60 litres every hour.
From 12:00 to 20:00 is 8 more hours, so it loses another 8 x 60 = 480 litres.
2960 - 480 = 2480 litres.
Working from 08:00 across 12 hours gives the same answer: 3200 - 12 x 60 = 2480. Subtracting 240 once more, as though it were per eight hours, gives 2720 and is the common slip.
142 marks
144 cm2
- 1 mark for a square of side 12 cm.
- 1 mark for 144 square centimetres.
The rectangle's perimeter is 2 x (18 + 6) = 48 cm.
A square has four equal sides, so each side is 48 / 4 = 12 cm.
The area of the square is 12 x 12 = 144 square centimetres.
Notice that the rectangle's area is only 108 square centimetres. Equal perimeters do not mean equal areas, and assuming they do is the trap.
151 mark
3/8
- Accept 3/8 only. 375/1000 and 75/200 are correct values but not in simplest form.
0.375 is 375 thousandths, so start with 375/1000.
Divide both by 125: 375 / 125 = 3 and 1000 / 125 = 8, giving 3/8.
It is worth learning that 1/8 = 0.125, so 0.375 is three of those eighths.
163 marks
9/23
- 1 mark for 10 strawberry sweets at the start.
- 1 mark for 23 sweets remaining, of which 9 are strawberry.
- 1 mark for 9/23.
One third of 24 is 8 lemon sweets, and one quarter of 24 is 6 orange sweets.
That leaves 24 - 8 - 6 = 10 strawberry sweets.
Priya has eaten one strawberry sweet, so 23 sweets are left and only 9 of them are strawberry.
The probability is 9/23. It will not simplify, because 23 is prime.
Answering 10/24 or 5/12 ignores the sweet that has already gone, and answering 9/24 changes only the top number when both have changed.
172 marks
54
- 1 mark for seeing that the gap between them is 36 pounds, so Ben has 18 pounds.
- 1 mark for 54 pounds.
Handing over 18 pounds moves Ana down by 18 and Ben up by 18, so it closes a gap of 36 pounds.
The gap between them is Ana's amount minus Ben's, which is 3 shares minus 1 share, or 2 shares. So 2 shares are 36 pounds and 1 share is 18 pounds.
Ben has 18 pounds and Ana has 3 x 18 = 54 pounds.
Check: 54 - 18 = 36 and 18 + 18 = 36, so they match.
Treating the 18 pounds as the whole gap gives Ben 9 pounds and Ana 27 pounds, which does not work: 27 - 18 = 9 but 9 + 18 = 27.
181 mark
12
The range is the highest value minus the lowest value.
The highest reading is 21 degrees and the lowest is 9 degrees.
21 - 9 = 12 degrees Celsius. The range is a single number, not a pair of numbers.
192 marks
40 per cent
- 1 mark for a profit of 18 pounds.
- 1 mark for 40 per cent.
Profit = 63 - 45 = 18 pounds.
The question asks for that profit as a percentage of the 45 pounds the shop paid.
10 per cent of 45 is 4.50, so 40 per cent is 18. The profit is therefore 40 per cent.
Comparing the 18 pounds with the selling price of 63 pounds gives about 29 per cent and answers a different question. Read carefully which amount the percentage is measured against.
201 mark
61
The first square costs 4 matchsticks and every square after that costs only 3 more, because one side is shared.
There are 19 squares after the first, so that is 19 x 3 = 57 extra matchsticks.
4 + 57 = 61 matchsticks.
Multiplying 20 by 4 gives 80 and counts every shared matchstick twice.
213 marks
17 minutes
- 1 mark for 36 litres collected in the first 9 minutes.
- 1 mark for the remaining 24 litres taking 8 minutes.
- 1 mark for a total of 17 minutes.
In the first 9 minutes the butt collects 9 x 4 = 36 litres.
That leaves 60 - 36 = 24 litres to go.
At 3 litres a minute the last 24 litres take 24 / 3 = 8 minutes.
The total time is 9 + 8 = 17 minutes.
Averaging the two rates to 3.5 litres a minute and dividing 60 by it gives about 17.1 minutes, which looks close but is not a correct method: the two rates do not run for equal lengths of time.
221 mark
5 cm
A cube has 6 identical square faces, so one face has area 150 / 6 = 25 square centimetres.
A square of area 25 square centimetres has sides of 5 cm, because 5 x 5 = 25.
So each edge is 5 cm. Dividing 150 by 4, as though the cube were a flat square, is the error to watch for.

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

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