NWSSEE Mathematics Mock Paper 6

Preparation for the Nonsuch and Wallington Second Stage Entrance Examination, sat for admission to Nonsuch High School for Girls and Wallington High School for Girls. 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: 45 minutes
Total marks: 25
Questions: 25
Level: Strong candidate

You have 45 minutes. There are 25 questions and each one is worth 1 mark.
Write your answer on the line under each question. Only the final answer is marked, so you get no marks for working.
Use any spare space on the paper for your working out. There is no rough paper and you may not use a calculator.
The questions do not get harder as you go through the paper. If one is taking too long, move on and come back to it.
Diagrams are not drawn to size. Work from the measurements you are given, never by measuring the picture.

Mathematics

Answer every question. Show your answer clearly on the line.

11 mark
A market stall sells punnets of strawberries at 2 pounds 65 pence each. On Saturday it sells 48 punnets.
How much money does the stall take? Give your answer in pounds.
Answer:
21 mark
A stew recipe uses 0.4 kg of tomatoes for each person. A cook is making the stew for 12 people, and the tomatoes come in tins holding 300 g each.
How many tins does the cook need?
Answer:
31 mark
Seven elevenths is a little larger than five eighths.
By how much is it larger? Give your answer as a fraction in its simplest form.
Answer:
41 mark
A rectangle measuring 18 cm by 8 cm has exactly the same area as a square.
How long is one side of the square? Give your answer in centimetres.
Answer:
51 mark
Freya cycles the first 12 km of a ride in 30 minutes. She then cycles a further 15 km in 60 minutes.
What is her average speed for the whole ride? Give your answer in kilometres per hour.
Answer:
61 mark
A designer makes patterns from small square tiles. Pattern 1 is a single tile. Pattern 2 is a 2 by 2 block of 4 tiles. Pattern 3 is a 3 by 3 block of 9 tiles, and the patterns carry on in the same way.
Which pattern uses exactly 144 tiles?
Answer:
71 mark
A car ferry can carry 38 cars on each crossing and makes 14 crossings in a day.
On Monday every crossing was full except the last one, which carried only 9 cars.
How many cars did the ferry carry on Monday?
Answer:
81 mark
The mean of four numbers is 17. A fifth number is then included, and the mean of all five numbers is 19.
What is the fifth number?
Answer:
91 mark
A school trip costs 14 pounds 75 pence for each pupil, and 32 pupils go. The school pays a coach company 180 pounds out of the money collected.
How much of the money collected is left? Give your answer in pounds.
Answer:
101 mark
The two side lengths of a rectangle are in the ratio 3 : 5. The perimeter of the rectangle is 64 cm.
What is the area of the rectangle? Give your answer in square centimetres.
The diagram is not drawn to size.
Answer:
111 mark
The four angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6.
What is the size of the largest angle? Give your answer in degrees.
Answer:
121 mark
A watering can holds 4.5 litres when it is full. A gardener empties 7 full cans onto the vegetable patch.
How much water is that altogether? Give your answer in millilitres.
Answer:
131 mark
A jacket costs 60 pounds. In a sale its price is cut by 25 per cent. The week after, the sale price is cut by a further 10 per cent.
What is the price of the jacket now? Give your answer in pounds.
Answer:
141 mark
Ravinder spends two fifths of her savings on a bicycle. She then spends one quarter of what is left on a helmet.
What fraction of her savings does she still have? Give your answer in its simplest form.
Answer:
151 mark
A box is a cuboid measuring 10 cm by 6 cm by 4 cm. It is to be covered exactly, with no overlap, by wrapping paper on all six of its faces.
How much paper is needed? Give your answer in square centimetres.
The diagram is not drawn to size.
Answer:
161 mark
A film starts at 19:45 and lasts 2 hours 40 minutes. It is followed by a 20 minute talk from the director.
At what time does the talk end? Give your answer using the 24-hour clock.
Answer:
171 mark
There are 32 pupils in a class and 12 of them walk to school.
What fraction of the class walks to school? Give your answer in its simplest form.
Answer:
181 mark
Isla thinks of a number. She adds 8 to it and then multiplies the result by 3. Her answer is 45.
What number did Isla think of?
Answer:
191 mark
A rectangular field measures 20 m by 12 m. A farmer runs one straight fence from a corner of the field to the corner diagonally opposite, making two plots of equal area.
What is the area of each plot? Give your answer in square metres.
The diagram is not drawn to size.
Answer:
201 mark
Eight pupils scored these marks in a spelling test.
7, 9, 6, 10, 9, 8, 9, 6
What is the median mark?
Answer:
211 mark
A pack of 6 yoghurts costs 2 pounds 70 pence. The same yoghurts cost 52 pence each when bought singly.
How much cheaper is one yoghurt when it is bought in the pack? Give your answer in pence.
Answer:
221 mark
A porridge recipe uses 250 g of oats to serve 4 people.
How many oats are needed to serve 26 people? Give your answer in kilograms.
Answer:
231 mark
Three tins of paint cover 51 square metres of wall.
How many square metres will seven tins cover, if each tin covers the same amount?
Answer:
241 mark
A rectangle has a perimeter of 30 cm and a length of 9 cm.
What is its area? Give your answer in square centimetres.
Answer:
251 mark
Two whole numbers add up to 30. When they are multiplied together the answer is 216.
What is the difference between the two numbers?
Answer:

Answers, mark scheme and worked explanations

11 mark
127.20
Break the price up. 48 lots of 2 pounds is 96 pounds.
48 lots of 65 pence is 48 x 65 = 3120 pence, which is 31 pounds 20 pence.
96 + 31.20 = 127 pounds 20 pence.
Writing the answer as 127.2 without the second decimal place is untidy for money, so write 127.20.
21 mark
16
First find the mass of tomatoes needed: 12 x 0.4 = 4.8 kg.
The tins are given in grams, so change the kilograms to grams: 4.8 kg = 4800 g.
4800 divided by 300 = 16 tins.
Dividing 4.8 by 300 without converting gives a tiny answer, and that is what this question is checking.
31 mark
1/88
- Accept 1/88 or one eighty-eighth. Any unsimplified equivalent such as 2/176 scores nothing.
Put both fractions over the same denominator. The smallest number both 11 and 8 divide into is 88.
7/11 = 56/88 because 7 x 8 = 56, and 5/8 = 55/88 because 5 x 11 = 55.
56/88 - 55/88 = 1/88, which is already in its simplest form.
Subtracting the tops and the bottoms separately to get 2/3 is the mistake to avoid.
41 mark
12 cm
Work out the area of the rectangle first: 18 x 8 = 144 square centimetres.
The square has the same area, so its side multiplied by itself must be 144.
12 x 12 = 144, so the side is 12 cm.
Halving the rectangle's perimeter, or averaging 18 and 8 to get 13, are both tempting and both wrong.
51 mark
18 km/h
Average speed means the total distance divided by the total time, not the average of the two speeds.
Total distance is 12 + 15 = 27 km. Total time is 30 + 60 = 90 minutes, which is 1.5 hours.
27 divided by 1.5 is 18, so her average speed is 18 km/h.
The two separate speeds are 24 km/h and 15 km/h. Averaging those gives 19.5 km/h, which is wrong because she spends twice as long going at the slower speed.
61 mark
12
Each pattern is a square block, so the number of tiles is the pattern number multiplied by itself.
You need the number that multiplies by itself to make 144.
12 x 12 = 144, so it is pattern 12.
Dividing 144 by 4, because pattern 2 used 4 tiles, gives 36 and does not fit the pattern at all.
71 mark
503
13 of the crossings were full: 13 x 38. That is 10 x 38 = 380 plus 3 x 38 = 114, giving 494 cars.
The last crossing carried 9 more: 494 + 9 = 503 cars.
Working out 14 x 38 = 532 and then taking away 9 gives 523, which is wrong because the last crossing was 29 cars short of full, not 9 cars short.
81 mark
27
Turn each mean back into a total. Four numbers with a mean of 17 add up to 4 x 17 = 68.
Five numbers with a mean of 19 add up to 5 x 19 = 95.
The fifth number is the difference: 95 - 68 = 27.
Answering 2, the amount the mean went up by, is the tempting wrong answer.
91 mark
292
First find the money collected: 32 x 14.75. That is 32 x 14 = 448, plus 32 x 0.75 = 24, giving 472 pounds.
Then take off the coach fee: 472 - 180 = 292 pounds.
101 mark
240 cm2
A perimeter is two lengths and two widths, so one length plus one width is half of 64, which is 32 cm.
That 32 cm is split in the ratio 3 : 5, which is 8 parts. One part is 32 divided by 8 = 4 cm.
So the sides are 3 x 4 = 12 cm and 5 x 4 = 20 cm.
The area is 12 x 20 = 240 square centimetres. Sharing the whole 64 cm in the ratio, giving 24 and 40, is the trap.
111 mark
144
The angles inside any quadrilateral add up to 360 degrees.
The ratio has 2 + 3 + 4 + 6 = 15 parts, so one part is 360 divided by 15 = 24 degrees.
The largest angle is 6 parts: 6 x 24 = 144 degrees.
Using 180 degrees instead of 360 is the mistake to watch for.
121 mark
31500 ml
7 x 4.5 = 31.5, so the gardener uses 31.5 litres.
There are 1000 millilitres in a litre, so multiply by 1000: 31.5 litres = 31 500 ml.
Answering 31.5 gives the right amount in the wrong unit and scores nothing.
131 mark
40.50
25 per cent is a quarter, so the first cut takes off 15 pounds and the sale price is 45 pounds.
The second cut is 10 per cent of the sale price, not of the original: 10 per cent of 45 pounds is 4 pounds 50 pence.
45 - 4.50 = 40 pounds 50 pence.
Adding the percentages to make 35 per cent off 60 pounds gives 39 pounds, which is wrong.
141 mark
9/20
- Accept 9/20 or nine twentieths. 27/60 and similar unsimplified forms score nothing.
After the bicycle she has 1 - 2/5 = 3/5 of her savings left.
She spends a quarter of that, so she keeps three quarters of it.
Three quarters of three fifths is 3/4 x 3/5 = 9/20.
Answering 3/4 forgets the money already spent on the bicycle.
151 mark
248 cm2
The faces come in matching pairs, so work out three of them and then double.
The three different faces are 10 x 6 = 60, 10 x 4 = 40 and 6 x 4 = 24 square centimetres.
60 + 40 + 24 = 124, and doubling gives 248 square centimetres.
Working out 10 x 6 x 4 = 240 gives the volume, which is a different measurement in different units.
161 mark
22:45
Add the hours first: 19:45 plus 2 hours is 21:45.
Then add the 40 minutes. 15 minutes takes you to 22:00, and the other 25 minutes takes you to 22:25.
Finally add the 20 minute talk: 22:25 becomes 22:45.
Writing 10:45 pm would be right in words but the question asks for the 24-hour clock.
171 mark
3/8
- Accept 3/8 or three eighths. 12/32 and 6/16 are not in simplest form and score nothing.
The fraction is 12 out of 32, written 12/32.
Both numbers divide by 4: 12 divided by 4 is 3, and 32 divided by 4 is 8.
So the fraction is 3/8, which cannot be simplified further because 3 is prime and does not divide 8.
Leaving the answer as 12/32 is correct as a fraction but does not follow the instruction, so it earns nothing.
181 mark
7
Work backwards, undoing the last step first.
Undo the multiplication: 45 divided by 3 = 15.
Undo the addition: 15 - 8 = 7.
Check forwards: 7 + 8 = 15, and 15 x 3 = 45.
191 mark
120 m2
The whole field has an area of 20 x 12 = 240 square metres.
The diagonal fence cuts the field into two triangles of exactly the same size, so each one is half of 240.
240 divided by 2 = 120 square metres.
You can check with the triangle rule: half of 20 x 12 is also 120.
201 mark
8.5
Put the marks in order first: 6, 6, 7, 8, 9, 9, 9, 10.
There are eight marks, so there is no single middle one. The two middle marks are the fourth and fifth: 8 and 9.
The median is halfway between them, which is 8.5.
The mode is 9 and the mean is 8, so both of those are tempting wrong answers.
211 mark
7 pence
One yoghurt from the pack costs 2.70 divided by 6, which is 45 pence.
Bought singly it costs 52 pence.
52 - 45 = 7 pence cheaper.
The answer must be in pence, so writing 0.07 or 7 pounds would not do.
221 mark
1.625 kg
One person needs 250 divided by 4 = 62.5 g of oats.
26 people need 62.5 x 26. That is 62.5 x 26 = 1625 g.
Divide by 1000 to change grams into kilograms: 1.625 kg.
You could also notice 26 people is 6.5 lots of 4 people, and 6.5 x 250 = 1625 g.
231 mark
119 m2
One tin covers 51 divided by 3 = 17 square metres.
Seven tins cover 7 x 17 = 119 square metres.
241 mark
54 cm2
One length plus one width is half the perimeter: 30 divided by 2 = 15 cm.
So the width is 15 - 9 = 6 cm.
The area is 9 x 6 = 54 square centimetres.
Taking 9 away from 30 to get a width of 21 cm is the mistake to avoid.
251 mark
6
List pairs that add to 30 and try their products: 15 and 15 gives 225, 14 and 16 gives 224, 13 and 17 gives 221.
Keep going: 12 and 18 gives 216, which is the product you want.
The difference is 18 - 12 = 6.
The question asks for the difference, not the numbers themselves, so 12 and 18 on its own would not answer it.

Nonsuch and Wallington Second Stage Entrance Examination, Second Stage, Mathematics. Written by Revision Library on 2026-08-28, independent check pending.

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