NWSSEE Mathematics Mock Paper 4

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.

Print the paper (PDF)Paper and mark scheme (PDF)

Time allowed: 45 minutes
Total marks: 25
Questions: 25
Level: Selective standard

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 apples at 1 pound 35 pence per kilogram. Mrs Okafor buys 4 kg and hands over a 10 pound note.
How much change should she be given? Give your answer in pounds and pence.
Answer:
21 mark
A rectangular label is 8.5 cm long and 6 cm wide.
What is the area of the label? Give your answer in square centimetres.
The diagram is not drawn to size.
Answer:
31 mark
A bottle contains 900 ml of apple juice. Ravi pours out and drinks two thirds of it.
How much juice is left in the bottle? Give your answer in millilitres.
Answer:
41 mark
An overnight ferry sails from Portsmouth at 21:35. The crossing takes 5 hours and 50 minutes.
At what time does the ferry dock? Give your answer using the 24-hour clock.
Answer:
51 mark
A plank of wood is 2 m 40 cm long. A joiner saws it into four pieces of equal length.
How long is each piece? Give your answer in centimetres.
Answer:
61 mark
In this sequence, each term after the first two is made by adding together the two terms before it.
2, 5, 7, 12, 19, ...
What is the next term?
Answer:
71 mark
A square garden has sides of 15 m. A straight path 2 m wide is laid across it, running from the middle of one side to the middle of the opposite side.
What area of the garden is left as grass? Give your answer in square metres.
The diagram is not drawn to size.
Answer:
81 mark
A whole number is multiplied by itself and the result is 196.
What is the number?
Answer:
91 mark
A rain gauge collects 0.24 of a litre of water overnight.
Write 0.24 as a fraction in its simplest form.
Answer:
101 mark
Before a school exchange trip, Sam changes 60 pounds into euros. The bureau gives 1.15 euros for every pound.
How many euros does Sam receive?
Answer:
111 mark
Three of the four angles inside a quadrilateral measure 85 degrees, 100 degrees and 62 degrees.
What is the size of the fourth angle? Give your answer in degrees.
The diagram is not drawn to size.
Answer:
121 mark
A bag holds 60 counters. Three fifths of them are red and the rest are blue.
Another 12 blue counters are dropped into the bag.
What fraction of the counters in the bag are now blue? Give your answer in its simplest form.
Answer:
131 mark
A stadium holds 4200 spectators. On one evening 7 per cent of the seats are empty.
How many seats are empty?
Answer:
141 mark
A bookshop records how many books it sells on each day of one week.
Monday 42, Tuesday 37, Wednesday 51, Thursday 46, Friday 64
What is the mean number of books sold per day?
Answer:
151 mark
At an interchange, a bus sets off every 12 minutes and a tram sets off every 18 minutes.
A bus and a tram both set off at 08:00. At what time do a bus and a tram next set off together? Give your answer using the 24-hour clock.
Answer:
161 mark
A square piece of card has a perimeter of 36 cm. It is cut into four identical smaller squares.
What is the perimeter of one of the small squares? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
171 mark
Three quarters of a litre of orange juice is shared equally between 5 glasses.
What fraction of a litre goes into each glass? Give your answer in its simplest form.
Answer:
181 mark
A pancake recipe uses 200 ml of milk to make 8 pancakes.
How much milk is needed to make 15 pancakes with the same recipe? Give your answer in millilitres.
Answer:
191 mark
A tank has a square base with sides of 20 cm and straight vertical sides. When it is filled to the very top it holds exactly 8 litres.
How deep is the tank? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
201 mark
At midnight the temperature on a mountain is 6 degrees Celsius below freezing, which is written as -6 degrees Celsius. By noon it has risen by 11 degrees.
What is the temperature at noon? Give your answer in degrees Celsius.
Answer:
211 mark
The rule for a sequence is: multiply the position number by 6, then subtract 2.
What is the ninth term of this sequence?
Answer:
221 mark
A bag of sweets is shared out. Leah takes one third of the bag and Sam takes three eighths of it. Ivy is given everything that is left.
What fraction of the bag does Ivy get? Give your answer in its simplest form.
Answer:
231 mark
A museum displays a model of a lighthouse built to a scale of 1 : 250, so every centimetre on the model stands for 250 cm on the real building.
The model is 68 cm tall. How tall is the real lighthouse? Give your answer in metres.
Answer:
241 mark
A bottling machine fills 250 bottles every 5 minutes and never stops.
How many bottles does it fill in one hour?
Answer:
251 mark
A caretaker stacks 500 chairs into piles, putting 7 chairs in every pile.
After he has made as many full piles as he can, how many chairs are left over?
Answer:

Answers, mark scheme and worked explanations

11 mark
4.60
The apples cost 4 x 1.35. Four lots of 1 pound is 4 pounds, and four lots of 35p is 140p, or 1 pound 40 pence.
So the apples cost 4.00 + 1.40 = 5.40.
Change from 10 pounds is 10.00 - 5.40 = 4.60, which is 4 pounds 60 pence.
21 mark
51 cm2
Area of a rectangle is length multiplied by width.
8 x 6 = 48, and 0.5 x 6 = 3.
48 + 3 = 51 square centimetres.
31 mark
300 ml
If Ravi drinks two thirds, one third is left.
One third of 900 ml is 900 divided by 3 = 300 ml.
Answering 600 gives the amount he drank rather than the amount left, which is what the question asked for.
41 mark
03:25
Add the 5 whole hours first: 21:35 plus 5 hours is 02:35, which is after midnight the next morning.
Now add the 50 minutes. 25 minutes takes you to 03:00, and the 25 minutes still to add takes you to 03:25.
The clock restarts at 00:00 after midnight, so an answer of 27:25 is not a time.
51 mark
60 cm
Write the whole plank in one unit: 2 m 40 cm is 240 cm.
240 divided by 4 = 60 cm for each piece.
Answering 0.6 would be the length in metres, and the question asked for centimetres.
61 mark
31
Test the rule on the terms you can see: 2 + 5 = 7, then 5 + 7 = 12, then 7 + 12 = 19.
So the next term is 12 + 19 = 31.
The gaps are not equal, so looking for a fixed step will send you the wrong way.
71 mark
195 m2
The whole garden covers 15 x 15 = 225 square metres.
The path goes right across the garden, so it is 15 m long and 2 m wide: 15 x 2 = 30 square metres.
225 - 30 = 195 square metres of grass.
The path only has to be counted once, however far across the garden it sits.
81 mark
14
Try the square numbers you know: 10 x 10 = 100 and 20 x 20 = 400, so the number is between 10 and 20.
Since 196 ends in a 6, the number ends in 4 or 6. Testing 14 gives 14 x 14 = 196.
So the number is 14.
91 mark
6/25
- Accept 6/25 or six twenty-fifths. 24/100 and 12/50 are not in simplest form.
The last digit is in the hundredths column, so 0.24 is 24/100.
Divide top and bottom by 4: 24 divided by 4 = 6, and 100 divided by 4 = 25, giving 6/25.
6 and 25 have no common factor left, so that is the simplest form.
101 mark
69 euros
Every pound becomes 1.15 euros, so multiply: 60 x 1.15.
60 x 1 = 60, and 60 x 0.15 = 9.
60 + 9 = 69 euros.
Dividing by 1.15 instead would give about 52 euros, which is what you would do to change euros back into pounds.
111 mark
113
The four angles inside any quadrilateral add up to 360 degrees, because it splits into two triangles.
85 + 100 + 62 = 247.
360 - 247 = 113 degrees. Using 180 by mistake would give a negative answer, which is a signal that the wrong total was used.
121 mark
1/2
- Accept 1/2, one half or 36/72 simplified. 36/72 left unsimplified scores nothing.
Three fifths of 60 is 36 red counters, so 60 - 36 = 24 are blue to start with.
Adding 12 more blue counters makes 24 + 12 = 36 blue.
The bag now holds 60 + 12 = 72 counters in total.
So the blue fraction is 36/72, which simplifies to 1/2.
Forgetting that the total also grew, and writing 36/60, is the mistake to avoid.
131 mark
294
1 per cent of 4200 is 4200 divided by 100 = 42.
7 per cent is 7 x 42 = 294 seats.
The 3906 seats that were used are the other 93 per cent.
141 mark
48
Add the five totals: 42 + 37 = 79, then 79 + 51 = 130, then 130 + 46 = 176, and 176 + 64 = 240.
There are 5 days, so divide: 240 divided by 5 = 48 books a day.
A useful check is that the mean must sit between the smallest value, 37, and the largest, 64.
151 mark
08:36
List the buses after 08:00: 12, 24, 36, 48 minutes past.
List the trams: 18, 36, 54 minutes past.
The first number in both lists is 36, which is the lowest common multiple of 12 and 18.
So they next leave together at 08:36. Adding 12 and 18 to get 30 minutes is the trap, because no tram leaves at 30 minutes past.
161 mark
18 cm
The big square has sides of 36 divided by 4 = 9 cm.
Cutting it into four identical squares means halving it both ways, so each small square has sides of 9 divided by 2 = 4.5 cm.
The perimeter of a small square is 4 x 4.5 = 18 cm.
Dividing the big perimeter by 4 to get 9 cm is the trap: four small squares do not have a quarter of the perimeter each, because new edges appear where the card is cut.
171 mark
3/20
- Accept 3/20 or three twentieths. An answer of 15/4, from multiplying instead of dividing, scores nothing.
Sharing between 5 glasses means dividing three quarters by 5.
Each quarter of a litre is split into 5 equal pieces, and each piece is one twentieth of a litre.
Three quarters gives 3 of those pieces, so each glass holds 3/20 of a litre.
3 and 20 share no factor, so it is already in its simplest form.
181 mark
375 ml
Work out the milk for one pancake: 200 divided by 8 = 25 ml.
For 15 pancakes: 15 x 25 = 375 ml.
Doubling the recipe would make 16 pancakes and use 400 ml, so an answer a little under 400 ml is the sensible size.
191 mark
20 cm
One litre fills 1000 cubic centimetres, so 8 litres is 8000 cubic centimetres.
The base covers 20 x 20 = 400 square centimetres.
Depth is the volume divided by the area of the base: 8000 divided by 400 = 20 cm.
So the tank is actually a cube, which is a neat check: 20 x 20 x 20 = 8000.
201 mark
5
Count up the number line from -6. Six of the 11 degrees take you up to 0.
That leaves 5 degrees still to rise, so the temperature ends at 5 degrees Celsius.
Answering -17 comes from adding the numbers and keeping the minus sign, but the temperature is rising, not falling.
211 mark
52
The position number for the ninth term is 9.
9 x 6 = 54, and 54 - 2 = 52.
Doing the steps the other way round, subtracting first, would give 7 x 6 = 42, which is not what the rule says.
221 mark
7/24
- Accept 7/24 or seven twenty-fourths. 17/24 is the part Leah and Sam took, not Ivy's share.
Rewrite both shares in twenty-fourths: one third is 8/24 and three eighths is 9/24.
Together Leah and Sam take 8/24 + 9/24 = 17/24.
The whole bag is 24/24, so Ivy gets 24/24 - 17/24 = 7/24.
7 and 24 share no factor, so it is already in its simplest form.
231 mark
170 m
Multiply the model height by the scale: 68 x 250.
68 x 25 = 1700, so 68 x 250 = 17 000 cm.
There are 100 cm in a metre, so 17 000 cm = 170 m.
Leaving the answer as 17 000 is the right size in the wrong unit, and the question asked for metres.
241 mark
3000
Work out the rate for one minute: 250 divided by 5 = 50 bottles a minute.
An hour has 60 minutes: 60 x 50 = 3000 bottles.
You could also count in five-minute blocks, since 60 divided by 5 = 12 blocks and 12 x 250 = 3000.
251 mark
3
Count 7s into 500. Seventy piles use 490 chairs.
That leaves 10 chairs, which is enough for one more full pile of 7.
71 full piles use 497 chairs, so 500 - 497 = 3 chairs are left over.

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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