NWSSEE Mathematics Mock Paper 2

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: Familiarisation

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 farm shop packs its eggs into trays. Every tray holds 12 eggs.
On Saturday the shop sells 27 full trays. How many eggs does it sell?
Answer:
21 mark
Priya has a roll of curtain tape 3.4 m long. She cuts off a piece 85 cm long to finish a blind.
How much ribbon is left on the roll? Give your answer in centimetres.
Answer:
31 mark
A charity has 342 wristbands and gives away five ninths of them at a fair.
How many wristbands does the charity give away?
Answer:
41 mark
Six identical revision guides cost 41 pounds 70 pence altogether.
At the same price each, what would ten of these guides cost? Give your answer in pounds and pence.
Answer:
51 mark
A notice board is a rectangle with a perimeter of 34 cm. One of its sides is 11 cm long.
How long is the side next to it? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
61 mark
A netball team scores these numbers of goals in five matches.
7, 4, 9, 12, 3
What is the mean number of goals per match?
Answer:
71 mark
Square tables are pushed together in a straight row for a party, so that each new table touches the one before it along a whole side.
One table seats 6 people. Two tables pushed together seat 10 people. Three tables seat 14 people.
How many people can sit at a row of 9 tables?
Answer:
81 mark
An evening sightseeing bus tour sets off at 18:45 and lasts 1 hour and 50 minutes.
At what time does the tour finish? Give your answer using the 24-hour clock.
Answer:
91 mark
A flapjack recipe uses 45 g of butter and 60 g of oats.
Write the ratio of butter to oats in its simplest form.
Answer:
101 mark
Each minibus can carry 15 children. A school is taking 100 children to a museum, and every child must have a seat.
What is the smallest number of minibuses the school needs?
Answer:
111 mark
A rectangular pond measures 3 m by 2 m. A safety fence is put up all the way round it, exactly 1 m away from the pond on every side.
What is the total length of the fence? Give your answer in metres.
The diagram is not drawn to size.
Answer:
121 mark
One half of a number is 3 more than one third of the same number.
What is the number?
Answer:
131 mark
A garden centre pours 1.5 kg of poppy seed into small packets. Each packet holds 12 g of seed.
How many packets can be filled?
Answer:
141 mark
A charity buys 15 identical sleeping bags and the bill comes to 96 pounds.
How much does one sleeping bag cost? Give your answer in pounds and pence.
Answer:
151 mark
A box with a volume of 1536 cubic centimetres is filled exactly by 24 identical wooden cubes, packed with no gaps.
What is the length of one edge of a cube? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
161 mark
Two identical mugs and one teaspoon cost 7 pounds 30 pence altogether. The teaspoon on its own costs 90 pence.
How much does one mug cost? Give your answer in pounds and pence.
Answer:
171 mark
On a shelf, two fifths of the books are novels and three tenths are poetry.
What fraction of the books on the shelf are novels or poetry? Give your answer in its simplest form.
Answer:
181 mark
A delivery lorry has a load with a mass of 3.25 tonnes.
What is the mass of the load in kilograms?
Answer:
191 mark
A garden tap fills a 45 litre water butt in 15 minutes.
Running at the same rate, how long would the tap take to fill a 120 litre barrel? Give your answer in minutes.
Answer:
201 mark
A running club has 260 members and 35 per cent of them enter a half marathon.
How many members enter the half marathon?
Answer:
211 mark
A rectangular sticker has an area of 48 square centimetres. Its length is 3 times its width.
How wide is the sticker? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
221 mark
A print shop charges 18 pounds to print 60 leaflets.
At the same rate for each leaflet, how much would it charge to print 150 leaflets? Give your answer in pounds.
Answer:
231 mark
In a stationery shop pencils cost 45p each and rulers cost 80p each.
Zara buys 6 pencils and some rulers, and spends 5 pounds 90 pence altogether.
How many rulers does Zara buy?
Answer:
241 mark
The school day runs from 09:00 until 15:15. Break and lunch together take 75 minutes of that time.
How many minutes are left for lessons? Give your answer in minutes.
Answer:
251 mark
A straight fence post leans across a level path. The two angles it makes with the path, on the same side, sit on a straight line. One of them is 118 degrees.
What is the size of the other angle? Give your answer in degrees.
The diagram is not drawn to size.
Answer:

Answers, mark scheme and worked explanations

11 mark
324
Split 27 into 20 and 7 to make the multiplication easier.
20 trays hold 20 x 12 = 240 eggs, and 7 trays hold 7 x 12 = 84 eggs.
240 + 84 = 324 eggs.
21 mark
255 cm
Put both lengths into the same unit first. There are 100 cm in a metre, so 3.4 m is 340 cm.
340 - 85 = 255 cm of ribbon left.
Writing 2.55 would be answering in metres when the question asked for centimetres, so it scores nothing.
31 mark
190
One ninth of 342 is 342 divided by 9, which is 38.
Five ninths is 5 x 38 = 190 wristbands.
The 152 left over are the four ninths that were not given away.
41 mark
69.50
Find the cost of one guide first: 41.70 divided by 6 = 6.95, so one guide costs 6 pounds 95 pence.
Ten guides cost 10 x 6.95 = 69.50.
Money answers are written to two decimal places, so 69.5 should be recorded as 69 pounds 50 pence.
51 mark
6 cm
A rectangle has two long sides and two short sides, so half the perimeter is one long side plus one short side.
Half of 34 is 17, so the two different sides add up to 17 cm.
17 - 11 = 6 cm. Taking 11 away from the whole 34 instead of from 17 gives 23, which is the trap.
61 mark
7
Add the five scores: 7 + 4 + 9 + 12 + 3 = 35.
Divide by how many matches there are: 35 divided by 5 = 7 goals per match.
71 mark
38
The first table seats 6. Each table added after that seats 4 more, because the two sides that touch cannot be used.
After the first table there are 8 more to add: 8 x 4 = 32.
6 + 32 = 38 people.
Multiplying 9 by 6 gives 54, which forgets that the places where tables meet are lost.
81 mark
20:35
Add the whole hour first: 18:45 becomes 19:45.
Then add the 50 minutes in two steps. 15 minutes takes you to 20:00, and the 35 minutes left takes you to 20:35.
Writing 8:35 pm answers the right time in the wrong format, and the question asked for the 24-hour clock.
91 mark
3 : 4
- Accept 3 : 4 or 3:4 only. 45 : 60, 9 : 12 and 4 : 3 all score nothing.
Start from 45 : 60. The largest number that divides into both is 15.
45 divided by 15 is 3, and 60 divided by 15 is 4, so the ratio is 3 : 4.
Butter is written first because the question asks for butter to oats. Answering 4 : 3 turns the ratio round.
101 mark
7
Six minibuses would carry 6 x 15 = 90 children, which leaves 10 children behind.
Seven minibuses carry 105, so 7 is the smallest number that works.
A remainder answer such as 6 remainder 10 is not a number of minibuses, and the last ten children still need one.
111 mark
18 m
The fence gains 1 m at each end of the pond, so it makes a rectangle 3 + 1 + 1 = 5 m by 2 + 1 + 1 = 4 m.
The length of the fence is the perimeter of that rectangle: 2 x (5 + 4) = 18 m.
Adding only 1 m to each measurement, instead of 1 m at both ends, gives 2 x (4 + 3) = 14 m, which is the trap.
121 mark
18
Halves and thirds are easiest to compare in sixths: one half is three sixths and one third is two sixths.
So one half is one sixth of the number bigger than one third of it, and that one sixth must be the 3.
If one sixth of the number is 3, the whole number is 6 x 3 = 18.
Check it: half of 18 is 9, a third of 18 is 6, and 9 is indeed 3 more than 6.
131 mark
125
Put both masses into grams first: 1.5 kg is 1500 g.
1500 divided by 12: twelve 100s make 1200, leaving 300, and twelve 25s make 300.
So 100 + 25 = 125 packets.
141 mark
6.40
96 divided by 15: fifteen 6s make 90, leaving 6 pounds still to share.
6 pounds shared between 15 is 600 pence divided by 15 = 40 pence.
So one sleeping bag costs 6 pounds 40 pence. Money is written with two decimal places: 6.40.
151 mark
4 cm
The 24 cubes share the whole 1536 cubic centimetres between them, so one cube has volume 1536 divided by 24 = 64 cubic centimetres.
For a cube, the volume is one edge multiplied by itself three times.
4 x 4 x 4 = 64, so each edge is 4 cm.
Answering 64 gives the volume of one cube rather than the length asked for.
161 mark
3.20
Take the teaspoon out of the total first: 7.30 - 0.90 = 6.40, which is the cost of the two mugs.
The mugs are identical, so one costs 6.40 divided by 2 = 3.20.
Check by building the total back up: 3.20 + 3.20 + 0.90 = 7.30.
171 mark
7/10
- Accept 7/10 or seven tenths. 14/20 is not in simplest form.
Give both fractions the same denominator. Tenths work, because 5 goes into 10.
Two fifths is 4/10, and three tenths stays as 3/10.
4/10 + 3/10 = 7/10, which is already in its simplest form because 7 and 10 share no factor.
181 mark
3250 kg
There are 1000 kilograms in a tonne, so multiply by 1000.
3.25 x 1000 = 3250 kilograms.
Multiplying by 1000 moves every digit three places, so 3.25 becomes 3250 and not 325.
191 mark
40 minutes
Work out the rate first: 45 litres in 15 minutes is 45 divided by 15 = 3 litres every minute.
120 litres at 3 litres a minute takes 120 divided by 3 = 40 minutes.
Another route is to notice 120 is not quite three times 45, so the answer must be a little under three lots of 15 minutes.
201 mark
91
Find 10 per cent first by dividing by 10: 26 members.
30 per cent is 3 x 26 = 78, and 5 per cent is half of 26, which is 13.
78 + 13 = 91 members.
211 mark
4 cm
Try widths in order and work out the matching length and area. A width of 3 gives a length of 9 and an area of 27, which is too small.
A width of 4 gives a length of 12, and 4 x 12 = 48, which is exactly right.
So the sticker is 4 cm wide and 12 cm long.
Dividing 48 by 3 to get 16 finds neither side, because it treats the area as if it were a length.
221 mark
45
Find the cost of one leaflet: 18 pounds divided by 60 = 0.30, so 30 pence each.
150 leaflets cost 150 x 0.30 = 45 pounds.
Another way is to notice that 150 is two and a half times 60, and 18 x 2.5 = 45.
231 mark
4
The pencils cost 6 x 45p = 270p, which is 2 pounds 70 pence.
Take that off the total: 5.90 - 2.70 = 3.20, so the rulers cost 3 pounds 20 pence.
320 divided by 80 = 4 rulers.
Dividing the whole 5.90 by 0.80 forgets the pencils and does not give a whole number of rulers.
241 mark
300 minutes
From 09:00 to 15:15 is 6 hours and 15 minutes.
Turn that into minutes: 6 x 60 = 360, and 360 + 15 = 375 minutes.
Take off the breaks: 375 - 75 = 300 minutes of lessons.
Working in hours and minutes gives 5 hours and 0 minutes, which is the same answer, but the question asked for minutes.
251 mark
62
Angles that sit next to each other on a straight line always add up to 180 degrees.
180 - 118 = 62 degrees.
Using 360 instead of 180 would give 242, which is far too big to fit beside an obtuse angle on a line.

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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