NWSSEE Mathematics Mock Paper 3

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 concert hall is laid out with 28 rows of seats, and every row has 24 seats in it.
How many seats are there in the hall?
Answer:
21 mark
A youth orchestra has 96 players, and seven twelfths of them play a stringed instrument.
How many of the players play a stringed instrument?
Answer:
31 mark
A shortbread recipe needs 0.75 kg of flour and 250 g of caster sugar.
What is the total mass of the flour and the sugar? Give your answer in grams.
Answer:
41 mark
A rectangular kitchen floor measures 4.5 m by 3 m. It is to be covered with square tiles measuring 50 cm along each side, with no tiles cut.
How many tiles are needed to cover the floor exactly?
The diagram is not drawn to size.
Answer:
51 mark
The sleeper service pulls out of the platform at 07:48 and the whole journey takes 3 hours and 27 minutes.
At what time does it reach its destination? Give your answer using the 24-hour clock.
Answer:
61 mark
A post office weighs five parcels. Their masses are recorded below.
1.2 kg, 0.8 kg, 2.5 kg, 1.1 kg, 0.4 kg
What is the difference in mass between the heaviest parcel and the lightest parcel? Give your answer in grams.
Answer:
71 mark
A novel has 240 pages. Elsie reads one third of the book on Monday.
On Tuesday she reads three eighths of the pages that are still left.
How many pages of the novel has Elsie still not read?
Answer:
81 mark
Work out the value of the calculation below. Deal with the brackets before anything else.
3 x (17 + 48) - 90
Answer:
91 mark
A regular pentagon is cut from card. The distance all the way round its edge is 47.5 cm.
How long is one side of the pentagon? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
101 mark
A broadband contract is charged at 34 pounds 80 pence every month.
How much does the contract cost for a full year? Give your answer in pounds and pence.
Answer:
111 mark
In this sequence every term is double the term before it, minus 1.
3, 5, 9, 17, ...
What is the sixth term of the sequence?
Answer:
121 mark
Concrete is mixed using cement and sand in the ratio 2 : 7 by mass. A builder uses 21 kg of sand.
What is the total mass of the concrete he mixes? Give your answer in kilograms.
Answer:
131 mark
A car park charges 1 pound 60 pence for the first hour and then 90 pence for every extra half hour or part of one.
Mrs Hollis parks from 09:30 until 12:00. How much does she pay? Give your answer in pounds and pence.
Answer:
141 mark
A wooden cube is painted on every face. The total area painted is 96 square centimetres.
How long is one edge of the cube? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
151 mark
A cinema sells 320 tickets for a screening. Adult tickets cost 9 pounds and child tickets cost 5 pounds.
Exactly 180 of the tickets sold are adult tickets.
How much money does the cinema take altogether? Give your answer in pounds.
Answer:
161 mark
A water tank is four fifths full. One sixth of a full tank is then used on the allotment.
What fraction of the tank is left? Give your answer in its simplest form.
Answer:
171 mark
A cookery book says a joint of beef should be roasted for 1 hour and 25 minutes. The oven timer can only be set in whole minutes.
How many minutes should the timer be set to?
Answer:
181 mark
Two of the angles in a triangle are equal to each other. The third angle is 3 times the size of each of those two.
What is the size of the largest angle in the triangle? Give your answer in degrees.
The diagram is not drawn to size.
Answer:
191 mark
A cyclist rides 36 km and it takes her 1 hour and 30 minutes.
What is her average speed? Give your answer in kilometres per hour.
Answer:
201 mark
A rectangle drawn on squared paper measures 0.4 units along one edge and 0.7 units along the other.
Multiply those two decimals together and write down the result.
Answer:
211 mark
A water butt in a garden holds 210 litres when it is full. It is emptied using a watering can that holds 7.5 litres.
How many full watering cans can be taken from the butt?
Answer:
221 mark
A gardener plants tulip bulbs and daffodil bulbs in the ratio 5 : 3. She plants 96 bulbs altogether.
Write down how many tulip bulbs and how many daffodil bulbs she plants, in that order.
Answer:
231 mark
A packing crate is a cuboid measuring 24 cm by 20 cm by 12 cm on the inside. It is filled with wooden cubes of side 4 cm, packed with no gaps.
How many cubes fit inside the crate?
The diagram is not drawn to size.
Answer:
241 mark
Ben has twice as many football stickers as Amy. Between them they have 51 stickers.
How many stickers does Ben have?
Answer:
251 mark
A rectangular park measures 240 m by 160 m. Aisha jogs right round the edge of the park three times.
How far does Aisha jog? Give your answer in kilometres.
The diagram is not drawn to size.
Answer:

Answers, mark scheme and worked explanations

11 mark
672
Break 24 into 20 and 4.
28 x 20 = 560, and 28 x 4 = 112.
560 + 112 = 672 seats.
21 mark
56
One twelfth of 96 is 96 divided by 12, which is 8 players.
Seven twelfths is 7 x 8 = 56 players.
The other five twelfths, 40 players, are on wind, brass and percussion.
31 mark
1000 g
Convert the flour into the same unit as the sugar. There are 1000 g in a kilogram, so 0.75 kg is 750 g.
750 + 250 = 1000 g.
That is the same as 1 kg, but the question asked for grams, so write 1000.
41 mark
54
Work in the same unit. Each tile is 50 cm, which is half a metre, so two tiles fit in every metre.
Along the 4.5 m side: 4.5 divided by 0.5 = 9 tiles.
Along the 3 m side: 3 divided by 0.5 = 6 tiles.
The tiles sit in 6 rows of 9: 6 x 9 = 54 tiles.
Dividing the floor area of 13.5 square metres by 50 mixes metres with centimetres and gives nonsense.
51 mark
11:15
Add the 3 whole hours first: 07:48 becomes 10:48.
Now add 27 minutes. 12 minutes reaches 11:00, and there are 15 minutes still to add.
That takes you to 11:15.
61 mark
2100 g
Read the biggest and smallest values off the list: the heaviest is 2.5 kg and the lightest is 0.4 kg.
2.5 - 0.4 = 2.1 kg.
The answer must be in grams, so multiply by 1000: 2.1 kg = 2100 g.
71 mark
100
Monday: one third of 240 is 80 pages, so 240 - 80 = 160 pages are left.
Tuesday: three eighths of those 160 pages. One eighth of 160 is 20, so three eighths is 60 pages.
160 - 60 = 100 pages still unread.
The trap is taking three eighths of the whole 240 instead of the 160 that remained, which would give 90 and the wrong final answer.
81 mark
105
Brackets come first: 17 + 48 = 65.
Then multiplication before subtraction: 3 x 65 = 195.
Finally 195 - 90 = 105.
Ignoring the brackets and working left to right gives 3 x 17 = 51, then 51 + 48 - 90 = 9, which is wrong.
91 mark
9.5 cm
A regular pentagon has 5 sides that are all the same length.
47.5 divided by 5 = 9.5 cm.
Check by multiplying back: 5 x 9.5 = 47.5 cm.
101 mark
417.60
A year has 12 months, so work out 34.80 x 12.
34.80 x 10 = 348.00, and 34.80 x 2 = 69.60.
348.00 + 69.60 = 417.60, so the contract costs 417 pounds 60 pence.
111 mark
65
Check the rule on the numbers you are given: 3 doubled is 6, minus 1 is 5. Then 5 doubled is 10, minus 1 is 9.
The fifth term is 17 doubled minus 1 = 33.
The sixth term is 33 doubled minus 1 = 65.
The gaps grow each time, so guessing that the numbers go up in a fixed step will not work here.
121 mark
27 kg
The sand is 7 parts and weighs 21 kg, so one part is 21 divided by 7 = 3 kg.
The cement is 2 parts: 2 x 3 = 6 kg.
The whole mix is 9 parts, so 9 x 3 = 27 kg. Answering 6 gives only the cement, not the total.
131 mark
4.30
From 09:30 to 12:00 is 2 hours and 30 minutes in total.
The first hour costs 1 pound 60 pence and leaves 1 hour 30 minutes to pay for.
1 hour 30 minutes is three half hours, costing 3 x 90p = 270p, which is 2 pounds 70 pence.
1.60 + 2.70 = 4.30, so she pays 4 pounds 30 pence.
Charging all five half hours at 90p forgets that the first hour has its own price.
141 mark
4 cm
A cube has 6 identical square faces, so one face has area 96 divided by 6 = 16 square centimetres.
A square of area 16 has sides of 4 cm, because 4 x 4 = 16.
So each edge is 4 cm. Its volume would be 64 cubic centimetres, but that is not what was asked for.
151 mark
2320
Work out the child tickets first: 320 - 180 = 140 of them.
Adults bring in 180 x 9 = 1620 pounds.
Children bring in 140 x 5 = 700 pounds.
1620 + 700 = 2320 pounds altogether.
161 mark
19/30
- Accept 19/30 or nineteen thirtieths. Subtracting the tops and bottoms to get 3/1 scores nothing.
Thirtieths work for both fractions, because 30 is the smallest number that 5 and 6 both divide into.
Four fifths is 24/30 and one sixth is 5/30.
24/30 - 5/30 = 19/30, which cannot be simplified because 19 is prime and does not divide 30.
171 mark
85 minutes
One hour is 60 minutes.
60 + 25 = 85 minutes.
Writing 125 comes from treating the hour as 100 minutes, which is a common slip when a clock reading is copied straight across.
181 mark
108
Count the angles in equal parts: the two matching angles are 1 part each and the third is 3 parts, making 5 parts altogether.
The angles of a triangle total 180 degrees, so one part is 180 divided by 5 = 36 degrees.
The largest angle is 3 parts: 3 x 36 = 108 degrees.
Check: 36 + 36 + 108 = 180 degrees.
191 mark
24 km/h
In 1 hour and 30 minutes there are three half hours, and she covers the same distance in each on average.
36 divided by 3 = 12 km in every half hour, so in a whole hour she covers 2 x 12 = 24 km.
So her average speed is 24 km/h. Dividing 36 by 1.30 does not work, because 30 minutes is half an hour, not 0.30 of one.
201 mark
0.28
Ignore the decimal points to begin with: 4 x 7 = 28.
Each of the two numbers has one digit after the decimal point, so the answer has two.
That makes 0.28. Answering 2.8 is the classic slip, and it would mean the rectangle was bigger than a unit square, which is impossible when both sides are under 1.
211 mark
28
Doubling both numbers keeps the answer the same and gets rid of the decimal: 420 divided by 15.
15 x 28 = 420, so the answer is 28 cans.
Check it another way: two cans hold 15 litres, and 210 divided by 15 = 14 pairs of cans, which is 28 cans.
221 mark
60 tulips and 36 daffodils
- Accept 60 and 36 in that order, however it is written. Both numbers are needed for the mark.
- 36 and 60 the other way round scores nothing, and so does giving only one of the two numbers.
The ratio 5 : 3 has 5 + 3 = 8 parts altogether.
96 divided by 8 = 12 bulbs in one part.
Tulips take 5 parts: 5 x 12 = 60. Daffodils take 3 parts: 3 x 12 = 36.
Check that they add back to the total: 60 + 36 = 96.
231 mark
90
Work out how many cubes fit along each edge: 24 divided by 4 = 6, 20 divided by 4 = 5, and 12 divided by 4 = 3.
So the cubes sit in a block 6 by 5 by 3.
6 x 5 = 30 cubes in one layer, and there are 3 layers: 30 x 3 = 90 cubes.
You can check with volumes: the crate holds 5760 cubic centimetres and each cube is 64, and 5760 divided by 64 = 90.
241 mark
34
Think of Amy's pile as one part. Ben has two of those parts, so together they have 3 parts.
51 divided by 3 = 17 stickers in one part, which is Amy's pile.
Ben has two parts: 2 x 17 = 34 stickers. Check: 17 + 34 = 51.
251 mark
2.4 km
Once round the edge is 2 x (240 + 160) = 2 x 400 = 800 m.
Three laps are 3 x 800 = 2400 m.
There are 1000 m in a kilometre, so 2400 m = 2.4 km.
Leaving the answer as 2400 would be metres, and the question asked for kilometres.

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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