NWSSEE Mathematics Mock Paper 8

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: Hard

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 shop buys 35 boxes of chocolate bars, and every box holds 24 bars. The shop sells every bar for 85 pence.
How much money does the shop take? Give your answer in pounds.
Answer:
21 mark
A water tank is three eighths full. Another 90 litres of water is poured in, and the tank is then three quarters full.
How many litres does the tank hold when it is completely full?
Answer:
31 mark
The area of a rectangle is 72 square centimetres and its length is twice its width.
Work out the perimeter of the rectangle. Give your answer in centimetres.
Answer:
41 mark
A car travels at a steady speed of 72 kilometres per hour.
How far does it travel in 25 minutes? Give your answer in kilometres.
Answer:
51 mark
Three friends buy a present costing 47 pounds 40 pence and share the cost equally. Two of them each pay with a 20 pound note.
How much change do those two friends receive between them? Give your answer in pounds.
Answer:
61 mark
Tins are stacked so that the top row has 1 tin, the next row has 2 tins, the row below has 3 tins, and so on down the stack.
A complete stack uses exactly 78 tins.
How many rows does the stack have?
Answer:
71 mark
Five numbers have a mean of 12. Two of the five numbers are taken away, and the mean of the three that are left is 10.
What is the mean of the two numbers that were taken away?
Answer:
81 mark
A lorry can carry a load of at most 2.5 tonnes. Crates each have a mass of 180 kg.
What is the greatest number of whole crates the lorry can carry?
Answer:
91 mark
In a sale a bicycle is sold with 15 per cent off its usual price. The sale price is 204 pounds.
What was the usual price? Give your answer in pounds.
Answer:
101 mark
The three edge lengths of a cuboid are in the ratio 1 : 2 : 3, and its volume is 750 cubic centimetres.
How long is its longest edge? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
111 mark
Here are four fractions.
4/9 5/11 7/15 9/20
Which one is closest to one half?
Answer:
121 mark
At a summer fete, adult tickets cost 4 pounds and child tickets cost 2 pounds 50 pence. Altogether 60 tickets are sold and 195 pounds is taken.
How many adult tickets were sold?
Answer:
131 mark
The first bus of the day leaves at 06:20, and buses then leave every 18 minutes.
At what time does the 10th bus of the day leave? Give your answer using the 24-hour clock.
Answer:
141 mark
One of the angles in an isosceles triangle is 116 degrees.
What is the size of each of the other two angles? Give your answer in degrees.
The diagram is not drawn to size.
Answer:
151 mark
In a sequence, every term after the first two is made by adding the two terms before it.
The 3rd term is 11 and the 5th term is 29.
What is the 1st term?
Answer:
161 mark
A rectangular field measures 250 m by 120 m. One hectare is 10 000 square metres.
What is the area of the field? Give your answer in hectares.
Answer:
171 mark
A recipe for 12 muffins uses 300 g of flour and 180 g of sugar.
How much sugar is needed to make 18 muffins? Give your answer in grams.
Answer:
181 mark
A school hires 4 minibuses for a trip. Each minibus has 17 seats, and every seat costs 25 pounds.
What is the total cost? Give your answer in pounds.
Answer:
191 mark
A room has a floor measuring 4.5 m by 3 m. It is covered with square carpet tiles with sides of 50 cm, and no tile is cut.
How many tiles are needed?
The diagram is not drawn to size.
Answer:
201 mark
Four classes collect tins for a food bank.
Class 6A collects 132, class 6B collects 96, class 6C collects 154 and class 6D collects 118.
What is the mean number of tins collected by a class?
Answer:
211 mark
A jug contains 1.2 litres of juice. 350 ml is poured out.
How much juice is left in the jug? Give your answer in millilitres.
Answer:
221 mark
There are 30 children in a class and 18 of them are girls.
Write down the ratio of boys to girls in its simplest form.
Answer:
231 mark
A tap fills a bath at 12 litres a minute, but at the same time water leaks out of the plughole at 2 litres a minute.
The bath holds 150 litres. How long does it take to fill? Give your answer in minutes.
Answer:
241 mark
A fish tank is a cuboid, 50 cm long, 25 cm wide and 30 cm deep. It is filled right to the top.
How much water does it hold? Give your answer in litres.
The diagram is not drawn to size.
Answer:
251 mark
What is the smallest whole number, greater than zero, that divides exactly by 4, by 6 and by 15?
Answer:

Answers, mark scheme and worked explanations

11 mark
714
First count the bars: 35 x 24. That is 35 x 20 = 700 plus 35 x 4 = 140, giving 840 bars.
Now find the takings: 840 x 85 pence. 840 x 80 = 67 200 pence and 840 x 5 = 4200 pence.
67 200 + 4200 = 71 400 pence, which is 714 pounds.
An easier route is to see that 4 bars cost 3 pounds 40 pence, so 840 bars cost 210 x 3.40 = 714 pounds.
21 mark
240 litres
Write both fractions in eighths so they can be compared: three quarters is six eighths.
So the 90 litres filled it from three eighths to six eighths, which is three eighths of the tank.
One eighth is 90 divided by 3 = 30 litres.
The full tank is eight eighths: 8 x 30 = 240 litres. Treating 90 litres as three eighths of what was missing is the muddle to avoid.
31 mark
36 cm
If the width is one part, the length is two parts, so the area is two parts multiplied together.
Try widths: 5 by 10 gives 50 and 7 by 14 gives 98, but 6 by 12 gives exactly 72.
So the rectangle is 6 cm by 12 cm.
The perimeter is 2 x (6 + 12) = 36 cm. Answering 72 or 18 would be the area or half the perimeter.
41 mark
30 km
In one minute the car travels 72 divided by 60 = 1.2 km.
In 25 minutes it travels 25 x 1.2 = 30 km.
You could also see 25 minutes as five twelfths of an hour: five twelfths of 72 is 5 x 6 = 30 km.
51 mark
8.40
Each friend owes 47.40 divided by 3 = 15 pounds 80 pence.
A 20 pound note leaves change of 20 - 15.80 = 4 pounds 20 pence.
Two friends do this, so the change between them is 2 x 4.20 = 8 pounds 40 pence.
Answering 4.20 gives one person's change, and the question asks for both.
61 mark
12
Add the rows up until you reach 78. After 5 rows there are 15 tins, after 10 rows there are 55.
Keep going: 11 rows gives 55 + 11 = 66, and 12 rows gives 66 + 12 = 78.
So the stack has 12 rows.
A neat check is that the rows from 1 to 12 pair up as 1 + 12, 2 + 11 and so on: six pairs of 13, which is 78.
71 mark
15
The five numbers add up to 5 x 12 = 60.
The three that remain add up to 3 x 10 = 30.
So the two that were taken away add up to 60 - 30 = 30.
Their mean is 30 divided by 2 = 15. Answering 30 gives their total, not their mean.
81 mark
13
One tonne is 1000 kg, so 2.5 tonnes is 2500 kg.
Count up in crates: 180 x 10 = 1800, 180 x 13 = 2340, and 180 x 14 = 2520.
14 crates would be over the limit, so the lorry can carry 13 crates.
Rounding 2500 divided by 180 up to 14 is the trap: with loads like this you always round down.
91 mark
240
If 15 per cent has come off, the 204 pounds is 85 per cent of the usual price.
So 1 per cent is 204 divided by 85 = 2 pounds 40 pence.
The usual price is 100 per cent: 100 x 2.40 = 240 pounds.
Adding 15 per cent onto 204 gives 234.60, which is wrong because the percentage is of the larger, original price.
101 mark
15 cm
Call the shortest edge one part. The other two are 2 parts and 3 parts, so the volume is 1 x 2 x 3 = 6 lots of one part multiplied by itself three times.
750 divided by 6 = 125, so one part multiplied by itself three times is 125.
5 x 5 x 5 = 125, so one part is 5 cm.
The longest edge is 3 parts: 3 x 5 = 15 cm. Check: 5 x 10 x 15 = 750.
111 mark
7/15
- Accept 7/15 or seven fifteenths only.
Every one of these is just below a half, because in each case the top number is a little less than half the bottom number.
Compare each one with half of its own denominator. Half of 9 is 4.5, so 4/9 is half a ninth short. Half of 15 is 7.5, so 7/15 is half a fifteenth short.
The gaps are 1/18, 1/22, 1/30 and 1/20 in that order, and the smallest gap is 1/30.
So 7/15 is the closest to a half. Picking 4/9 because its numbers are smallest is the trap.
121 mark
30
Start by pretending all 60 tickets were child tickets: 60 x 2.50 = 150 pounds.
The real takings are 195 pounds, which is 45 pounds more.
Changing one child ticket into an adult ticket adds 4 - 2.50 = 1 pound 50 pence.
45 divided by 1.50 = 30, so 30 adult tickets were sold. Check: 30 x 4 = 120 and 30 x 2.50 = 75, and 120 + 75 = 195.
131 mark
09:02
There are only 9 gaps between the 1st bus and the 10th bus, not 10.
9 x 18 = 162 minutes, which is 2 hours and 42 minutes.
06:20 plus 2 hours is 08:20, and plus 42 minutes is 09:02.
Using 10 gaps gives 09:20, which is the trap this question is built around.
141 mark
32
A triangle cannot have two angles of 116 degrees, because that alone is more than 180 degrees. So 116 degrees must be the odd angle out and the other two are equal.
The two equal angles share 180 - 116 = 64 degrees.
Each one is 64 divided by 2 = 32 degrees.
151 mark
4
The 5th term is the 3rd term plus the 4th term, so the 4th term is 29 - 11 = 18.
The 4th term is the 2nd term plus the 3rd term, so the 2nd term is 18 - 11 = 7.
The 3rd term is the 1st plus the 2nd, so the 1st term is 11 - 7 = 4.
Check the whole sequence: 4, 7, 11, 18, 29.
161 mark
3 hectares
The area in square metres is 250 x 120 = 30 000.
Divide by 10 000 to change square metres into hectares: 30 000 divided by 10 000 = 3 hectares.
Leaving the answer as 30 000 ignores the unit the question asks for.
171 mark
270 g
18 muffins is one and a half times 12 muffins.
So the sugar is one and a half times 180 g: 180 + 90 = 270 g.
The flour amount is given only to see whether you pick the right number to scale up.
181 mark
1700
There are 4 x 17 = 68 seats altogether.
The cost is 68 x 25 pounds.
A quick way is to multiply by 100 and then divide by 4, because 25 is a quarter of 100: 6800 divided by 4 = 1700 pounds.
191 mark
54
Work in centimetres: the floor is 450 cm by 300 cm.
Along the longer side, 450 divided by 50 = 9 tiles.
Along the shorter side, 300 divided by 50 = 6 tiles.
That is 9 rows of 6, which is 54 tiles. Dividing the areas is another route: 135 000 divided by 2500 also gives 54.
201 mark
125
Add the four totals: 132 + 96 = 228, and 154 + 118 = 272.
228 + 272 = 500 tins altogether.
The mean is 500 divided by 4 = 125 tins.
211 mark
850 ml
Change the litres into millilitres first: 1.2 litres = 1200 ml.
1200 - 350 = 850 ml.
Answering 0.85 would be the right amount in the wrong unit, and the question asks for millilitres.
221 mark
2 : 3
- Accept 2 : 3 or 2:3. 12 : 18 is not simplified and 3 : 2 is the wrong way round; neither scores.
There are 30 - 18 = 12 boys.
The ratio of boys to girls is 12 : 18.
Divide both sides by 6 to get 2 : 3.
The order matters. The question says boys to girls, so the boys' number is written first.
231 mark
15 minutes
Work out how fast the water level really rises: 12 - 2 = 10 litres a minute.
150 divided by 10 = 15 minutes.
Using 12 litres a minute and ignoring the leak gives 12.5 minutes, which is the trap.
241 mark
37.5 litres
The volume is 50 x 25 x 30. First 50 x 25 = 1250, then 1250 x 30 = 37 500 cubic centimetres.
There are 1000 cubic centimetres in a litre, so divide by 1000: 37.5 litres.
Leaving the answer as 37 500 uses the wrong unit.
251 mark
60
Multiples of 15 are the least common, so run through them and test each one: 15, 30, 45, 60.
15, 30 and 45 do not divide by 4. 60 divides by 4 to give 15, by 6 to give 10 and by 15 to give 4.
So the answer is 60. Multiplying 4 x 6 x 15 to get 360 gives a number that works but is not the smallest.

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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