NWSSEE Mathematics Mock Paper 5

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: 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 machine in a sorting office seals 45 envelopes every minute and runs without stopping for 1 hour and 20 minutes.
How many envelopes does the machine seal?
Answer:
21 mark
A sack of birdseed holds 3.2 kg. A wildlife group uses five eighths of the sack in one week.
What mass of birdseed does the group use? Give your answer in grams.
Answer:
31 mark
A rectangular window pane has an area of 96 square centimetres and is 6 cm wide.
What is the perimeter of the pane? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
41 mark
Two whole numbers add up to 74. When the smaller is taken away from the larger, the answer is 18.
What is the larger of the two numbers?
Answer:
51 mark
A dripping tap loses 3 ml of water every 5 seconds, hour after hour.
How much water does the tap waste in one hour? Give your answer in litres.
Answer:
61 mark
A chart shows how the 30 children in one class travel to school.
Walk 12, bus 9, car 6, cycle 3
What fraction of the class walk to school? Give your answer in its simplest form.
Answer:
71 mark
A shade of pink is mixed from red paint and white paint in the ratio 3 : 5.
Ali has 12 litres of red paint and 25 litres of white paint, and no way of getting more.
What is the greatest amount of pink paint he can mix? Give your answer in litres.
Answer:
81 mark
Three tins in a shopping bag have a total mass of 5.06 kg. One tin with a mass of 1.28 kg is taken out, and a jar with a mass of 0.9 kg is put in.
What is the total mass in the bag now? Give your answer in kilograms.
Answer:
91 mark
An equilateral triangle has sides of 12 cm. A regular hexagon has exactly the same perimeter as the triangle.
How long is one side of the hexagon? Give your answer in centimetres.
The diagrams are not drawn to size.
Answer:
101 mark
A carpenter joins a piece of skirting board 1 and 3 quarters of a metre long to a piece 2 and 5 sixths of a metre long.
What is the total length in metres? Give your answer as a mixed number in its simplest form.
Answer:
111 mark
An express service keeps up an average speed of 96 km per hour for the whole of a 168 km trip.
How long does the trip take? Give your answer in hours and minutes.
Answer:
121 mark
A badge is made by joining an equilateral triangle with sides of 10 cm to one edge of a square with sides of 10 cm, so the joined edges meet exactly and the badge is one closed shape.
What is the perimeter of the badge? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
131 mark
A garden centre stacks bags of compost onto a pallet. Each bag has a mass of 22.5 kg and a full pallet takes 40 bags.
What is the mass of a full pallet of compost? Give your answer in tonnes.
Answer:
141 mark
A shop adds a service charge of 8 per cent to a bill of 3 pounds 50 pence.
How much is the service charge? Give your answer in pence.
Answer:
151 mark
An outdoor centre buys 3 identical tents and 2 identical stoves for 445 pounds altogether.
One tent costs 35 pounds more than one stove.
How much does one tent cost? Give your answer in pounds.
Answer:
161 mark
The rule for this sequence is: halve the term before, then add 10.
100, 60, 40, 30, ...
What is the next term?
Answer:
171 mark
In a survey about school lunches, two fifths of the people asked chose the pasta and one third chose the curry. The remaining 32 people chose the salad.
How many people took part in the survey?
Answer:
181 mark
A tank measuring 30 cm by 20 cm by 15 cm is full of water. All of the water is poured into a second, empty tank whose base measures 25 cm by 24 cm and which is deep enough to hold it all.
How deep is the water in the second tank? Give your answer in centimetres.
The diagrams are not drawn to size.
Answer:
191 mark
Two cyclists set off at the same moment from opposite ends of a straight 60 km towpath and ride towards each other.
One rides at 14 km per hour and the other at 16 km per hour.
How long is it before they meet? Give your answer in hours.
Answer:
201 mark
A kitchen clock runs 4 minutes slow. It shows the time as 14:37.
What is the correct time? Give your answer using the 24-hour clock.
Answer:
211 mark
Two whole numbers that follow one after the other are multiplied together, and the answer is 156.
What is the smaller of the two numbers?
Answer:
221 mark
A wildlife park counts 24 deer and 96 rabbits on its heath.
Write the ratio of deer to rabbits in the form 1 : n.
Answer:
231 mark
A solid block of wood measures 12 cm by 8 cm by 5 cm. Every face of the block is painted red.
The block is then cut into cubes with edges of 1 cm.
How many of these small cubes have no red paint on them at all?
The diagram is not drawn to size.
Answer:
241 mark
Kai is 4 years older than Mia. In three years' time their two ages will add up to 32.
How old is Mia now?
Answer:
251 mark
A clothes shop runs an offer: buy any three jumpers and the cheapest of the three is free.
Kim chooses jumpers priced at 24 pounds, 30 pounds and 27 pounds.
How much does Kim pay? Give your answer in pounds.
Answer:

Answers, mark scheme and worked explanations

11 mark
3600
First turn the running time into minutes: 1 hour and 20 minutes is 60 + 20 = 80 minutes.
80 x 45: eighty 40s make 3200 and eighty 5s make 400.
3200 + 400 = 3600 envelopes.
21 mark
2000 g
Change the mass into grams first: 3.2 kg is 3200 g.
One eighth of 3200 is 3200 divided by 8 = 400 g.
Five eighths is 5 x 400 = 2000 g.
That is 2 kg, but the question asked for grams, so the answer on the line is 2000.
31 mark
44 cm
Find the missing side by dividing: 96 divided by 6 = 16 cm long.
The perimeter is 2 x (16 + 6) = 2 x 22 = 44 cm.
Adding 16 and 6 to get 22 counts only two of the four sides.
41 mark
46
If the two numbers were equal they would be 37 each, because 74 divided by 2 = 37.
The difference of 18 is shared out evenly, so one number is 9 above 37 and the other is 9 below it.
The larger is 37 + 9 = 46, and the smaller is 28.
Check both facts: 46 + 28 = 74 and 46 - 28 = 18.
51 mark
2.16 litres
There are 60 seconds in a minute, so 5 seconds happens 12 times a minute: 12 x 3 = 36 ml every minute.
An hour has 60 minutes: 60 x 36 = 2160 ml.
There are 1000 ml in a litre, so 2160 ml = 2.16 litres.
An answer of 2160 is the right amount in the wrong unit and scores nothing here.
61 mark
2/5
- Accept 2/5 or two fifths. 12/30 and 6/15 are not in simplest form.
Read the walking figure off the chart: 12 children out of the 30 in the class.
That is the fraction 12/30.
Divide top and bottom by 6: 12 divided by 6 = 2, and 30 divided by 6 = 5, giving 2/5.
It is worth checking the four numbers add to 30, because a chart question is only as good as the total you read from it.
71 mark
32 litres
Think in batches, where one batch is 3 litres of red with 5 litres of white and makes 8 litres of pink.
The red allows 12 divided by 3 = 4 batches. The white allows 25 divided by 5 = 5 batches.
He can only make as many batches as his scarcest colour allows, so 4 batches.
4 batches make 4 x 8 = 32 litres of pink, using all 12 litres of red and 20 litres of the white.
Adding 12 and 25 to get 37 ignores the ratio and would leave 5 litres of white with no red to go with it.
81 mark
4.68 kg
Take the tin out first: 5.06 - 1.28 = 3.78 kg.
Then add the jar: 3.78 + 0.90 = 4.68 kg.
Writing 0.9 as 0.90 keeps the columns lined up, which is where this kind of question is usually lost.
91 mark
6 cm
An equilateral triangle has 3 equal sides, so its perimeter is 3 x 12 = 36 cm.
The hexagon has the same perimeter and 6 equal sides.
36 divided by 6 = 6 cm for each side.
Halving 12 by luck gives the right number here, but the reason matters: the hexagon has twice as many sides, so each one is half as long.
101 mark
4 7/12
- Accept 4 7/12, four and seven twelfths, or 55/12. An answer of 3 8/10 or 4 19/12 left unfinished scores nothing.
Add the whole metres first: 1 + 2 = 3.
Then add the fractions over 12, because both 4 and 6 divide into 12. Three quarters is 9/12 and five sixths is 10/12.
9/12 + 10/12 = 19/12, which is 1 whole and 7/12.
3 + 1 and 7/12 = 4 and 7/12 metres. 7 and 12 share no factor, so it is in its simplest form.
111 mark
1 hour 45 minutes
In one hour the train covers 96 km, which leaves 168 - 96 = 72 km still to go.
In a quarter of an hour it covers 96 divided by 4 = 24 km, and 72 divided by 24 = 3 of those quarter hours.
Three quarters of an hour is 45 minutes, so the whole trip takes 1 hour and 45 minutes.
Writing 1.75 hours is the same length of time, but the question asked for hours and minutes.
121 mark
50 cm
The joined edge is inside the badge now, so it is not part of the outline and must not be counted.
That leaves 3 sides of the square on the outside: 3 x 10 = 30 cm.
It also leaves 2 sides of the triangle: 2 x 10 = 20 cm.
30 + 20 = 50 cm. Adding the two whole perimeters, 40 + 30 = 70 cm, counts the shared edge twice.
131 mark
0.9 tonnes
40 x 22.5: four lots of 22.5 is 90, so forty lots is 900 kg.
There are 1000 kg in a tonne, so divide by 1000: 900 kg = 0.9 tonnes.
Since 900 is less than 1000, the answer has to be under 1 tonne, which rules out 9 or 90.
141 mark
28p
Work in pence from the start: 3 pounds 50 pence is 350p.
10 per cent of 350p is 35p, so 1 per cent is 3.5p.
8 per cent is 8 x 3.5 = 28p.
Writing 0.28 would be pounds, and the question asked for the answer in pence.
151 mark
103
Imagine each tent losing its extra 35 pounds, so everything costs the same as a stove.
That takes 3 x 35 = 105 pounds off the total: 445 - 105 = 340 pounds for 5 stove-priced items.
340 divided by 5 = 68 pounds, which is the price of a stove.
A tent costs 35 pounds more: 68 + 35 = 103 pounds.
Check: 3 x 103 = 309 and 2 x 68 = 136, and 309 + 136 = 445 pounds.
161 mark
25
Test the rule on what you can see: half of 100 is 50, add 10 to get 60. Half of 60 is 30, add 10 to get 40.
Apply it to 30: half of 30 is 15, and 15 + 10 = 25.
The steps down are getting smaller each time, so a fixed difference will not work. The terms creep towards 20 without ever reaching it.
171 mark
120
Write both fractions in fifteenths, because 15 is the smallest number both 5 and 3 divide into.
Two fifths is 6/15 and one third is 5/15, so pasta and curry together take 11/15.
The salad is what is left: 15/15 - 11/15 = 4/15, and that is the 32 people.
So one fifteenth is 32 divided by 4 = 8 people.
The whole survey is 15 x 8 = 120 people.
181 mark
15 cm
Work out how much water there is: 30 x 20 x 15 = 9000 cubic centimetres.
The base of the second tank covers 25 x 24 = 600 square centimetres.
The water spreads over that base, so its depth is 9000 divided by 600 = 15 cm.
The amount of water does not change when it is poured, only the shape it makes.
191 mark
2 hours
Because they ride towards each other, the gap between them closes at both speeds at once: 14 + 16 = 30 km every hour.
The gap starts at 60 km, so it takes 60 divided by 30 = 2 hours to close.
Check it: in 2 hours one has ridden 28 km and the other 32 km, and 28 + 32 = 60 km.
201 mark
14:41
A slow clock is behind the real time, so the real time is later than the clock says.
Add the 4 minutes: 14:37 becomes 14:41.
Taking the 4 minutes off, and answering 14:33, is what you would do for a clock that runs fast.
211 mark
12
The two numbers are close together, so each is near the number that multiplies by itself to give about 156.
12 x 12 = 144 and 13 x 13 = 169, so the pair must be 12 and 13.
12 x 13 = 156, which is right, so the smaller number is 12.
221 mark
1 : 4
- Accept 1 : 4 or 1:4 only. 24 : 96 is not simplified, and 4 : 1 puts the animals the wrong way round.
Start from 24 : 96. To make the left side 1, divide both sides by 24.
24 divided by 24 = 1, and 96 divided by 24 = 4, so the ratio is 1 : 4.
It says deer to rabbits, and there are more rabbits, so the second number must be the bigger one.
231 mark
180
A cube with no paint must be buried inside, with a painted layer of cubes on every side of it.
That removes one cube from each end of every measurement, so the unpainted block inside is 12 - 2 = 10 by 8 - 2 = 6 by 5 - 2 = 3.
10 x 6 x 3 = 180 cubes with no paint.
Taking only one cube off each measurement, rather than one from each end, gives 11 x 7 x 4 = 308 and is the usual error.
241 mark
11
In three years both of them will be 3 years older, so their ages then are 6 more than their ages now added together.
That means their ages now add up to 32 - 6 = 26.
Kai is 4 more than Mia, so taking that 4 off leaves two equal amounts: 26 - 4 = 22, and 22 divided by 2 = 11.
Mia is 11 now and Kai is 15.
Check: in three years they are 14 and 18, and 14 + 18 = 32.
251 mark
57
The cheapest of the three jumpers is the 24 pound one, so that is the one she does not pay for.
She pays for the other two: 30 + 27 = 57 pounds.
Adding all three gives 81 pounds, which is what she would have paid without the offer, and 81 - 24 = 57 confirms the answer.

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

The rest of the set

Free 11+ mock papers, no login

Original papers with full mark schemes and worked explanations, printable as PDFs.

Choose a subject →