NWSSEE Mathematics Mock Paper 10

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: Stretch

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 print shop charges 12 pounds to set up a job and then 8 pence for each copy it prints. Ravi pays 46 pounds altogether.
How many copies did he order?
Answer:
21 mark
In a car park two fifths of the cars are red. One third of the cars that are not red are blue. There are 24 blue cars.
How many cars are in the car park altogether?
Answer:
31 mark
A square has an area of 64 square centimetres. Four squares of this size are joined edge to edge in a straight row to make a long rectangle.
What is the perimeter of the rectangle? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
41 mark
A car and a lorry set off at the same moment along the same 120 km route. The car keeps up an average speed of 80 km/h and the lorry an average speed of 60 km/h.
How long after the car does the lorry arrive? Give your answer in minutes.
Answer:
51 mark
In a sequence, each term after the first is made by doubling the term before it and then subtracting 3.
The 4th term is 11.
What is the 1st term?
Answer:
61 mark
A shopkeeper mixes 3 kg of nuts costing 6 pounds a kilogram with 2 kg of nuts costing 11 pounds a kilogram.
What is the cost of one kilogram of the mixture? Give your answer in pounds.
Answer:
71 mark
What is the largest three-digit number that divides exactly by 7?
Answer:
81 mark
A cuboid has a volume of 480 cubic centimetres and a base measuring 12 cm by 5 cm.
A second cuboid is the same height, but its base is twice as long and twice as wide.
What is the volume of the second cuboid? Give your answer in cubic centimetres.
The diagrams are not drawn to size.
Answer:
91 mark
Tickets for a show cost 9 pounds 50 pence each. A book of 6 tickets costs 50 pounds. A club needs 27 tickets and may buy any mixture of books and single tickets.
What is the least amount the club can pay? Give your answer in pounds.
Answer:
101 mark
A bag holds red counters and blue counters in the ratio 2 : 7. If 15 more red counters were put in, there would be equal numbers of red and blue counters.
How many blue counters are in the bag?
Answer:
111 mark
Six glasses are filled from a jug, and each glass holds 175 ml. There is 50 ml still left in the jug afterwards.
How much did the jug hold to start with? Give your answer in litres.
Answer:
121 mark
Sara scored 39 marks out of 60 in a test.
What percentage of the marks did she score?
Answer:
131 mark
A faulty clock loses 4 minutes every hour. It is set to exactly the right time at 08:00.
What time will the faulty clock show when the true time is 14:00? Give your answer using the 24-hour clock.
Answer:
141 mark
A rectangular photograph measures 12 cm by 8 cm. It is mounted on card so that a border of the same width runs all the way round it.
The photograph and the border together cover 192 square centimetres.
How wide is the border? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
151 mark
Square tables each seat 4 people, one along each side. When tables are pushed together in a straight row, nobody can sit at a joined edge, so two tables seat 6 people and three tables seat 8.
How many tables are needed to seat 30 people?
Answer:
161 mark
A rectangle measures 12 cm by 6 cm. A square is drawn with exactly the same perimeter as the rectangle.
How much larger is the area of the square than the area of the rectangle? Give your answer in square centimetres.
The diagrams are not drawn to size.
Answer:
171 mark
Squash and water are mixed in the ratio 1 : 7 to make a drink.
How much squash is needed to make 3 litres of the drink? Give your answer in millilitres.
Answer:
181 mark
What is one quarter of three fifths of 100?
Answer:
191 mark
A footpath is 1.2 km long. Marker posts are placed along it every 150 m, with one post at each end.
How many posts are needed?
Answer:
201 mark
Amina has 20 coins. Every coin is either a 20p coin or a 50p coin, and together they are worth 7 pounds 60 pence.
How many 50p coins does she have?
Answer:
211 mark
A car travels 14 km on each litre of fuel.
How much fuel does it need for a journey of 224 km? Give your answer in litres.
Answer:
221 mark
Eight numbers have a mean of 6.5.
What is the total of the eight numbers?
Answer:
231 mark
One batch of bread uses three eighths of a kilogram of flour. Petra has 3.5 kg of flour and makes as many complete batches as she can.
What fraction of a kilogram of flour is left over? Give your answer in its simplest form.
Answer:
241 mark
A container shaped like a cuboid has a base measuring 25 cm by 20 cm. It holds water to a depth of 6 cm. A stone is lowered in and sinks, and the water level rises to 7.5 cm.
What is the volume of the stone? Give your answer in cubic centimetres.
The diagram is not drawn to size.
Answer:
251 mark
Today is a Tuesday.
What day of the week will it be in 100 days' time?
Answer:

Answers, mark scheme and worked explanations

11 mark
425
Take the set-up charge off first: 46 - 12 = 34 pounds is spent on the copies themselves.
34 pounds is 3400 pence.
Each copy costs 8 pence, so there are 3400 divided by 8 = 425 copies.
Dividing the whole 46 pounds by 8 pence gives 575, which is the trap for anyone who skips the first step.
21 mark
120
If two fifths are red, then three fifths are not red.
The blue cars are one third of that three fifths, and one third of 3/5 is 1/5.
So the 24 blue cars are one fifth of the car park.
The whole car park is 5 x 24 = 120 cars. Treating 24 as one third of the whole car park gives 72, which is the mistake to avoid.
31 mark
80 cm
Each square has a side of 8 cm, because 8 x 8 = 64.
Four in a row make a rectangle 4 x 8 = 32 cm long and 8 cm wide.
The perimeter is 2 x (32 + 8) = 80 cm.
Multiplying one square's perimeter of 32 cm by 4 gives 128 cm, which is wrong because the joined edges are inside the shape and are not part of its perimeter.
41 mark
30 minutes
The car takes 120 divided by 80 = 1.5 hours, which is 1 hour 30 minutes.
The lorry takes 120 divided by 60 = 2 hours.
The difference is half an hour, which is 30 minutes.
Subtracting the speeds to get 20 and calling that the answer is the trap: 20 km/h is a speed, not a length of time.
51 mark
4
Work backwards, undoing each step: add 3, then halve.
The 3rd term is (11 + 3) divided by 2 = 7.
The 2nd term is (7 + 3) divided by 2 = 5, and the 1st term is (5 + 3) divided by 2 = 4.
Check forwards: 4 gives 5, 5 gives 7, 7 gives 11.
61 mark
8
Find the total cost first: 3 x 6 = 18 pounds and 2 x 11 = 22 pounds, so the mixture costs 40 pounds.
The mixture weighs 3 + 2 = 5 kg.
One kilogram costs 40 divided by 5 = 8 pounds.
Averaging 6 and 11 to get 8.50 is the trap, and it is wrong because there is more of the cheaper kind.
71 mark
994
The largest three-digit number is 999, so start there and divide by 7.
7 x 140 = 980, and 999 - 980 = 19. Since 7 x 2 = 14, that gives 7 x 142 = 994 with 5 left over.
So 994 is the largest multiple of 7 below 999. The next one, 1001, has four digits.
81 mark
1920 cm3
The first base has an area of 12 x 5 = 60 square centimetres, so the height is 480 divided by 60 = 8 cm.
The second base measures 24 cm by 10 cm, an area of 240 square centimetres.
Its volume is 240 x 8 = 1920 cubic centimetres.
Doubling the volume to 960 is the trap: doubling two of the three measurements multiplies the volume by 4, not by 2.
91 mark
228.50
A book works out at 50 divided by 6, which is under 8 pounds 34 pence a ticket, so books are much better value than singles.
Four books give 24 tickets for 200 pounds, and the last 3 tickets cost 3 x 9.50 = 28 pounds 50 pence, making 228 pounds 50 pence.
Five books would give 30 tickets for 250 pounds, which is more, and three books plus 9 singles costs 150 + 85.50 = 235 pounds 50 pence.
So the cheapest way is 228 pounds 50 pence.
101 mark
21
Red is 2 parts and blue is 7 parts, so red is 5 parts short of blue.
The 15 extra counters would make them equal, so 5 parts is 15 counters and one part is 3 counters.
Blue is 7 parts: 7 x 3 = 21 counters.
Check: there are 2 x 3 = 6 red counters, and 6 + 15 = 21, which matches the blue.
111 mark
1.1 litres
The glasses take 6 x 175 = 1050 ml.
Add what is left over: 1050 + 50 = 1100 ml.
There are 1000 ml in a litre, so the jug held 1.1 litres.
Answering 1100 gives the right amount in millilitres, but the question asks for litres.
121 mark
65
One way is to find 1 per cent: 60 divided by 100 is 0.6 marks, and 39 divided by 0.6 = 65.
Another way is to notice 60 x 5 = 300 and 39 x 5 = 195, so the score is 195 out of 300, which is 65 out of 100.
So she scored 65 per cent.
131 mark
13:36
From 08:00 to 14:00 is 6 true hours.
The clock loses 4 minutes in each of those hours, so it loses 6 x 4 = 24 minutes.
A clock that loses time shows a time earlier than the truth: 14:00 take away 24 minutes is 13:36.
Adding the 24 minutes to give 14:24 is the trap. Lost minutes are minutes the clock never counted.
141 mark
2 cm
The border adds its width to both ends of each side, so a border w cm wide makes the whole card (12 + 2w) cm by (8 + 2w) cm.
Try 1 cm: 14 x 10 = 140 square centimetres, which is too small.
Try 2 cm: 16 x 12 = 192 square centimetres, which is exactly right.
So the border is 2 cm wide. Adding the width only once, and trying 13 x 9, is the usual slip.
151 mark
14
Each extra table adds only 2 more seats, because two of its four sides are lost or shared at the joins.
So the number of seats is 2 lots of the number of tables, plus 2. Check: three tables gives 3 x 2 + 2 = 8.
Take the 2 off: 30 - 2 = 28, then divide by 2 to get 14 tables.
Dividing 30 by 4 to get 8 tables would leave 8 people standing.
161 mark
9 square centimetres
The rectangle's perimeter is 12 + 6 + 12 + 6 = 36 cm, and its area is 12 x 6 = 72 square centimetres.
The square has the same 36 cm all the way round, so each side is 36 divided by 4 = 9 cm.
The square's area is 9 x 9 = 81 square centimetres.
81 - 72 = 9 square centimetres larger. Equal perimeters do not mean equal areas: of all the rectangles with a given perimeter, the square holds the most.
171 mark
375 ml
The drink is made of 1 + 7 = 8 parts altogether.
3 litres is 3000 ml, so one part is 3000 divided by 8 = 375 ml.
The squash is 1 part, so 375 ml of squash is needed.
Dividing by 7 instead of 8 is the classic ratio slip, and answering 0.375 uses the wrong unit.
181 mark
15
Three fifths of 100 is 100 divided by 5 = 20, times 3 = 60.
One quarter of 60 is 15.
191 mark
9
Change the length into metres: 1.2 km = 1200 m.
1200 divided by 150 = 8, so there are 8 gaps between posts.
A line of 8 gaps has a post at each end, which is 9 posts.
Answering 8 forgets the post at the far end, and that off-by-one is exactly what this question is testing.
201 mark
12
Suppose all 20 coins were 20p coins. That would be 20 x 20 = 400 pence, which is 4 pounds.
The real total is 7.60, which is 360 pence more.
Swapping a 20p coin for a 50p coin adds 30 pence each time, so 360 divided by 30 = 12 coins were swapped.
So there are 12 fifty-pence coins and 8 twenty-pence coins. Check: 600 + 160 = 760 pence.
211 mark
16 litres
Divide the distance by the distance covered per litre: 224 divided by 14.
14 x 10 = 140, and 224 - 140 = 84, which is 14 x 6.
So the answer is 10 + 6 = 16 litres.
221 mark
52
The mean is the total shared equally between the numbers, so the total is the mean multiplied by how many numbers there are.
8 x 6.5 = 52.
231 mark
1/8
- Accept 1/8 or one eighth, with or without kg. 0.125 is also accepted. 2/16 and 0.1 score nothing.
Work in eighths of a kilogram. 3.5 kg is 28 eighths, because 3.5 x 8 = 28.
Each batch uses 3 eighths, and 3 x 9 = 27, so she can make 9 batches.
That uses 27 eighths and leaves 28 - 27 = 1 eighth of a kilogram.
Answering 9, the number of batches, is the tempting wrong answer, and the question asks for what is left.
241 mark
750 cm3
The stone pushes the water up, so its volume is exactly the volume of the extra layer of water.
The level rises by 7.5 - 6 = 1.5 cm.
That layer is 25 x 20 x 1.5. First 25 x 20 = 500, then 500 x 1.5 = 750 cubic centimetres.
Working out the whole 7.5 cm of water, 3750 cubic centimetres, answers a different question.
251 mark
Thursday
- Accept Thursday only, spelled correctly enough to be unambiguous.
The days repeat every 7, so take out as many whole weeks as you can.
7 x 14 = 98, so 98 days from now is another Tuesday.
There are 100 - 98 = 2 days left over: Wednesday, then Thursday.
Dividing 100 by 7 and using the 2 left over is the same method done in one step.

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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