NWSSEE Mathematics Mock Paper 9

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: 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
What is the remainder when 2026 is divided by 7?
Answer:
21 mark
Concert tickets cost 18 pounds for an adult and 11 pounds 50 pence for a child. A group books tickets for 3 adults and 5 children.
How much does the group pay altogether? Give your answer in pounds.
Answer:
31 mark
Five eighths of a number is 45.
What is three quarters of the same number?
Answer:
41 mark
A square lawn has an area of 144 square metres. A fence is put along three of its four sides. Fencing costs 15 pounds for each metre.
What is the total cost of the fencing? Give your answer in pounds.
The diagram is not drawn to size.
Answer:
51 mark
A runner completes 6 laps of a 400 m track in 24 minutes, running at a steady pace.
What is her average speed? Give your answer in kilometres per hour.
Answer:
61 mark
Here are the first five terms of a sequence.
2, 6, 12, 20, 30, ...
What is the 10th term?
Answer:
71 mark
In a test the mean mark of the 10 girls in a class is 72. The mean mark of the 15 boys is 62.
What is the mean mark of all 25 children?
Answer:
81 mark
A signpost says a town is 45 miles away. Take 5 miles to be the same as 8 kilometres.
How far away is the town? Give your answer in kilometres.
Answer:
91 mark
A camera is priced at 80 pounds. The shop raises the price by 25 per cent. A month later the shop takes 25 per cent off the higher price.
What does the camera cost now? Give your answer in pounds.
Answer:
101 mark
Three children share a bag of sweets in the ratio 2 : 3 : 7. The largest share is 45 sweets more than the smallest share.
How many sweets are in the bag altogether?
Answer:
111 mark
An isosceles triangle has a perimeter of 42 cm. Each of its two equal sides is 3 cm longer than the third side.
How long is the third side? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
121 mark
Two consecutive whole numbers are multiplied together and the answer is 342.
What is the sum of the two numbers?
Answer:
131 mark
Nadia sets off on a ride at 09:15. She rides for 2 hours 50 minutes, rests for 25 minutes, and then rides for a further 1 hour 40 minutes.
At what time does she finish? Give your answer using the 24-hour clock.
Answer:
141 mark
What is three sevenths of 217?
Answer:
151 mark
A small square tile has sides of 6 cm. A large square tile has sides three times as long.
How many of the small tiles are needed to cover the large tile exactly, with no gaps and no overlap?
The tiles are not drawn to size.
Answer:
161 mark
A bottle of medicine holds 0.2 litres. One dose is 7.5 ml, and a dose is taken three times a day.
For how many complete days will the bottle last?
Answer:
171 mark
How many whole numbers from 1 to 60 are multiples of 3 or multiples of 5, or both?
Answer:
181 mark
A sponsored walk raises 4 pounds 60 pence for every kilometre walked. A group walks 35 km.
How much money does the walk raise? Give your answer in pounds.
Answer:
191 mark
One of the angles of a parallelogram is 62 degrees.
What is the size of each of the two larger angles? Give your answer in degrees.
The diagram is not drawn to size.
Answer:
201 mark
Eleven pupils sit a test and their mean mark is 14. One of the pupils, who scored 24, then leaves the class.
What is the mean mark of the ten pupils who are left?
Answer:
211 mark
A ticket machine takes only 20p coins. A ticket costs 7 pounds 40 pence.
How many 20p coins are needed to pay for one ticket?
Answer:
221 mark
Work out two thirds add one quarter subtract one half.
Give your answer as a fraction in its simplest form.
Answer:
231 mark
A machine takes 3 minutes 20 seconds to wash one tray of instruments, and washes the trays one after another with no pause.
How long does it take to wash 9 trays? Give your answer in minutes.
Answer:
241 mark
Three identical squares are joined edge to edge to make an L-shaped tile: two squares side by side, with the third square directly above the left-hand one.
The perimeter of the L-shaped tile is 40 cm. What is its area? Give your answer in square centimetres.
The diagram is not drawn to size.
Answer:
251 mark
A rope 120 cm long is cut into three pieces. The second piece is twice as long as the first. The third piece is 20 cm longer than the second.
How long is the first piece? Give your answer in centimetres.
Answer:

Answers, mark scheme and worked explanations

11 mark
3
Work up in easy chunks: 7 x 200 = 1400 and 7 x 280 = 1960.
2026 - 1960 = 66, and 7 x 9 = 63, which leaves 3.
So 2026 = 7 x 289 + 3, and the remainder is 3.
The question asks for the remainder, not for 289.
21 mark
111.50
The adults' tickets cost 3 x 18 = 54 pounds.
The children's tickets cost 5 x 11.50. Five lots of 11 is 55, and five lots of 50 pence is 2.50, so that is 57 pounds 50 pence.
54 + 57.50 = 111 pounds 50 pence.
31 mark
54
Find one eighth first: five eighths is 45, so one eighth is 45 divided by 5 = 9.
The whole number is 8 x 9 = 72.
Three quarters of 72 is 72 divided by 4 = 18, times 3 = 54.
Taking three quarters of 45 gives 33.75, which answers a different question.
41 mark
540
The lawn is square, and 12 x 12 = 144, so each side is 12 m.
Three sides need fencing: 3 x 12 = 36 m.
The cost is 36 x 15 = 540 pounds.
Fencing all four sides would cost 720 pounds, so read the question carefully.
51 mark
6 km/h
She runs 6 x 400 = 2400 m, which is 2.4 km.
24 minutes is 24 divided by 60 = 0.4 of an hour.
In one hour she would run 2.5 times as far, because 0.4 x 2.5 = 1: that is 2.4 x 2.5 = 6 km.
So her average speed is 6 km/h. Answering 100 would be her speed in metres per minute, which is the wrong unit.
61 mark
110
The gaps are 4, 6, 8, 10, so each gap is 2 bigger than the one before.
Carrying on, the gaps to the 10th term are 12, 14, 16, 18 and 20.
30 + 12 = 42, then 56, 72, 90 and finally 110.
There is a pattern worth spotting: each term is its position multiplied by the next number up, so the 10th term is 10 x 11 = 110.
71 mark
66
Turn each mean back into a total. The girls scored 10 x 72 = 720 marks and the boys scored 15 x 62 = 930 marks.
Altogether that is 720 + 930 = 1650 marks.
The mean of all 25 children is 1650 divided by 25 = 66.
Averaging 72 and 62 to get 67 is the trap, and it is wrong because there are more boys than girls.
81 mark
72 km
45 miles is 9 lots of 5 miles, because 45 divided by 5 = 9.
Each of those is 8 km, so the distance is 9 x 8 = 72 km.
Kilometres are shorter than miles, so the number must get bigger. An answer smaller than 45 would show the conversion had been done the wrong way round.
91 mark
75
25 per cent of 80 pounds is 20 pounds, so the raised price is 100 pounds.
The second change is 25 per cent of 100 pounds, which is 25 pounds, so the price falls to 75 pounds.
The two changes do not cancel out, because the rise is a quarter of 80 but the fall is a quarter of 100.
Answering 80 pounds because the price went up and down by the same percentage is exactly the trap.
101 mark
108
The largest share is 7 parts and the smallest is 2 parts, so the difference is 5 parts.
5 parts is 45 sweets, so one part is 9 sweets.
The bag holds 2 + 3 + 7 = 12 parts: 12 x 9 = 108 sweets.
Answering 63, the largest share, is a common slip when the last line is not read properly.
111 mark
12 cm
Each equal side carries an extra 3 cm compared with the third side, and there are two of them, so 6 cm of the perimeter is extra.
Take that off: 42 - 6 = 36 cm, which is now three lots of the third side.
The third side is 36 divided by 3 = 12 cm.
Check: the sides are 12, 15 and 15, and 12 + 15 + 15 = 42 cm.
121 mark
37
The two numbers are close together, and 18 x 18 = 324 while 20 x 20 = 400, so they must be around 18 or 19.
Try 18 x 19 = 342, which works.
Their sum is 18 + 19 = 37.
The question asks for the sum, so 18 and 19 on its own does not answer it.
131 mark
14:10
Add the first ride: 09:15 plus 2 hours is 11:15, plus 50 minutes is 12:05.
Add the rest: 12:05 plus 25 minutes is 12:30.
Add the second ride: 12:30 plus 1 hour is 13:30, plus 40 minutes is 14:10.
Adding the three times first also works: 2 h 50 min plus 25 min plus 1 h 40 min is 4 hours 55 minutes, and 09:15 plus that is 14:10.
141 mark
93
One seventh of 217 is 217 divided by 7. Since 7 x 31 = 217, one seventh is 31.
Three sevenths is 3 x 31 = 93.
151 mark
9
The large tile has sides of 3 x 6 = 18 cm.
Its area is 18 x 18 = 324 square centimetres, and each small tile covers 6 x 6 = 36 square centimetres.
324 divided by 36 = 9 tiles. Laying them out as 3 rows of 3 gives the same answer without any multiplying.
Answering 3 is the trap: the sides are three times longer, but the area is three times three, so nine times bigger.
161 mark
8
One day uses 3 x 7.5 = 22.5 ml.
Change the bottle into millilitres: 0.2 litres = 200 ml.
22.5 x 8 = 180 ml, and 22.5 x 9 = 202.5 ml, which is more than the bottle holds.
So the bottle lasts 8 complete days. Rounding 200 divided by 22.5 up to 9 is the trap.
171 mark
28
Multiples of 3 up to 60: there are 60 divided by 3 = 20 of them.
Multiples of 5 up to 60: there are 60 divided by 5 = 12 of them.
Adding gives 32, but the multiples of 15 have been counted twice. There are 60 divided by 15 = 4 of those.
So the answer is 32 - 4 = 28. Answering 32 is the trap this question is built on.
181 mark
161
Split the multiplication: 35 x 4 = 140 pounds, and 35 x 60 pence = 2100 pence, which is 21 pounds.
140 + 21 = 161 pounds.
191 mark
118
The four angles of a parallelogram add up to 360 degrees, and opposite angles are equal, so there are two angles of 62 degrees.
That leaves 360 - 124 = 236 degrees to share between the two larger angles.
Each larger angle is 236 divided by 2 = 118 degrees.
A quicker route is that angles next to each other in a parallelogram add up to 180, so 180 - 62 = 118.
201 mark
13
The eleven pupils scored 11 x 14 = 154 marks between them.
Taking away the pupil who scored 24 leaves 154 - 24 = 130 marks.
The mean of the remaining ten is 130 divided by 10 = 13.
The mean drops because the pupil who left scored more than the mean.
211 mark
37
Change the price into pence so both amounts match: 7 pounds 40 pence = 740 pence.
740 divided by 20 = 37 coins.
A quick check: 37 coins is 7 pounds 40 pence, because 5 coins make a pound and 35 coins make 7 pounds, leaving 2 coins for the 40 pence.
221 mark
5/12
- Accept 5/12 or five twelfths. 10/24 is not simplified and scores nothing.
The smallest number that 3, 4 and 2 all divide into is 12.
2/3 = 8/12, 1/4 = 3/12 and 1/2 = 6/12.
8/12 + 3/12 = 11/12, and 11/12 - 6/12 = 5/12, which cannot be simplified.
231 mark
30 minutes
3 minutes 20 seconds is 200 seconds.
Nine trays take 9 x 200 = 1800 seconds.
There are 60 seconds in a minute, so 1800 divided by 60 = 30 minutes.
Multiplying the minutes and the seconds separately, to get 27 minutes 180 seconds, gives the same answer only if you then convert the 180 seconds; forgetting to do so is the trap.
241 mark
75 cm2
Count the sides on the outside of the L. Three squares have 12 sides altogether, but the two joins hide 2 sides each, which is 4 sides.
So the perimeter is made of 12 - 4 = 8 sides of a square.
8 sides make 40 cm, so one side is 40 divided by 8 = 5 cm.
One square has an area of 5 x 5 = 25 square centimetres, and there are three of them: 3 x 25 = 75 square centimetres.
Dividing 40 by 12 forgets that the joined edges are inside the tile and are not part of its perimeter.
251 mark
20 cm
Think of the first piece as one part. The second is 2 parts, and the third is 2 parts plus 20 cm.
Altogether that is 5 parts plus 20 cm, which comes to 120 cm.
Take off the extra 20 cm first: 120 - 20 = 100 cm for the 5 parts, so one part is 20 cm.
Check: the pieces are 20 cm, 40 cm and 60 cm, and they add up to 120 cm.

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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