NWSSEE Mathematics Mock Paper 7

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
Work out 199 x 14.
Answer:
21 mark
Four friends share the cost of a taxi fare of 27 pounds 60 pence. Three of them pay the same amount as each other, and the fourth pays twice as much as one of the others.
How much does the fourth friend pay? Give your answer in pounds.
Answer:
31 mark
A railcard allows a single journey of up to 4 hours 15 minutes.
How long is that? Give your answer in minutes.
Answer:
41 mark
What is three quarters of two thirds of 480?
Answer:
51 mark
A square has a perimeter of 36 cm.
A rectangle has a length that is twice the side of the square, and a width that is 3 cm less than the side of the square.
What is the area of the rectangle? Give your answer in square centimetres.
The diagrams are not drawn to size.
Answer:
61 mark
A conveyor belt carries 24 boxes past a checkpoint every minute, without stopping.
How long does it take for 900 boxes to pass the checkpoint? Give your answer in minutes and seconds.
Answer:
71 mark
In a sequence the same amount is added each time. The 5th term is 23 and the 9th term is 43.
What is the 1st term?
Answer:
81 mark
Five plants are measured. Their heights are 23 cm, 31 cm, 18 cm, 27 cm and 26 cm.
What is the difference between the median height and the mean height? Give your answer in centimetres.
Answer:
91 mark
In a survey of a whole school, 40 per cent of the pupils chose football and 15 per cent chose netball. Exactly 60 pupils chose netball.
How many pupils chose football?
Answer:
101 mark
Blue paint and yellow paint are mixed in the ratio 2 : 5 to make green paint.
How much blue paint is needed to make 4.9 litres of green paint? Give your answer in litres.
Answer:
111 mark
A parallelogram has a base of 9 cm and a perpendicular height of 6 cm. A triangle has exactly the same area as the parallelogram and a base of 12 cm.
What is the perpendicular height of the triangle? Give your answer in centimetres.
The diagrams are not drawn to size.
Answer:
121 mark
Cheese costs 9 pounds 60 pence for one kilogram.
What is the cost of 350 g of the cheese? Give your answer in pounds and pence.
Answer:
131 mark
Work out the value of the calculation below. There are no brackets, so do the multiplication before the adding and subtracting.
40 - 6 x 5 + 2
Answer:
141 mark
A chicken must be cooked for 40 minutes, plus an extra 20 minutes for every kilogram it weighs. The chicken weighs 2.5 kg and must be ready at 13:15.
At what time should it go into the oven? Give your answer using the 24-hour clock.
Answer:
151 mark
Three eighths of the seats in a theatre are empty. There are 250 people sitting in the theatre, one to a seat.
How many seats does the theatre have altogether?
Answer:
161 mark
A square piece of card has sides of 20 cm. A strip 2 cm wide is shaded all the way round the outside edge of the card.
What is the area of the unshaded part in the middle? Give your answer in square centimetres.
The diagram is not drawn to size.
Answer:
171 mark
The terms of a sequence go up by 7 every time. The first term is 4.
What is the largest term of the sequence that is still less than 100?
Answer:
181 mark
Aisha buys 4 plants at 3 pounds 85 pence each and one bag of compost at 6 pounds 99 pence. She has a voucher that takes 5 pounds off the total.
How much does she pay? Give your answer in pounds.
Answer:
191 mark
A shelf is 2.4 m long. Books that are each 32 mm thick are stood upright on it, side by side.
How many books fit on the shelf?
Answer:
201 mark
The minute hand of a clock turns all the way round once every hour.
Through how many degrees does it turn in 25 minutes? Give your answer in degrees.
Answer:
211 mark
Work out five sixths subtract three eighths.
Give your answer as a fraction in its simplest form.
Answer:
221 mark
Work out 7.2 divided by 0.9.
Answer:
231 mark
Ali has three times as many marbles as Beth. If Ali gives 12 of his marbles to Beth, they will have the same number each.
How many marbles does Ali have to start with?
Answer:
241 mark
A room is shaped like the letter L. It is made from a rectangle 6 m by 4 m joined along one edge to a rectangle 3 m by 2 m. Wooden flooring costs 28 pounds for each square metre.
What is the cost of flooring the whole room? Give your answer in pounds.
The diagram is not drawn to size.
Answer:
251 mark
A photograph is 15 cm wide and 10 cm tall. It is enlarged so that its width becomes 24 cm, and the shape is not stretched.
How tall is the enlarged photograph? Give your answer in centimetres.
Answer:

Answers, mark scheme and worked explanations

11 mark
2786
199 is one less than 200, so work out 200 x 14 first: that is 2800.
You have used one extra 14, so take it away: 2800 - 14 = 2786.
Long multiplication gives the same answer, but the near-200 shortcut is much quicker under time pressure.
21 mark
11.04
Count the shares: three single shares plus one double share makes 5 equal parts.
One part is 27.60 divided by 5 = 5 pounds 52 pence.
The fourth friend pays two parts: 2 x 5.52 = 11 pounds 4 pence.
Dividing by 4 to get 6.90 is the trap, because it ignores the double share.
31 mark
255
Each hour is 60 minutes, so 4 hours is 4 x 60 = 240 minutes.
Add the extra 15 minutes: 240 + 15 = 255 minutes.
Writing 415, by squashing the hours and minutes together, is the slip to avoid.
41 mark
240
Work from the inside out. Two thirds of 480 is 480 divided by 3, which is 160, times 2, which is 320.
Three quarters of 320 is 320 divided by 4 = 80, times 3 = 240.
There is a shortcut: three quarters of two thirds is one half, so the answer is simply half of 480.
51 mark
108 cm2
The square has four equal sides, so each side is 36 divided by 4 = 9 cm.
The rectangle is twice as long as that: 2 x 9 = 18 cm.
Its width is 3 cm less than 9 cm, which is 6 cm.
The area is 18 x 6 = 108 square centimetres. Using 36 cm as the side of the square is the mistake to avoid.
61 mark
37 minutes 30 seconds
24 x 37 = 888, so after 37 minutes 888 boxes have gone past and 12 are still to come.
12 boxes is half a minute's worth, because 24 go past in a whole minute.
So the time is 37 and a half minutes, which is 37 minutes 30 seconds.
Writing 37.5 is the same length of time, but the question asks for minutes and seconds.
71 mark
3
Going from the 5th term to the 9th term is 4 steps, and the value rises by 43 - 23 = 20.
So each step adds 20 divided by 4 = 5.
Going back from the 5th term to the 1st term is also 4 steps, so take away 4 x 5 = 20.
23 - 20 = 3. The usual slip is counting 9 - 5 as 5 steps rather than 4.
81 mark
1 cm
For the mean, add them: 23 + 31 + 18 + 27 + 26 = 125, then divide by 5 to get 25 cm.
For the median, put them in order: 18, 23, 26, 27, 31. The middle one is 26 cm.
The difference is 26 - 25 = 1 cm.
Taking the middle number of the unordered list, 18, is the trap here.
91 mark
160
15 per cent of the school is 60 pupils, so 1 per cent is 60 divided by 15 = 4 pupils.
40 per cent is 40 x 4 = 160 pupils.
You could also notice that 40 per cent is not quite three times 15 per cent, so the answer should be a bit under 180.
The whole school has 400 pupils, but that is not what the question asks for.
101 mark
1.4 litres
The mixture has 2 + 5 = 7 parts altogether.
One part is 4.9 divided by 7 = 0.7 litres.
Blue is 2 parts: 2 x 0.7 = 1.4 litres.
Taking 2 sevenths of 4.9 gives the same answer. Using 2 fifths would be the transposed-ratio error.
111 mark
9 cm
The area of a parallelogram is base times perpendicular height: 9 x 6 = 54 square centimetres.
The triangle has the same area, and a triangle's area is half its base times its height.
Half of 12 is 6, so 6 x height = 54.
The height is 54 divided by 6 = 9 cm. Forgetting to halve the base gives 4.5 cm, which is the trap.
121 mark
3.36
100 g costs 9.60 divided by 10 = 96 pence.
350 g is three and a half lots of 100 g: 3 x 96 = 288 pence, plus half of 96, which is 48 pence.
288 + 48 = 336 pence, which is 3 pounds 36 pence.
Money must be written with two decimal places, so 3.36 rather than 3.4.
131 mark
12
Multiplication comes first: 6 x 5 = 30.
That leaves 40 - 30 + 2.
Now work from left to right: 40 - 30 = 10, and 10 + 2 = 12.
Working strictly left to right from the start gives 40 - 6 = 34, then 34 x 5 = 170, which is the error this question is looking for.
141 mark
11:45
The extra time is 2.5 x 20 = 50 minutes.
The whole cooking time is 40 + 50 = 90 minutes, which is 1 hour 30 minutes.
Count back from 13:15: one hour back is 12:15, and 30 minutes further back is 11:45.
Forgetting the fixed 40 minutes, and counting back only 50 minutes to 12:25, is the trap.
151 mark
400
If three eighths are empty then five eighths are taken, and that is the 250 people.
One eighth is 250 divided by 5 = 50 seats.
The whole theatre is eight eighths: 8 x 50 = 400 seats.
Working out three eighths of 250 answers a different question entirely.
161 mark
256 cm2
The strip takes 2 cm off the left and 2 cm off the right, so the middle is 20 - 4 = 16 cm across.
The same happens from top and bottom, so the middle is a 16 cm square.
Its area is 16 x 16 = 256 square centimetres.
Taking off only one lot of 2 cm, and working out 18 x 18 = 324, is the usual mistake.
171 mark
95
The terms are 4, 11, 18, 25 and so on, and every term is 4 more than a multiple of 7.
Count up in sevens towards 100: 4 + 70 = 74, then 81, 88, 95, and the next one would be 102.
102 is over 100, so the largest term below 100 is 95.
Answering 98 is tempting because it is a multiple of 7, but 98 is not in this sequence.
181 mark
17.39
The plants cost 4 x 3.85. Doubling twice is easiest: 3.85 doubled is 7.70, and 7.70 doubled is 15.40.
Add the compost: 15.40 + 6.99 = 22.39.
Take off the voucher: 22.39 - 5 = 17 pounds 39 pence.
191 mark
75
Change both lengths into millimetres: 2.4 m = 2400 mm.
2400 divided by 32: since 32 x 75 = 2400, exactly 75 books fit.
If you work in centimetres instead, 240 cm divided by 3.2 cm gives the same 75.
Mixing metres with millimetres without converting is the mistake that wrecks this question.
201 mark
150
A full turn is 360 degrees and takes 60 minutes.
So one minute is 360 divided by 60 = 6 degrees.
25 minutes is 25 x 6 = 150 degrees.
Answering 25 degrees, or 90 degrees because 25 minutes looks like a quarter of an hour, are the two tempting slips.
211 mark
11/24
- Accept 11/24 or eleven twenty-fourths. 22/48 scores nothing because it is not simplified.
The smallest number both 6 and 8 divide into is 24.
5/6 = 20/24 and 3/8 = 9/24.
20/24 - 9/24 = 11/24, and 11 is prime so it cannot be simplified further.
221 mark
8
Multiply both numbers by 10 so you are dividing by a whole number. That turns it into 72 divided by 9.
72 divided by 9 = 8.
Dividing by a number less than 1 makes the answer bigger than you started with, so 8 is sensible and 0.8 is not.
231 mark
36
When Ali hands over 12 marbles he loses 12 and Beth gains 12, so the gap between them closes by 24.
That means the gap was 24 marbles to begin with.
Ali has three times as many as Beth, so the gap is two of Beth's lots: Beth has 24 divided by 2 = 12.
Ali has 3 x 12 = 36 marbles. Check: 36 - 12 = 24 and 12 + 12 = 24.
241 mark
840
Split the L into its two rectangles and work out each area: 6 x 4 = 24 and 3 x 2 = 6 square metres.
The room covers 24 + 6 = 30 square metres.
The cost is 30 x 28 = 840 pounds.
Adding the measurements instead of the areas, or forgetting the smaller rectangle, both give too little.
251 mark
16 cm
Compare the widths: 24 divided by 15 does not give a whole number, so use a simpler route.
The photograph is one and a half times as wide as it is tall, and that stays true after the enlargement.
So the new height is 24 divided by 1.5 = 16 cm.
You can check with parts of 5: the width goes up by 9 cm, which is three fifths of 15, so the height goes up by three fifths of 10, which is 6 cm, giving 16 cm.
Adding 9 cm to the height as well, giving 19 cm, is the trap: an enlargement multiplies, it does not add.

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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