NWSSEE Mathematics Mock Paper 1

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: Familiarisation

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 theatre sells 34 tickets for a matinee. Each ticket costs 12 pounds 50 pence.
How much money does the theatre take altogether? Give your answer in pounds.
Answer:
21 mark
A bag of flour has a mass of 650 g. A baker buys 8 bags.
What is the total mass of the flour? Give your answer in kilograms.
Answer:
31 mark
What is three eighths of 240?
Answer:
41 mark
Three consecutive whole numbers add up to 258.
What is the largest of the three numbers?
Answer:
51 mark
Five consecutive odd numbers add up to 195.
What is the largest of the five numbers?
Answer:
61 mark
A shape is made by cutting a rectangle measuring 5 cm by 4 cm out of one corner of a rectangle measuring 14 cm by 9 cm.
What is the perimeter of the shape that is left? Give your answer in centimetres.
The diagram is not drawn to size.
Answer:
71 mark
Work out 20 minus the total of 4.65 and 3.8.
Answer:
81 mark
A coach leaves the station at 09:40. The journey takes 2 hours and 55 minutes.
At what time does the coach arrive? Give your answer using the 24-hour clock.
Answer:
91 mark
Four of these five numbers are equal to three fifths. One of them is not.
6/10 9/15 0.6 15/25 12/24
Which one is not equal to three fifths?
Answer:
101 mark
Maya and Owen share 58 pounds 50 pence in the ratio 2 : 3, with Owen taking the larger share.
How much does Owen receive? Give your answer in pounds.
Answer:
111 mark
Two of the angles in a triangle are 47 degrees and 68 degrees.
What is the size of the third angle? Give your answer in degrees.
Answer:
121 mark
A rectangle measures 12 cm by 7 cm. A square of side 3 cm is cut out of it.
What is the area of the shape that is left? Give your answer in square centimetres.
The diagram is not drawn to size.
Answer:
131 mark
A coat costs 45 pounds. In a sale the shop raises the price by 20 per cent instead of lowering it.
What is the new price? Give your answer in pounds.
Answer:
141 mark
A museum records the number of visitors on four days.
Monday 128, Tuesday 96, Wednesday 145, Thursday 111.
How many more visitors came on Wednesday than on Tuesday?
Answer:
151 mark
Use the same visitor numbers as question 14.
How many visitors came to the museum over the four days altogether?
Answer:
161 mark
A cuboid measures 8 cm by 5 cm by 3 cm.
What is its volume? Give your answer in cubic centimetres.
Answer:
171 mark
A different cuboid measures 6 cm by 4 cm by 5 cm.
Write down the ratio of the area of its 6 cm by 4 cm face to its volume.
Give your answer in its simplest form.
Answer:
181 mark
A train leaves at 14:52 and arrives at 16:20.
How long is the journey? Give your answer in hours and minutes.
Answer:
191 mark
Regular hexagons with sides of 3 cm are joined in a straight row, edge to edge.
Three hexagons joined this way have a perimeter of 42 cm.
What is the perimeter of six hexagons joined in the same way? Give your answer in centimetres.
Answer:
201 mark
Here are the first four terms of a sequence.
7, 11, 15, 19, ...
The number 63 is a term in this sequence. Which term is it? Give your answer as a number, for example 12 for the twelfth term.
Answer:
211 mark
Priya buys 3 notebooks costing 2 pounds 45 pence each and 2 pens costing 1 pound 15 pence each. She pays with a 20 pound note.
How much change does she get? Give your answer in pounds.
Answer:
221 mark
Work out two thirds multiplied by nine fourteenths.
Give your answer as a fraction in its simplest form.
Answer:
231 mark
Three quarters of a cake is left after a party. Ravi eats one third of what is left.
What fraction of the whole cake does Ravi eat? Give your answer in its simplest form.
Answer:
241 mark
Five numbers have a mean of 14. Four of the numbers are 9, 12, 18 and 11.
What is the fifth number?
Answer:
251 mark
Nadia thinks of a number. She multiplies it by 4 and then subtracts 7. Her answer is 45.
What number did Nadia think of?
Answer:

Answers, mark scheme and worked explanations

11 mark
425
Split the price: 34 lots of 12 pounds is 408 pounds, and 34 lots of 50 pence is 17 pounds.
408 + 17 = 425, so the theatre takes 425 pounds.
21 mark
5.2 kg
8 x 650 = 5200, so the flour weighs 5200 g.
There are 1000 g in a kilogram, so divide by 1000: 5200 g = 5.2 kg.
The question asks for kilograms, so 5200 on its own would score nothing.
31 mark
90
One eighth of 240 is 240 divided by 8, which is 30.
Three eighths is 3 x 30 = 90.
41 mark
87
For three consecutive numbers the middle one is always the mean, so it is 258 divided by 3, which is 86.
The three numbers are 85, 86 and 87, so the largest is 87.
51 mark
43
The middle number of five consecutive odd numbers is the mean, so it is 195 divided by 5, which is 39.
Odd numbers go up in twos, so the five numbers are 35, 37, 39, 41 and 43.
The largest is 43. Going up in ones instead of twos is the mistake to avoid here.
61 mark
46 cm
Cutting a rectangle out of a corner does not change the perimeter. Each side you remove is replaced by a side of exactly the same length facing the other way.
So the perimeter is the same as the perimeter of the whole 14 cm by 9 cm rectangle: 2 x (14 + 9) = 46 cm.
Adding up all six sides carefully gives the same answer, but spotting the shortcut saves a minute.
71 mark
11.55
First add inside the total: 4.65 + 3.80 = 8.45. Writing 3.8 as 3.80 keeps the columns lined up.
Then 20 - 8.45 = 11.55.
81 mark
12:35
Add the 2 hours first: 09:40 becomes 11:40.
Then add 55 minutes. 20 minutes takes you to 12:00, and the remaining 35 minutes takes you to 12:35.
91 mark
12/24
- Accept 12/24 or a clear description such as twelve twenty-fourths, or one half.
Three fifths is 0.6, so the decimal 0.6 does belong with the others. It is put there to be mistaken for the odd one out.
6/10 divides by 2 to give 3/5. 9/15 divides by 3 to give 3/5. 15/25 divides by 5 to give 3/5.
12/24 divides by 12 to give 1/2, which is not 3/5. So 12/24 is the odd one out.
101 mark
35.10
The ratio 2 : 3 has 5 parts altogether, so one part is 58.50 divided by 5, which is 11.70.
Owen has 3 parts: 3 x 11.70 = 35.10, so he receives 35 pounds 10 pence.
111 mark
65
The three angles in a triangle add up to 180 degrees.
47 + 68 = 115, and 180 - 115 = 65 degrees.
121 mark
75 cm2
The area of the whole rectangle is 12 x 7 = 84 square centimetres.
The square that is removed has area 3 x 3 = 9 square centimetres.
84 - 9 = 75 square centimetres. Note that the perimeter would not change but the area does.
131 mark
54
10 per cent of 45 pounds is 4 pounds 50 pence, so 20 per cent is 9 pounds.
The price goes up, so add: 45 + 9 = 54 pounds. Subtracting would give 36 pounds, which is the trap.
141 mark
49
145 - 96 = 49 more visitors on Wednesday.
151 mark
480
128 + 96 = 224, and 145 + 111 = 256.
224 + 256 = 480 visitors.
161 mark
120 cm3
Volume is length x width x height: 8 x 5 = 40, and 40 x 3 = 120 cubic centimetres.
171 mark
1 : 5
- Accept 1 : 5 only. 24 : 120 is unsimplified and scores nothing.
The named face has area 6 x 4 = 24 square centimetres.
The volume is 6 x 4 x 5 = 120 cubic centimetres.
The ratio is 24 : 120. Divide both sides by 24 to get 1 : 5. The question asks for the simplest form, so leaving it as 24 : 120 earns no mark.
181 mark
1 hour 28 minutes
From 14:52 to 15:52 is one hour.
From 15:52 to 16:20 is 28 minutes: 8 minutes to reach 16:00, then 20 more.
So the journey takes 1 hour and 28 minutes.
191 mark
78 cm
One hexagon has a perimeter of 6 x 3 = 18 cm.
Every hexagon you add joins along one edge, so it hides two edges and adds only four: that is 4 x 3 = 12 cm each time.
Check with three hexagons: 18 + 12 + 12 = 42 cm, which matches the question.
Six hexagons: 18 + 5 x 12 = 78 cm. Doubling 42 to get 84 is the trap, because the joins are not doubled.
201 mark
15
The sequence goes up by 4 each time, and the first term is 7, so a term is 4 lots of its position, plus 3.
Check: position 1 gives 4 + 3 = 7, and position 4 gives 16 + 3 = 19.
For 63: 63 - 3 = 60, and 60 divided by 4 = 15. So 63 is the fifteenth term.
211 mark
10.35
The notebooks cost 3 x 2.45 = 7.35 pounds.
The pens cost 2 x 1.15 = 2.30 pounds.
Together that is 7.35 + 2.30 = 9.65 pounds.
Change from 20 pounds is 20 - 9.65 = 10.35 pounds.
221 mark
3/7
- Accept 3/7 only. 18/42 and 9/21 are not in simplest form.
Multiply the top numbers and the bottom numbers: 2 x 9 = 18 and 3 x 14 = 42, giving 18/42.
Divide both by 6 to simplify: 18/42 = 3/7.
You could also cancel first, dividing the 9 and the 3 by 3, which turns the calculation into 2/1 x 3/14 = 6/14 = 3/7.
231 mark
1/4
- Accept 1/4 or one quarter. 3/12 is not in simplest form.
Ravi eats one third of three quarters, so work out 1/3 x 3/4.
That is 3/12, which simplifies to 1/4.
The common mistake is to answer 1/3, which is the fraction of the leftovers rather than of the whole cake.
241 mark
20
If the mean of five numbers is 14, they add up to 5 x 14 = 70.
The four numbers given add up to 9 + 12 + 18 + 11 = 50.
The fifth number is 70 - 50 = 20.
251 mark
13
Work backwards, undoing each step in reverse order.
Undo the subtraction first: 45 + 7 = 52.
Then undo the multiplication: 52 divided by 4 = 13.
Check forwards: 13 x 4 = 52, and 52 - 7 = 45.

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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