Sutton Boys' Second Stage Maths Mock Paper 1

84

Brackets first: 37 - 19 = 18.

Then multiply before you add: 4 x 18 = 72.

Finally 72 + 12 = 84. Working left to right instead would give 4 x 37 = 148, and that is the trap.

182 pounds

• 1 mark for 30 per cent of 260 pounds, which is 78 pounds.
• 1 mark for the under-16 price of 182 pounds. Award both marks for 182 with no working.

10 per cent of 260 pounds is 26 pounds, so 30 per cent is 3 x 26 = 78 pounds.

The under-16 pays 30 per cent LESS, so take it off: 260 - 78 = 182 pounds.

Answering 78 pounds gives the saving rather than the price paid.

1/4

• Accept 1/4 or one quarter. 3/12 is not in its simplest form and scores nothing.

Count every counter first: 5 + 3 + 4 = 12 counters in the bag.

Three of the twelve are blue, so the probability is 3/12.

Divide the top and bottom by 3 to simplify: 3/12 = 1/4.

117 square centimetres

• 1 mark for a width of 9 cm and a length of 13 cm.
• 1 mark for the area 117 square centimetres.

A perimeter is two lengths plus two widths, so half of it is one length plus one width: 44 divided by 2 is 22.

The length is 4 cm more than the width, so take that 4 cm off the 22: 22 - 4 = 18, which is two widths. The width is 9 cm.

The length is 9 + 4 = 13 cm. Check: 2 x (9 + 13) = 44 cm.

Area is 13 x 9 = 117 square centimetres.

48

The sequence goes up by 5 each time.

To get from the first term to the tenth you take nine steps of 5, which is 45.

3 + 45 = 48. Multiplying 3 by 10 to get 30 is the mistake to avoid.

73.80 pounds

• 1 mark for either 36 pounds from the lemonade or 37.80 pounds from the popcorn.
• 1 mark for the total 73.80 pounds.

Lemonade: 45 x 80p. Ten cups cost 8 pounds, so 40 cups cost 32 pounds and 5 cups cost 4 pounds. That is 36 pounds.

Popcorn: 28 x 1.35. Split it up as 28 x 1 = 28 pounds and 28 x 0.35 = 9.80 pounds, giving 37.80 pounds.

Add the two: 36.00 + 37.80 = 73.80 pounds.

33

• 1 mark for the total 132.
• 1 mark for the mean 33.

Add the four figures: 34 + 27 = 61, and 41 + 30 = 71. Then 61 + 71 = 132 books.

The mean is the total shared between the four classes: 132 divided by 4 = 33.

Dividing by 5 because there are five numbers on the page, counting the total, is the error to watch for.

9/20

• Accept 9/20 only. 45/100 and 9/20 written as a decimal do not answer the question.

Per cent means out of a hundred, so start with 45/100.

Both 45 and 100 divide by 5: 45/100 = 9/20.

9 and 20 share no factor, so 9/20 is as simple as it goes.

52 square metres

• 1 mark for splitting the L into two rectangles, or for treating it as a 10 m by 6 m rectangle with a piece cut out.
• 1 mark for both part areas, for example 40 and 12, or for 60 and the missing 8.
• 1 mark for the area 52 square metres.

Sketch the walk. Go 10 m east, 6 m north, 4 m west, 2 m south, 6 m west and 4 m south, and you arrive back where you started.

The shape sits inside a rectangle 10 m by 6 m, which has area 60 square metres.

The bite taken out of the top right is 4 m by 2 m, which is 8 square metres.

So the area is 60 - 8 = 52 square metres.

Splitting instead of subtracting gives the same answer: a strip 10 m by 4 m is 40 square metres, and the block above it is 6 m by 2 m, which is 12. 40 + 12 = 52.

255 cm

Put both lengths in the same unit. 3.4 m is 340 cm.

340 - 85 = 255 cm.

Subtracting 85 from 3.4 without converting gives nonsense, so always convert first.

60

• 1 mark for 24 tulips, or for seeing that five sevenths are daffodils.
• 1 mark for 60 daffodils.

One seventh of 84 is 84 divided by 7, which is 12.

Two sevenths is 2 x 12 = 24 tulips.

The daffodils are the rest: 84 - 24 = 60. You could also work out five sevenths straight away: 5 x 12 = 60.

Answering 24 gives the tulips, which is not what was asked.

28

Three whole symbols stand for 3 x 8 = 24 trees.

Half a symbol stands for half of 8, which is 4 trees.

24 + 4 = 28 trees. Reading the half symbol as one whole symbol would give 32, which is the trap.

8

• 1 mark for 404 people, or for 7 coaches with 40 people left over.
• 1 mark for 8 coaches.

Everybody needs a seat, so count adults as well: 380 + 24 = 404 people.

52 x 7 = 364, and 404 - 364 = 40 people still standing.

Those 40 need a coach of their own, so the school books 8 coaches.

Rounding 404 divided by 52 down to 7 leaves 40 children behind, which is why you always round up here.

1250 ml

• 1 mark for 2 litres written as 2000 ml.
• 1 mark for 8 parts altogether and one part equal to 250 ml.
• 1 mark for 1250 ml of orange juice.

The answer is wanted in millilitres, so change the 2 litres first: 2 litres = 2000 ml.

The ratio 5 : 3 has 5 + 3 = 8 parts altogether.

One part is 2000 divided by 8, which is 250 ml.

Orange juice is 5 parts: 5 x 250 = 1250 ml.

Check it: the apple juice is 3 x 250 = 750 ml, and 1250 + 750 = 2000 ml. Answering 750 swaps the two juices over.

70 degrees

The angles of any triangle add up to 180 degrees, so the two remaining angles share 180 - 40 = 140 degrees.

The angle given sits between the two equal sides, so the other two angles are equal to each other.

140 divided by 2 = 70 degrees each.

5/8

• 1 mark for listing the factors of 12 that appear on the spinner: 1, 2, 3, 4 and 6.
• 1 mark for the probability 5/8.

The factors of 12 are 1, 2, 3, 4, 6 and 12.

Only 1, 2, 3, 4 and 6 are on the spinner, because it stops at 8. That is 5 winning sections.

So the probability is 5 out of 8, or 5/8, which is already in its simplest form.

Counting 8 as a factor of 12 is the common slip. 12 divided by 8 is not a whole number.

432

18 x 24 can be split up: 18 x 20 = 360 and 18 x 4 = 72.

360 + 72 = 432 seats.

150 square centimetres

• 1 mark for an edge of 5 cm.
• 1 mark for the total surface area 150 square centimetres.

Every edge of a cube is the same, and 5 x 5 x 5 = 125, so each edge is 5 cm.

One face is a 5 cm square, with area 5 x 5 = 25 square centimetres.

A cube has 6 faces, so the total surface area is 6 x 25 = 150 square centimetres.

Stopping at 25 gives one face only.

12

• 1 mark for 15 pupils choosing swimming.
• 1 mark for 24 pupils choosing football.
• 1 mark for 12 pupils choosing tennis.

A quarter of 60 is 60 divided by 4, which is 15 for swimming.

Two fifths of 60: one fifth is 12, so two fifths is 24 for football.

So far that is 15 + 24 + 9 = 48 pupils.

The rest chose tennis: 60 - 48 = 12 pupils.

1 minute 40 seconds

• 1 mark for a correct method, such as 15 divided by 6 = 2.5, or 40 divided by 6 seconds for each litre.
• 1 mark for 1 minute 40 seconds. Accept 100 seconds only if it is then written as 1 minute 40 seconds.

15 litres is two and a half times as much as 6 litres.

So it takes two and a half times as long: 40 x 2.5 = 100 seconds.

100 seconds is 1 minute and 40 seconds, because a minute is 60 seconds.

Writing 1 minute 40 seconds as 1.40 minutes is wrong. Time does not work in hundredths.

48

• 1 mark for Bea having 24 and Alfie having 72.
• 1 mark for the difference 48.

Think of Bea's pile as one part. Alfie has three of those parts, so between them they have 4 parts.

4 parts is 96 stickers, so one part is 96 divided by 4 = 24. Bea has 24 and Alfie has 3 x 24 = 72.

The question asks how many MORE, so subtract: 72 - 24 = 48.

Answering 72 gives Alfie's total rather than the difference.

76

• 1 mark for noticing that each new square adds 3 matchsticks.
• 1 mark for a correct method, such as 4 + 24 x 3, or 3 x 25 + 1.
• 1 mark for 76 matchsticks.

The first square costs 4 matchsticks. Every square after that shares one side, so it only costs 3 more.

Going from pattern 1 to pattern 25 means adding 24 more squares: 24 x 3 = 72 matchsticks.

4 + 72 = 76 matchsticks.

You can write the rule as 3 lots of the pattern number plus 1: 3 x 25 + 1 = 76. Check it on pattern 3: 3 x 3 + 1 = 10, which matches.

Multiplying 4 by 25 to get 100 forgets that the squares share sides.