Sutton Boys' Second Stage Maths Mock Paper 3

2890

Take the numbers away one at a time: 5000 - 1247 = 3753.

Then 3753 - 863 = 2890.

Adding 1247 and 863 first and subtracting the total, 2110, from 5000 gives the same 2890, so either route works.

513

• 1 mark for 35 per cent of 380, which is 133.
• 1 mark for the final value 513.

10 per cent of 380 is 38, so 30 per cent is 114.

5 per cent is half of 10 per cent, so 19. That makes 35 per cent equal to 114 + 19 = 133.

The question says increase, so add: 380 + 133 = 513.

Stopping at 133 gives the increase rather than the new amount.

62 degrees, 118 degrees and 62 degrees

• 1 mark for all three angles: two of 62 degrees and one of 118 degrees. Award nothing for a partly correct set.

The angle straight across the crossing point from the 118 degree angle is vertically opposite it, so it is also 118 degrees.

Each of the other two sits on a straight line with the 118 degree angle, so each is 180 - 118 = 62 degrees.

Check: 118 + 62 + 118 + 62 = 360 degrees, a full turn.

168 pounds

• 1 mark for 3 extra people.
• 1 mark for 42 pounds a night.
• 1 mark for the total 168 pounds.

Two of the five people are already covered by the 24 pounds, so there are 5 - 2 = 3 extra people.

The extra people cost 3 x 6 = 18 pounds a night.

One night therefore costs 24 + 18 = 42 pounds.

Four nights cost 4 x 42 = 168 pounds.

Charging for all five extra people would give 24 + 30 = 54 a night, and that misreading is the trap.

No

• 1 mark for a correct test, such as subtracting 5 from 100 and checking whether 95 divides by 7, or listing terms past 100.
• 1 mark for the answer no, supported by that test. No mark for an unsupported yes or no.

The sequence goes up by 7 each time, starting at 5.

So every term is 5 plus a whole number of 7s. Test 100: 100 - 5 = 95, and 95 divided by 7 is 13 remainder 4, which is not a whole number.

So 100 is not a term. You can see it in the list too: 89, 96, 103 steps straight past 100.

Noticing only that 100 is bigger than 26 proves nothing, which is why the method carries a mark of its own.

1/2

• Accept 1/2 or one half. 10/20 is not in its simplest form and scores nothing.

There are 4 + 6 + 10 = 20 marbles altogether.

The ones that are not green are the 4 red and the 6 blue, so 10 marbles.

10 out of 20 is 10/20, which simplifies to 1/2.

3

• 1 mark for the mean of 2 goals.
• 1 mark for the answer 3 matches.

Add the goals: 2 + 0 + 3 + 1 + 3 + 4 + 1 = 14.

There are 7 matches, so the mean is 14 divided by 7 = 2 goals.

Now count the matches above 2: the 3, the other 3 and the 4. That is 3 matches.

The match with exactly 2 goals does not count, because 2 is not more than 2. Including it gives 4, which is the trap.

750 kg

Put both masses in kilograms first: 2.4 tonnes is 2.4 x 1000 = 2400 kg.

3150 - 2400 = 750 kg.

Subtracting 2.4 from 3150 without converting is the mistake to avoid.

104

• 1 mark for one part equal to 8 items.
• 1 mark for 16 glass items and 48 plastic items.
• 1 mark for the total 104 items.

The paper is the 5 in the ratio 2 : 5, and it is worth 40 items, so one part is 40 divided by 5 = 8 items.

Glass is 2 parts: 2 x 8 = 16 items.

Plastic is three times the glass: 3 x 16 = 48 items.

Total: 16 + 40 + 48 = 104 items.

Reading the ratio the wrong way round, so that glass is 5 parts, gives 100 glass items and wrecks everything after it.

16 cm

The square has 4 equal sides, so its perimeter is 4 x 12 = 48 cm.

An equilateral triangle has 3 equal sides, so each one is 48 divided by 3 = 16 cm.

Dividing 12 by 3 to get 4 uses one side of the square instead of the whole perimeter.

126

• 1 mark for realising the number must be a multiple of 42.
• 1 mark for 126.

A number that is a multiple of both 6 and 7 must be a multiple of 6 x 7 = 42, because 6 and 7 share no factor.

The multiples of 42 are 42, 84, 126, 168, and so on.

Only 126 lies between 100 and 150.

Check: 126 divided by 6 = 21 and 126 divided by 7 = 18, both whole numbers.

40

The whole pie chart is 360 degrees and stands for all 180 people, so 2 degrees stands for 1 person.

80 degrees therefore stands for 80 divided by 2 = 40 people.

Answering 80 reads the angle as if it were a number of people.

2

• 1 mark for the wall area 20.4 square metres.
• 1 mark for 2 tins.

Area of the wall: 8.5 x 2.4. Split it up as 8 x 2.4 = 19.2 and 0.5 x 2.4 = 1.2, giving 20.4 square metres.

One tin covers 12 square metres, which is not enough. Two tins cover 24 square metres, which is enough.

So 2 tins are needed. You cannot buy 1.7 tins, so always round up when buying whole items.

50 square metres

• 1 mark for the outer rectangle measuring 16 m by 11 m.
• 1 mark for the two areas 176 and 126 square metres.
• 1 mark for the area of the path, 50 square metres.

The path goes round the outside, so it adds 1 m at each end of the length and 1 m at each end of the width.

That makes the outer rectangle 14 + 2 = 16 m by 9 + 2 = 11 m.

Outer area: 16 x 11 = 176 square metres. Lawn area: 14 x 9 = 126 square metres.

The path is what is left: 176 - 126 = 50 square metres.

Adding only 1 m rather than 2 m to each side gives a 15 m by 10 m outer rectangle and the wrong answer of 24.

35%

A percentage is a fraction out of 100. Twenty goes into 100 five times, so multiply top and bottom by 5.

7/20 becomes 35/100, which is 35 per cent.

7/20

• 1 mark for writing the two probabilities with a common denominator, for example 5/20 and 8/20.
• 1 mark for 7/20.

All the probabilities together must make 1, because the spinner has to land on something.

Put the two known ones over 20: one quarter is 5/20 and two fifths is 8/20.

Together they are 13/20, so yellow is 20/20 - 13/20 = 7/20.

7 and 20 share no factor, so this is already in its simplest form.

Adding one quarter and two fifths as 3/9 is the classic slip. You cannot add the tops and bottoms separately.

18

Brackets first: 8 - 5 = 3.

Then the multiplying and dividing: 3 x 3 = 9 and 12 divided by 4 = 3.

That leaves 24 - 9 + 3. Work from left to right: 24 - 9 = 15, then 15 + 3 = 18.

Doing the addition before the subtraction, as 24 - 12, would give 12 and is wrong.

3600 pounds

• 1 mark for 300 seats sold.
• 1 mark for 3600 pounds.

One eighth of 480 is 60, so three eighths, the empty seats, is 180.

Seats sold: 480 - 180 = 300. You could also take five eighths straight away: 5 x 60 = 300.

300 x 12 = 3600 pounds.

Working with the 180 empty seats instead would give 2160 pounds, which is money nobody paid.

29

• 1 mark for 14 boys coming by bus.
• 1 mark for 42 girls, and 15 girls coming by bus.
• 1 mark for the total 29 pupils.

Boys first. Half of 48 walk, so 24 walk, and 10 cycle. That is 34, so 48 - 34 = 14 boys come by bus.

Now the girls. There are 90 - 48 = 42 girls. Of those, 18 walk and 9 cycle, which is 27, so 42 - 27 = 15 girls come by bus.

Altogether: 14 + 15 = 29 pupils come by bus.

The easy slip is to forget to work out the number of girls and use 90 somewhere it does not belong.

5 cm

The volume is the area of the base times the height.

The base area is 12 x 8 = 96 square centimetres.

So the height is 480 divided by 96 = 5 cm.

11/12

• 1 mark for writing both amounts over a common denominator of 12, for example 33/12 and 22/12.
• 1 mark for 11/12.

Turn both mixed numbers into improper fractions: two and three quarters is 11/4, and one and five sixths is 11/6.

The smallest number both 4 and 6 go into is 12, so rewrite them: 11/4 = 33/12 and 11/6 = 22/12.

33/12 - 22/12 = 11/12.

11 and 12 share no factor, so that is the simplest form.

Taking the whole numbers and the fractions apart, as 1 and then 3/4 - 5/6, needs care because 3/4 is smaller than 5/6.

5

• 1 mark for 5 steps between the fourth and ninth terms.
• 1 mark for a step size of 6.
• 1 mark for the first term 5.

Going from the fourth term to the ninth term is 9 - 4 = 5 steps.

Over those 5 steps the value rises by 53 - 23 = 30, so each step is 30 divided by 5 = 6.

From the first term to the fourth is 3 steps back, so go down by 3 x 6 = 18 from 23: 23 - 18 = 5.

Check: 5, 11, 17, 23, 29, 35, 41, 47, 53. The fourth is 23 and the ninth is 53.

Counting 9 - 4 as 4 steps, rather than 5, is the trap that spoils this question.