Sutton Boys' Second Stage Maths Mock Paper 5

15

• 1 mark for working out the bracket correctly as 3.
• 1 mark for the final answer 15.

Start inside the bracket, and even inside a bracket multiplying comes before subtracting: 2 x 6 = 12, so 15 - 12 = 3.

The calculation is now 3 + 4 x 3.

Multiply before you add: 4 x 3 = 12, then 3 + 12 = 15.

Working the bracket left to right, as 13 x 6, is the trap, and adding the 3 first would give 7 x 3 = 21.

3/8

• Accept 3/8 only. 375/1000 and 75/200 are not in simplest form.

0.375 is 375 thousandths, so begin with 375/1000.

Both divide by 125: 375 divided by 125 = 3 and 1000 divided by 125 = 8.

That gives 3/8. If you cannot see the 125, halve three times instead: 375/1000 does not halve, so divide by 5 first to get 75/200, then 15/40, then 3/8.

84 square centimetres

• 1 mark for the correct side lengths of the largest piece, 12 cm by 7 cm.
• 1 mark for the area 84 square centimetres.

The vertical line splits the 20 cm width into 8 cm on the left and 20 - 8 = 12 cm on the right.

The horizontal line splits the 12 cm height into 5 cm at the top and 12 - 5 = 7 cm at the bottom.

So the four pieces measure 8 by 5, 12 by 5, 8 by 7 and 12 by 7, with areas 40, 60, 56 and 84 square centimetres.

The largest is 12 x 7 = 84 square centimetres, the piece in the bottom right.

Check: 40 + 60 + 56 + 84 = 240, which is 20 x 12, so nothing has been lost. Using the 8 cm and 5 cm measurements as if they were the biggest piece is the misreading to avoid.

144

These are the square numbers: 1 x 1, 2 x 2, 3 x 3, 4 x 4, 5 x 5.

So the twelfth term is 12 x 12 = 144.

Adding the gaps one at a time gets there too, but it is slow and easy to slip on.

150 cm

• 1 mark for the total height of the class, 4440 cm.
• 1 mark for the total height of the girls, 1740 cm, and 18 boys.
• 1 mark for the mean height of the boys, 150 cm.

A mean is a total shared out, so turn each mean back into a total.

The whole class: 30 x 148 = 4440 cm.

The girls: 12 x 145 = 1740 cm.

The boys therefore have 4440 - 1740 = 2700 cm between them, and there are 30 - 12 = 18 boys.

Mean height of the boys: 2700 divided by 18 = 150 cm.

Averaging the two means, to get about 146.5, is the trap. It ignores that there are more boys than girls.

28

7 x 400 = 2800.

0.07 is 7 divided by 100, so divide 2800 by 100 to get 28.

Answering 2.8 or 280 means the decimal point has moved the wrong number of places.

39.60 pounds

• 1 mark for the price after the rise, 44 pounds.
• 1 mark for the final price, 39 pounds 60.

10 per cent of 40 pounds is 4 pounds, so after the rise the ticket costs 44 pounds.

The reduction is 10 per cent of the NEW price, not of the old one: 10 per cent of 44 pounds is 4 pounds 40.

44.00 - 4.40 = 39.60 pounds.

Answering 40 pounds, on the grounds that the two changes cancel out, is the trap. The rise is 10 per cent of a smaller amount than the fall, so the ticket ends up cheaper than it started.

3/50

• Accept 3/50 only. 15/250 is not in its simplest form and scores nothing.

Yusuf holds 15 of the 250 tickets, and any one of the 250 is equally likely to win, so the probability is 15/250.

Both numbers divide by 5: 15 divided by 5 = 3 and 250 divided by 5 = 50.

So the probability is 3/50. Writing 15/235, by taking Yusufs tickets off the total, is the mistake to avoid: his tickets are part of the 250.

320 pounds

• 1 mark for a cost of 1 pound 50 for each poster.
• 1 mark for a setting-up fee of 20 pounds.
• 1 mark for the total 320 pounds.

Compare the two orders. The bigger one has 120 - 50 = 70 more posters and costs 200 - 95 = 105 pounds more.

The setting-up fee is charged on both, so that extra 105 pounds pays only for posters: 105 divided by 70 = 1.50 pounds each.

Now find the fee. 50 posters cost 50 x 1.50 = 75 pounds, and the order came to 95 pounds, so the fee is 95 - 75 = 20 pounds.

Check with the other order: 20 + 120 x 1.50 = 20 + 180 = 200 pounds. It fits.

200 posters: 20 + 200 x 1.50 = 20 + 300 = 320 pounds.

Simply doubling the 200 pound order to get 400 pounds charges the setting-up fee twice.

204 minutes

3.4 hours is 3 hours plus 0.4 of an hour.

3 hours is 180 minutes, and 0.4 of 60 minutes is 24 minutes.

180 + 24 = 204 minutes.

Reading 3.4 hours as 3 hours 40 minutes, and answering 220, is the trap. Time is not written in hundredths.

111 degrees

• 1 mark for seeing that a and b sit on a straight line and so add to 180 degrees.
• 1 mark for a = 111 degrees.

An a and a b next to each other make a straight line, so a + b = 180 degrees.

If the two angles were equal they would be 90 each. The 42 degrees of difference has to be shared out, half on to a and half off b.

Half of 42 is 21, so a = 90 + 21 = 111 degrees and b = 90 - 21 = 69 degrees.

Check: 111 + 69 = 180, and 111 - 69 = 42. Both conditions hold.

Taking 42 off 180 to get 138 and then halving is a common wrong route, and it gives 69, which is b rather than a.

8

8 or more means the rows for 8, 9 and 10.

Add their frequencies: 4 + 3 + 1 = 8 pupils.

Adding the marks themselves, 8 + 9 + 10 = 27, answers a different question.

60

• 1 mark for 60 per cent of the members being boys.
• 1 mark for the difference of 12 members being 20 per cent of the club.
• 1 mark for the total of 60 members.

If 40 per cent are girls then 100 - 40 = 60 per cent are boys.

The boys outnumber the girls by 60 - 40 = 20 per cent of the club.

That 20 per cent is the 12 extra boys, so 20 per cent of the club is 12 members.

The whole club is five lots of 20 per cent: 5 x 12 = 60 members.

Check: 40 per cent of 60 is 24 girls and 60 per cent is 36 boys, and 36 - 24 = 12.

Treating the 12 as 40 per cent of the club, and answering 30, is the trap.

1.6 km

• 1 mark for the real distance 1600 m.
• 1 mark for 1.6 km.

Each centimetre stands for 250 m, so 6.4 cm stands for 6.4 x 250 m.

6 x 250 = 1500 and 0.4 x 250 = 100, so the distance is 1600 m.

The answer is wanted in kilometres, so divide by 1000: 1600 m = 1.6 km.

Leaving the answer as 1600 does not answer the question as it is asked.

9

A triangular prism has a triangle at each end. Each triangle has 3 edges, so that is 6.

Three more edges join the two triangles together, one at each corner.

6 + 3 = 9 edges.

120

• 1 mark for 180 visitors from the school trip sector and 60 from the newspaper sector.
• 1 mark for the difference 120 visitors.

A whole pie chart is 360 degrees and stands for 720 visitors, so 1 degree stands for 2 visitors.

A right angle is 90 degrees, so the school trip sector is 90 x 2 = 180 visitors.

The newspaper sector is 30 x 2 = 60 visitors.

The difference is 180 - 60 = 120 visitors.

You can also do it in one step: the sectors differ by 60 degrees, and 60 x 2 = 120.

7 cm

Every edge of a cube is the same length, and the volume is that length multiplied by itself three times.

Try a few: 6 x 6 x 6 = 216, which is too small. 7 x 7 x 7 = 343.

So each edge is 7 cm. Dividing 343 by 3 to get about 114 confuses multiplying three times with multiplying by 3.

60

• 1 mark for three quarters of 96, which is 72.
• 1 mark for the answer 60.

Work from the inside out. Three quarters of 96: a quarter of 96 is 24, so three quarters is 72.

Now five sixths of 72: a sixth of 72 is 12, so five sixths is 5 x 12 = 60.

You can also multiply the fractions first: five sixths of three quarters is 15/24, which is 5/8, and five eighths of 96 is 60.

Adding the fractions instead of taking one of the other is the error to avoid.

5

• 1 mark for working backwards by subtracting, giving a fifth term of 31.
• 1 mark for the fourth and third terms, 19 and 12.
• 1 mark for the first term 5.

If two terms add to make the next one, then subtracting takes you backwards.

The fifth term is 81 - 50 = 31, because the fifth and sixth make the seventh.

The fourth term is 50 - 31 = 19. The third is 31 - 19 = 12. The second is 19 - 12 = 7. The first is 12 - 7 = 5.

Check forwards: 5, 7, 12, 19, 31, 50, 81. The sixth is 50 and the seventh is 81.

Adding rather than subtracting when you go backwards is the mistake this question is built to catch.

42

Both numbers are even and both divide by 3, so both divide by 6: 84 = 6 x 14 and 126 = 6 x 21.

Now 14 and 21 both divide by 7, so both original numbers divide by 6 x 7 = 42.

84 divided by 42 = 2 and 126 divided by 42 = 3, and 2 and 3 share nothing, so 42 is as high as it goes.

2.40 pounds

• 1 mark for the total spent, 7 pounds 60.
• 1 mark for the change, 2 pounds 40.

Carrots: 4 x 85p. Four lots of 80p is 3.20 and four lots of 5p is 20p, giving 3.40 pounds.

Potatoes: 3 x 1.40 = 4.20 pounds.

Total spent: 3.40 + 4.20 = 7.60 pounds.

Change from 10 pounds: 10.00 - 7.60 = 2.40 pounds.

1/3

• 1 mark for 24 blue beads and 36 white beads.
• 1 mark for 72 beads altogether.
• 1 mark for the probability 1/3. 24/72 unsimplified scores 2 marks only.

Start from the reds, because everything is measured against them: there are 12.

Blue: twice as many, so 2 x 12 = 24 beads. White: three times as many, so 3 x 12 = 36 beads.

Altogether: 12 + 24 + 36 = 72 beads.

The probability of blue is 24 out of 72, which is 24/72.

Divide top and bottom by 24: 24/72 = 1/3.

Answering 1/2, on the grounds that there are twice as many blue as red, forgets the white beads entirely.