Sutton Boys' Second Stage Maths Mock Paper 2

47

Multiplying and dividing both come before subtracting.

7 x 8 = 56 and 36 divided by 4 = 9.

56 - 9 = 47. Doing the subtraction first would give 56 - 36 = 20, then 20 divided by 4 = 5, which is wrong.

10

• 1 mark for 20 pupils walking to school.
• 1 mark for 10 pupils walking with a friend.

One eighth of 32 is 4, so five eighths is 5 x 4 = 20 pupils who walk.

Half of those 20 walk with a friend: 20 divided by 2 = 10 pupils.

Halving the whole class instead of just the walkers gives 16, which is the trap.

6

Each term is half of the one before it: 96 halves to 48, 48 halves to 24, 24 halves to 12.

Half of 12 is 6.

Looking for a subtraction rule does not work, because the gaps keep shrinking.

Between 10:00 and 12:00, a rise of 6 degrees

• 1 mark for identifying the interval from 10:00 to 12:00.
• 1 mark for the rise of 6 degrees.

Work out each gap in turn: 12 to 17 is a rise of 5, 17 to 23 is a rise of 6, 23 to 26 is a rise of 3, and 26 to 21 is a fall of 5.

The biggest rise is 6 degrees, between the 10:00 and 12:00 readings.

The steepest part of the graph is not the highest point. Answering 26 degrees at 14:00 confuses the largest reading with the largest change.

150 degrees

A full turn is 360 degrees and there are 12 numbers on a clock face, so the hand turns 360 divided by 12 = 30 degrees between one number and the next.

From 12 to 5 is five of those steps: 5 x 30 = 150 degrees.

31.25 pounds

• 1 mark for either 17 pounds for the adults or 14 pounds 25 for the children.
• 1 mark for the total 31 pounds 25.

Adults: 2 x 8.50 = 17.00 pounds.

Children: 3 x 4.75. Think of it as 3 x 5 = 15 pounds, then take off 3 x 25p = 75p, giving 14.25 pounds.

17.00 + 14.25 = 31.25 pounds.

20

• 1 mark for 15 g of oats for each flapjack.
• 1 mark for a correct division, such as 300 divided by 15.
• 1 mark for 20 flapjacks.

First find how much oats one flapjack needs: 180 divided by 12 = 15 g.

Now see how many lots of 15 g are in 300 g: 300 divided by 15 = 20.

So Ellie can make 20 flapjacks. Only the oats matter, because she has plenty of the other two.

Check it the other way: 300 g is 300 divided by 180, and 12 x that, which also gives 20.

1/3

• Accept 1/3 or one third. 2/6 is not in its simplest form and scores nothing.

Numbers greater than 4 on a dice are 5 and 6, so 2 of the 6 faces win.

That is 2/6, which simplifies by dividing top and bottom by 2 to give 1/3.

Counting 4 itself would give 3/6, but 4 is not greater than 4.

32

• 1 mark for 13 full trays, or for 468 rolls packed.
• 1 mark for 32 rolls left over.

Count in trays: 36 x 10 = 360, and 36 x 3 = 108, so 36 x 13 = 468.

Another tray would need 504 rolls, and he only has 500, so 13 trays is the most he can fill.

500 - 468 = 32 rolls left over.

Answering 13 gives the number of trays, not the number of rolls left.

3 hours 25 minutes

Count on in whole hours first: 09:55 to 12:55 is 3 hours.

From 12:55 to 13:20 is 25 minutes: 5 minutes takes you to 13:00, then 20 more.

So the crossing takes 3 hours and 25 minutes.

Subtracting the digits as 13:20 - 09:55 in columns gives 4:65, which is not a real time.

44 degrees

• 1 mark for 180 - 48 = 132 degrees shared between the other two angles.
• 1 mark for x = 44 degrees.

Angles on a straight line add up to 180 degrees.

Take off the 48: 180 - 48 = 132 degrees left for the other two.

The third angle is twice the second, so those 132 degrees are three equal shares of x: 132 divided by 3 = 44.

Check: 48 + 44 + 88 = 180 degrees. Dividing 132 by 2 instead of 3 gives 66, which is the error to avoid.

5

• 1 mark for putting the marks in order: 9, 9, 12, 14, 16, 17, 20.
• 1 mark for the median 14 and the mode 9.
• 1 mark for the difference 5.

Put the marks in order first: 9, 9, 12, 14, 16, 17, 20.

The median is the middle one. With seven marks the middle is the fourth, which is 14.

The mode is the mark that appears most often, and only 9 appears twice, so the mode is 9.

14 - 9 = 5.

Taking the median from the unordered list would give 12, so the ordering step is the one that earns the first mark.

36 square centimetres

The area of a rectangle is its length multiplied by its width.

9 x 4 = 36 square centimetres.

Adding the two measurements, or working out 9 + 4 + 9 + 4 = 26, gives the distance all the way round instead. That is the perimeter, and it is measured in centimetres rather than square centimetres.

three fifths, 65 per cent, 0.7

• 1 mark for changing all three into the same form, for example 0.7, 0.6 and 0.65.
• 1 mark for the correct order: three fifths, then 65 per cent, then 0.7.

The safest move is to turn everything into decimals.

Three fifths is 3 divided by 5 = 0.6. 65 per cent is 65 out of 100 = 0.65. The third number is already 0.7.

In order, smallest first: 0.6, 0.65, 0.7, which is three fifths, 65 per cent, 0.7.

Judging by the size of the digits you can see, so that 65 per cent looks biggest, is the trap.

12

List the factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

List the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

The largest number in both lists is 12. Note that 24 divides 48 but not 60, so it does not count.

60 km/h

• 1 mark for writing 2 hours 30 minutes as 2.5 hours, or for a correct method.
• 1 mark for 60 kilometres per hour.

Speed is distance shared out over time, so the time has to be in hours: 2 hours 30 minutes is 2.5 hours.

150 divided by 2.5 = 60 kilometres per hour.

You can check it without dividing by a decimal: in 2 hours the car would do 120 km and in the extra half hour another 30 km, giving 150 km.

Writing the time as 2.3 hours is the mistake to avoid.

55 minutes

The range is the longest time take away the shortest time.

So the longest time is the shortest plus the range: 8 + 47 = 55 minutes.

Subtracting instead, to get 39, is the slip. It would give a longest time shorter than the range itself.

15

• 1 mark for 9 red pens, or for five eighths being green.
• 1 mark for 15 green pens.

One eighth of 24 is 3, so three eighths is 3 x 3 = 9 red pens.

Every other pen is green: 24 - 9 = 15 green pens.

You could also go straight there: five eighths of the pens are green, and 5 x 3 = 15.

Answering 9 gives the red pens, which is not what was asked.

576 cubic centimetres

• 1 mark for a base measuring 12 cm by 12 cm.
• 1 mark for a height of 4 cm.
• 1 mark for the volume 576 cubic centimetres.

Along one edge of the card, 4 cm is lost at each end, so the base of the box measures 20 - 4 - 4 = 12 cm. The card is square, so the base is 12 cm by 12 cm.

The flaps that fold up are 4 cm tall, so the box is 4 cm high.

Volume: 12 x 12 = 144, and 144 x 4 = 576 cubic centimetres.

Taking only 4 cm off each side, to get a 16 cm base, is the trap. A corner square is cut from BOTH ends of every edge.

120

One eighth of 320 is 320 divided by 8, which is 40.

Three eighths is 3 x 40 = 120.

65

• 1 mark for the gaps 3, 5, 7, 9 and for seeing that the next gaps are 11, 13 and 15.
• 1 mark for continuing the sequence correctly to 37 and 50.
• 1 mark for the eighth term 65.

Look at the gaps: 5 - 2 = 3, 10 - 5 = 5, 17 - 10 = 7, 26 - 17 = 9. The gaps go up in twos.

So the next gaps are 11, 13 and 15.

Sixth term: 26 + 11 = 37. Seventh term: 37 + 13 = 50. Eighth term: 50 + 15 = 65.

Treating the gap as a fixed 9 would give 26 + 27 = 53, which is the trap.

41

• 1 mark for a saving of 1 pound 50 on each journey.
• 1 mark for 40 journeys, where the two costs are exactly equal.
• 1 mark for 41 journeys, the first journey at which she is actually better off.

With the ticket each journey is 1 pound 50 cheaper, because 3.50 - 2.00 = 1.50.

Those savings have to pay back the 60 pounds the ticket cost: 60 divided by 1.50 = 40 journeys.

At exactly 40 journeys the two ways cost the same. With the ticket: 60 + 40 x 2 = 140 pounds. Without it: 40 x 3.50 = 140 pounds.

So she has not saved anything yet. On the 41st journey she is ahead for the first time, so the answer is 41.

Answering 40 is the tempting mistake, because 40 is where the ticket breaks even rather than where it saves.