Sutton SET Mathematics Mock Paper 2

A

One decimal place means one digit after the point, so you are choosing between 1.8 and 1.9. Look at the next digit along, the 4 in the hundredths column. It is less than 5, so the tenths digit stays as it is and the answer is 1.8.

Before you round anything you can cross out 1.84 and 1.85. They have two digits after the point, so they cannot be answers to one decimal place.

1.9 is the tempting one. It comes from rounding twice: 1.847 up to 1.85, then 1.85 up to 1.9. Always round once, from the number you were given. 2.0 is rounded to the nearest whole number instead.

D

Multiplying and dividing come before adding and subtracting. Work out 4 x 9 = 36 and 12 divided by 3 = 4 first.

That leaves 6 + 36 - 4, which is 42 - 4 = 38.

26 comes from working straight from left to right, which is the commonest mistake here. 86 comes from adding the 6 and the 4 first, 30 from leaving the dividing out altogether, and 10 from doing the subtraction before the division. A quick size check helps: 4 x 9 = 36 is the biggest part of this calculation, so the answer should be somewhere near 40, which rules out 10 and 86 at a glance.

D

One fifth of 350 g is 350 divided by 5 = 70 g. Three fifths is 3 x 70 = 210 g.

1050 g can go on size alone: it is three times the whole recipe, and Marek cannot use more flour than the full recipe needs. 175 g is exactly half, and three fifths is more than a half, so that is out too.

140 g is the tempting wrong answer. It is two fifths, which is the flour Marek does not use.

B

Change the litres into millilitres first: 5 litres = 5 x 1000 = 5000 ml.

Now count on in 800s: 800, 1600, 2400, 3200, 4000, 4800. That is six plants, with 200 ml left in the can.

62 and 625 come from dividing by 80 or by 8 instead of by 800, and one look at their size rules them out: a 5 litre can cannot water sixty plants. 7 is the trap, because a seventh plant would only get 200 ml, not a full 800 ml.

A

Angles on a straight line add up to 180 degrees. The two you are given come to 47 + 62 = 109 degrees.

So the third angle is 180 - 109 = 71 degrees.

251 degrees is impossible before you calculate anything, because no angle on a straight line can be 180 degrees or more. 109 degrees is the sum of the two known angles rather than the missing one, and 133 and 118 come from taking only one of them away from 180.

B

Add them up: 2 + 0 + 9 + 3 + 6 = 20. Then divide by the number of afternoons, which is 5 and not 4. The afternoon with none still counts as an afternoon.

20 divided by 5 = 4 tomatoes.

20 is the total, so it can be crossed out at once: a mean always sits between the smallest reading and the largest, which here means between 0 and 9. 5 is what you get by dividing by 4 and forgetting the empty afternoon, and 3 is the middle value when the numbers are put in order, which is the median.

B

3 parts and 2 parts make 5 parts altogether, so one part is 45 divided by 5 = 9 litres.

Sand is 2 parts, so it is 2 x 9 = 18 litres.

Sand is the smaller share, so the answer has to be less than half of 45. That rules out 27 and 30 with no working at all. 27 litres is the loam, which is what you get by reading the ratio the wrong way round, and 9 litres is only one part.

D

Start at -6 and count upwards 11 degrees. Six of those degrees take you to 0, and the other five take you to 5 degrees C.

-17 is what you get by going down 11 instead of up. 17 comes from adding 6 and 11 and losing the minus sign, and -5 from working out 6 - 11 as if the starting temperature were positive.

4 is the near miss, and it comes from counting 0 as one of the eleven degrees. Zero is a point you pass through, not a step of its own.

B

Turn the fractions into decimals: 13/25 is the same as 52/100, which is 0.52, and 3/5 is 0.6.

Now compare the tenths digit first. Anything starting 0.5 is smaller than anything starting 0.6, which leaves only 0.605 and 3/5. Then 0.605 beats 0.600, so 0.605 is the largest.

3/5 is the tempting answer because it is written differently from the rest and the digits look large. Sorting on the tenths digit is much faster than working every value out in full.

C

Split the 24 up: 20 x 35 = 700 and 4 x 35 = 140. Add them together: 700 + 140 = 840.

Two options can go without any multiplying. The last digits are 4 and 5, and 4 x 5 = 20, so the answer must end in a zero. That removes 804 and 875 straight away.

420 is half the answer, from halving the 24 and forgetting to double at the end. 1680 is double the answer, from doubling when you should have halved.

B

Count to the hour first: 07:48 to 08:00 is 12 minutes. Then 08:00 to 08:31 is another 31 minutes. 12 + 31 = 43 minutes.

83 and 103 can go immediately. 08:31 is less than an hour after 07:48, so the answer has to be under 60.

17 comes from subtracting 31 from 48, which is the wrong way round. 53 comes from thinking that 07:48 to 08:00 is 22 minutes rather than 12.

A

A rhombus is a quadrilateral with four equal sides, rather like a squashed square. That is what makes it a rhombus, so the first statement is true of every one.

Right angles and equal diagonals only turn up when the rhombus happens to be a square, so those two statements are true of some rhombuses but not all of them. The word every is doing the work in this question.

Exactly one pair of parallel sides describes a trapezium; a rhombus has two pairs. The last statement is the near miss, because a rhombus does have lines of symmetry, but it has two of them, along its diagonals.

D

10% of 250 is 25, so 30% is 75. 1% is 2.5, so 6% is 15. Adding those gives 75 + 15 = 90 members.

A rough check does most of the work here. 36% is a bit more than a third, so the answer must be a bit more than 83 and nowhere near half. Only 90 fits, so you can mark it before you finish the arithmetic.

160 is the number who do not take the newsletter and 64 is the percentage who do not. 36 is the percentage copied out as though it were a number of people, and 25 is 10% rather than 36%.

D

Rounding to the nearest thousand means choosing between 148,000 and 149,000. Look at the hundreds digit, which is 6. It is 5 or more, so round up to 149,000.

Two options can go on sight. A number rounded to the nearest thousand ends in three zeros, so 148,600 and 148,700 are not even the right shape.

148,000 is the trap for anyone who chops the end off the number instead of rounding it, and 150,000 has been rounded to the nearest ten thousand.

A

Ben and Dee borrowed 9 + 6 = 15 books between them, and Chidi borrowed 21.

21 - 15 = 6 books.

30 and 36 come from adding rather than subtracting, and both are larger than 21, so neither can be a difference. 12 is the answer if you forget Dee and 15 is the answer if you forget Ben.

B

6 x 25 = 150, which is as close to 154 as you can get without going past it. Each shelf takes 25 books, and 154 - 150 = 4 books are left over.

Three options can be ruled out before you divide. A remainder after dividing by 6 must be smaller than 6, so 25 and 26 are impossible, and 6 itself is impossible too, because another whole book would then fit on every shelf.

25 is the tempting one, because it is the number of books on each shelf rather than the number left over.

A

The fourth corner sits directly above (1, 2), so its first coordinate is 1. It also sits level with (7, 6), so its second coordinate is 6. That gives (1, 6).

Just deciding that the answer must start with a 1 leaves only two options standing, and the height then settles it.

(6, 1) is the same pair of numbers written the wrong way round, which is the classic slip. (6, 6) uses the width of the bed, 6 squares, in place of the first coordinate, and (1, 7) counts one grid line too far up.

C

Put both fractions over 12: one third is 4/12 and one quarter is 3/12. Together she has read 4/12 + 3/12 = 7/12.

The whole book is 12/12, so what is left is 12/12 - 7/12 = 5/12.

She has read more than half the book, so what is left must be less than half. That rules out 7/12 and 5/7 at once. 2/7 comes from adding the tops and the bottoms, which is never how fractions are added, and 1/12 comes from subtracting the two fractions from each other.

B

Get both amounts into the same unit first: 1.25 kg = 1250 g.

1250 - 850 = 400 g.

0.4 is the right number in the wrong unit. 0.4 kg is the same amount of potato, but the question asks for grams, so it is not the answer here. 2100 comes from adding instead of subtracting, and 1250 is the whole amount the recipe needs rather than the extra.

B

The three angles of any triangle add to 180 degrees. Take the 96 off: 180 - 96 = 84 degrees left to share.

The two remaining angles are equal, so each one is 84 divided by 2 = 42 degrees.

132 degrees is impossible before you begin, because two angles of 132 would come to far more than 180 on their own. 84 degrees is the tempting answer: it is the two angles added together rather than one of them. 48 comes from halving the 96 instead.

B

First find the total number of tiles: 8 x 24 = 192. Take away the 36 blue tiles: 192 - 36 = 156. Then share the other tiles among 6 colours: 156 divided by 6 = 26. The answer is B.

You can rule out options quickly by size. If none of the tiles were blue, each colour could have 192 divided by 6 = 32 tiles. Some tiles are blue, so the answer must be less than 32. That crosses out 32, 38 and 156 before you finish the calculation.

18 comes from doing 24 - (36 divided by 6), which wrongly uses just one row of tiles. 32 ignores the 36 blue tiles. 38 adds the blue tiles instead of taking them away. 156 is the number of non-blue tiles before they are shared, so it stops one step too soon.

D

Find the amount for one person first: 300 divided by 4 = 75 ml each. Then 10 x 75 = 750 ml.

Ten people is more than double four people, so the answer must be more than 600 ml. That rules out 120, 375 and 600 in a single step, and 3000 ml is three litres of milk, which is far too much for pancakes.

600 ml is the tempting one, because it is the amount for 8 people. 375 ml is the amount for 5, and 120 ml comes from turning the scaling upside down.

B

Multiply the digits first: 7 x 4 = 28. Then count the decimal places in the question, one in 0.7 and one in 0.4, so the answer needs two. That gives 0.28 square metres.

There is a quicker sort. Multiplying by a number smaller than 1 makes things smaller, so the area must come to less than 0.4. Only 0.028 and 0.28 are, so you are down to two options before you multiply anything.

2.8 is the trap: it is the right digits with only one decimal place. 1.1 comes from adding the two lengths instead of multiplying them.

C

The number must be less than 6000, so put 5 in the thousands place to make it as large as possible. An odd number must end in an odd digit. With 5 already used, the units digit must be 3. Put the larger remaining digit, 8, in the hundreds place and 0 in the tens place. This makes 5803, so the answer is C.

Parity gives you a quick elimination. 5830 is even because it ends in 0, and 8053 is greater than 6000. Of the three options left, 5803 has the greatest thousands digit and then the greatest hundreds digit.

3805 keeps 5 for the units place, but that forces the smaller digit 3 into the thousands place. 5083 puts 0 in the hundreds place and 8 in the tens place, so those two digits are in the wrong order for the greatest number. 5830 transposes the last two digits and makes an even number. 8053 ignores the limit of 6000.

D

The range is the largest value take away the smallest. The largest is 12 and the smallest is 0, so the range is 12 - 0 = 12 mm.

9 is the trap. It comes from treating 3 as the smallest figure and ignoring the two dry days, but a day with no rain is still a reading of 0.

35 is the total rainfall for the week, 5 is the middle figure when they are put in order, and 0 is the figure that appears most often.

C

Going all the way round means the perimeter: 7 + 4 + 7 + 4 = 22 m, so Kwame needs 22 boards.

28 is the number to watch. It is 7 x 4, the area of the bed in square metres, which is the right sum for a different question. Boards go round the edge, not across the middle, so the units alone tell you that 28 square metres cannot be a number of boards.

11 is only half way round, 14 is the two long sides on their own, and 44 counts the whole edge twice.

A

Split the 47 into 40 + 7 and multiply the 8 by each part. Eight lots of 47 is eight lots of 40 plus eight lots of 7, which is the first option, and it comes to 320 + 56 = 376.

A rough size check throws two options out at once. 8 x 47 is a little under 8 x 50 = 400, but (8 x 4) + (8 x 7) is only 88 and 8 x 40 x 7 is 2240.

(8 x 50) - 3 is the clever looking trap. Starting from 8 x 50 is a good idea, but you have added three lots of 8 too many, not 3, so it should be (8 x 50) - (8 x 3). (8 x 40) + 7 forgets to multiply the 7 by 8 at all.

E

The largest number that divides into both 18 and 24 is 6. 18 divided by 6 is 3 and 24 divided by 6 is 4, so 18/24 = 3/4.

6/8 and 9/12 are equal to 3/4 in value, but neither is in its simplest form, because the top and bottom of each can still be divided again. They are what you get by stopping after halving once or after dividing by 3 once, and that is the commonest mistake on this kind of question.

4/3 is 3/4 written upside down, and since it is bigger than 1 it cannot equal 18/24. 2/3 comes from taking 6 away from the top and the bottom rather than dividing both by 6.

E

Change them all into metres: 1250 mm = 1.25 m, 128 cm = 1.28 m and 0.0014 km = 1.4 m.

The list now reads 1.25, 1.28, 1.3, 1.35 and 1.4 metres, so 0.0014 km is the longest.

1250 mm is the trap, because 1250 is easily the biggest number on the page. Until every length is in the same unit, the size of the number tells you nothing at all. 0.0014 looks tiny for exactly the same reason, which is why it is so easy to skip past.

C

Each line of symmetry runs from one corner to the middle of the opposite side. A regular pentagon has 5 corners, so it has 5 such lines.

It is worth remembering the general rule: a regular shape with equal sides and equal angles has exactly as many lines of symmetry as it has sides.

10 is the tempting one, because it comes from counting each line twice, once from each end. 6 comes from muddling a pentagon up with a hexagon.

A

Line the numbers up and subtract. The units need an exchange, giving 14 - 6 = 8; the tens then give 9 - 7 = 2; the hundreds give 11 - 8 = 3; the thousands give 2 - 1 = 1. The answer is 1328.

The last digit does a lot of the work. 4 - 6 needs an exchange and 14 - 6 = 8, so the answer must end in 8. That leaves only 1328, 1428 and 2328, and 5080, which comes from adding instead of subtracting, is out on size as well.

1428 comes from forgetting the exchange out of the hundreds column and 2328 from forgetting the one out of the thousands. 2672 comes from taking the smaller digit from the larger in every column, which is the mistake that never exchanges at all.

E

Two hours is four lots of 30 minutes, so the coach covers 4 x 45 = 180 km.

A size check clears most of the page: one hour on its own is 90 km, so two hours has to be more than 90. That leaves only 135 and 180, and 135 km is the distance for an hour and a half.

22.5 km comes from halving when you should be doubling, and 45 km is simply the distance for the first 30 minutes copied out again.

C

10% of 30 cm is 3 cm. Shrinking means taking that off, so the side becomes 30 - 3 = 27 cm.

33 cm can go straight away, because a square that shrinks cannot come out longer than it started. 3 cm and 20 cm go on size too: losing only a tenth leaves the side close to 30 cm.

3 cm is the amount lost rather than the length left, and 20 cm comes from reading 10% as 10 cm. 29 cm comes from taking off a tenth of 10 rather than a tenth of 30.

D

Two and a half symbols plus one and a half symbols makes 4 whole symbols. Each one stands for 8 books, so that is 4 x 8 = 32 books.

4 is the trap: it is the number of symbols, not the number of books. Any answer smaller than 8 must be wrong, because even a single symbol already means 8 books.

24 comes from ignoring the half symbols altogether and 40 from rounding both of them up to whole symbols. 16 comes from using 4 books per symbol instead of 8.

D

Read it in chunks. M is 1000. CM is 900, because a C in front of an M means take 100 away from 1000. LXX is 50 + 10 + 10 = 70, and IV is 4. Altogether that is 1000 + 900 + 70 + 4 = 1974.

The CM at the start settles a great deal on its own: it puts the year in the 1900s, so 1174 and 2074 are out before you read any further.

1954 comes from reading LXXIV as LIV, and 1964 from dropping one of the two X letters.

A

Angles at a point add up to 360 degrees. The three you know come to 90 + 145 + 62 = 297 degrees.

So the unknown angle is 360 - 297 = 63 degrees.

The three known angles already come to nearly 300, so the missing one has to be well under 90 degrees. That leaves only 63 and 73 standing, and adding carefully settles which. 297 is the sum of the known angles rather than the answer, and 153 comes from forgetting the right angle altogether.

C

Brackets first: 12 - 4 = 8. Then multiply: 5 x 8 = 40. Then add: 40 + 7 = 47.

The multiplying alone gives 40, so the answer must be a little more than 40. 39 is too small, and 63 and 75 are far too big, which leaves you choosing between 40 and 47.

63 comes from ignoring the brackets and working out 5 x 12 - 4 + 7. 75 comes from dragging the + 7 inside the brackets, and 40 from forgetting to add it at all.

E

Volume is length x width x depth. 20 x 15 = 300, and 300 x 10 = 3000 cubic centimetres.

A box of that size holds thousands of cubic centimetres, so the small answers can go on rough size alone. 45 comes from adding the three measurements instead of multiplying them.

300 and 200 come from using only two of the three measurements. 1300 is the surface area of the box in square centimetres, which is the right sort of working for a completely different question.

B

The blanket has 5 x 6 = 30 squares altogether and 10 of them are red. That is 10/30, and dividing top and bottom by 10 gives 1/3.

10/3 is impossible before you work anything out, because a fraction of a shape can never be bigger than the whole shape. It is 10/30 written upside down.

Ten red squares fill two of the six rows, which is 2/6 = 1/3, so answering 1/6 means counting one row where there are two. 2/3 is the fraction that is not red.

B

3/8 means 3 divided by 8. One eighth is 0.125, so three eighths is 3 x 0.125 = 0.375.

You can also close in on it without dividing. 3/8 is more than a quarter, which is 0.25, and less than a half, which is 0.5. Only 0.375 sits between those two, so it must be the answer.

0.38 is the tempting one because it uses the digits 3 and 8, and 0.83 is the same trick with the digits swapped. 0.125 is one eighth rather than three eighths.

E

A trapezium is the quadrilateral with exactly one pair of parallel sides, so it is the shape Rhys means.

The word exactly does the sorting for you. A parallelogram, a rectangle and a rhombus all have two pairs of parallel sides, so those three go out together as soon as you notice it.

A kite is the other tempting answer, because it has four sides and an unusual look, but none of its sides are parallel at all.

D

Saturday first: 7 x 18 = 126 books. Then add Sunday: 126 + 45 = 171 books.

There is a neat check here. 7 x 18 is even, and adding the odd number 45 makes the total odd, so the answer has to be odd. That rules out 70 and 126 in one glance, and 441 is far too big for the numbers involved.

126 is the tempting answer because it is Saturday's total on its own. 441 comes from adding 45 to 18 first and then multiplying by 7, and 70 from simply adding all three numbers in the question.

C

Hundredths are the second place after the decimal point. In 4.07 the 7 sits in exactly that place, so it stands for seven hundredths.

Counting places is far quicker than reading each number out in words. The 7 has to be the second digit after the point, and that only happens in 4.07.

0.7 is the trap, because a 7 straight after the point is seven tenths, not seven hundredths. 0.007 is seven thousandths, 7.4 has seven ones and 74 has seven tens.

B

Add the units: 6 + 9 + 2 + 3 = 20, so write 0 and carry 2. Add the tens: 4 + 3 + 5 + 4 = 16, plus the 2 carried makes 18. The total is 180 books.

The units column alone rules two options out. They add to 20, so the total must end in a zero, and neither 174 nor 184 does.

174 and 184 come from mishandling that carry, 190 from carrying 3 instead of 2, and 270 from carrying a whole hundred that is not there. Pairing the numbers is an easier route to the same place: 46 + 43 = 89, 39 + 52 = 91, and 89 + 91 = 180.

C

Add the hours first: 10:35 plus 6 hours is 16:35. Now add the 50 minutes: 35 + 50 = 85 minutes, which is 1 hour and 25 minutes, so 16:35 becomes 17:25.

Two options go without any arithmetic at all. No clock ever shows more than 59 minutes, so 16:85 and 17:85 are not times.

16:25 is the near miss. The 25 minutes is right, but the extra hour hidden inside those 85 minutes has been left out. 17:35 comes from rounding 6 hours 50 minutes up to a neat 7 hours.

C

The difference between 5 parts and 2 parts is 3 parts, and that difference is the 21 extra girls. So one part is 21 divided by 3 = 7 children.

The whole choir is 2 + 5 = 7 parts, so it is 7 x 7 = 49 children.

Check it: 14 boys and 35 girls, and 35 - 14 = 21. Those two numbers are the tempting wrong answers, because each is only part of the choir rather than all of it. 63 comes from multiplying the difference by 3 instead of dividing by it.

A

Write 1.5 as 1.50 so the columns line up, then subtract: 1.50 - 0.85 = 0.65 litres.

0.85 is more than half of 1.5, so less than half must be left. Half of 1.5 is 0.75, so anything of 0.75 or more is out, and that clears three options in one step, 2.35 among them.

0.7 comes from rounding 0.85 down to 0.8 before subtracting, and 0.85 is the amount poured out rather than the amount left behind.

E

A triangular prism has two triangular ends and three rectangular sides, which makes 5 faces. It has 3 edges round each triangle and 3 more joining them, which makes 9, and 3 corners at each end, which makes 6 vertices.

Counting faces first is the quick sort. A cube and a cuboid both have 6 faces, so they go straight away, and a triangular pyramid has only 4.

The square-based pyramid is the real trap, because it also has 5 faces. Use the vertices to separate them: it has 4 corners on its base and 1 at the top, which is 5, not 6.

B

Left makes the first coordinate smaller: 4 - 3 = 1. Up makes the second coordinate bigger: 3 + 2 = 5. The counter lands at (1, 5).

Deciding the direction of each change is enough on its own. Only one option has a first number smaller than 4 and a second number bigger than 3.

(7, 5) comes from sliding right instead of left, and (1, 1) from sliding down instead of up. (5, 1) and (7, 1) muddle the two movements up with each other.

D

Every centimetre on the plan stands for 2 metres in the garden, so multiply: 7.5 x 2 = 15 m.

The real path must be longer than the drawing of it, so 3.75 m and 7.5 m are out at once, and 150 m is longer than a football pitch, which is no sort of garden path.

3.75 m is what you get by dividing by 2 instead of multiplying, and 9.5 m comes from adding 2 rather than doubling.