Sutton SET Mathematics Mock Paper 4

B

A six-digit number cannot begin with 0, so put the smallest non-zero digit, 2, first. Put 0 next, then arrange the remaining digits from smallest to largest: 4, 5, 7, 9. This gives 204 579.

A rough size check rules out 240 579 and 975 420 because their early digits make them much larger. 024 579 has only five digits when the leading zero is ignored.

204 597 swaps the last two digits, putting the larger digit earlier, so it is greater than 204 579.

A

Do the brackets first: 5 + 3 = 8. Then multiply: 6 x 8 = 48. Finally, 84 - 48 = 36.

48 is the product inside the calculation but stops before the subtraction. 57 ignores the bracket and works out 84 - 6 x 5 + 3.

132 adds 48 instead of subtracting it. 624 comes from doing 84 - 6 first and then multiplying 78 by 8, which ignores the order of operations.

C

Use twentieths: 3/10 = 6/20 and 1/4 = 5/20. Altogether, 11/20 is used, so 20/20 - 11/20 = 9/20 is left.

For a quick magnitude check, the amount used is a little more than one half, so the amount left must be a little less than one half. That rules out 11/20, 7/10 and 5/7.

11/20 is the fraction used, 1/20 subtracts the two used fractions instead of adding them, and 7/10 forgets Saturday. 5/7 comes from adding the numerators and denominators before subtracting from one.

D

Convert first: 2.75 km = 2750 m. Then subtract the closed part: 2750 - 680 = 2070 m.

A unit sanity check shows that 2.07 m and 207 m are far too short for most of a 2.75 km trail. The answer should be just over 2000 m.

2750 m ignores the closure, while 3430 m adds the closed section instead of subtracting it. 2.07 m has the right digits for 2.07 km but the wrong unit.

E

A kite has two pairs of equal adjacent sides. Adjacent means next to each other. A kite can have no parallel sides, so it fits every clue.

A rhombus has all four sides equal and two pairs of parallel sides. A rectangle and a parallelogram also have two pairs of parallel sides.

A trapezium has one pair of parallel sides, so it fails the final clue even though it may look similar to a kite when tilted.

B

There are 2 + 3 + 4 = 9 equal parts. One part is 108 divided by 9 = 12. Green lanterns take 4 parts, so there are 4 x 12 = 48.

A rough size check helps: green is the largest group but is less than half of 108. Of the listed group-sized answers, 48 is the only one that fits.

12 is one part, 24 is the red group, 36 is the blue group and 108 is the total instead of the green share.

A

Put the times in order: 4, 6, 7, 9, 11, 14, 18. With seven values, the median is the fourth value, which is 9 minutes.

A magnitude check says the middle must lie between the low and high values, so 69, which is the total, cannot be the median.

7 is the middle entry of the unsorted list. 11 is halfway between the smallest and largest, but that is not how a median is found. 14 is the range, 18 - 4, rather than the median.

C

Moving right increases the first coordinate: -3 + 8 = 5. Moving down decreases the second coordinate: 5 - 6 = -1. The new point is (5, -1).

(5, 11) moves up instead of down. (-11, -1) moves left instead of right, and (-11, 11) reverses both directions.

(-1, 5) subtracts the two movement numbers from each other and does not apply them to the original coordinates.

D

Every whole number from 6345 to 6354 rounds to 6350. Of the options, only 6345 is in that interval.

The last digit gives a quick elimination. 6344 rounds down to 6340, while a final 5 in 6355 makes it round up to 6360.

6305 rounds to 6310 and 6450 is already a multiple of ten, so neither rounds to 6350.

E

Split 46 into 40 and 6. Then 27 x 40 = 1080 and 27 x 6 = 162. Add them: 1080 + 162 = 1242.

The last digit must be 2 because 7 x 6 ends in 2. Roughly, 30 x 50 is 1500, so 1242 has a sensible magnitude while 162 and 12 420 do not.

1080 and 162 are the two partial products left uncombined. 1196 is 26 groups, one group short, and 12 420 adds an extra zero.

E

Ten per cent of 180 is 18, so 30% is 54. Five per cent is half of 10%, which is 9. Add them: 54 + 9 = 63.

For a magnitude check, 35% is between one third of 180, which is 60, and 40% of 180, which is 72. Only 63 fits.

54 is only 30%, 6.3 has the decimal point one place too far left, 35 copies the percentage as a number of people, and 630 multiplies by 35 without dividing by 100.

B

From 09:48 to 10:00 is 12 minutes. From 10:00 to 10:17 is 17 minutes. The wait is 12 + 17 = 29 minutes.

A time sanity check shows that the wait is a little less than half an hour, so 29 minutes is sensible and 69 minutes is not.

12 and 17 count only one side of 10:00. 31 takes the difference between 48 and 17 without following the clock, while 69 treats the clock readings as base ten numbers.

A

A cuboid has 6 rectangular faces, 8 vertices and 12 edges. Its opposite faces match, giving three pairs that may have three different sizes.

A cube has the same numbers of faces, vertices and edges, but all its faces are equal squares, so they cannot come in three sizes.

A triangular prism and a square-based pyramid each have 5 faces. A cylinder has a curved surface and no vertices, so neither matches the description.

C

First add the visitors: 3475 + 2968 = 6443. Then subtract from the capacity: 8000 - 6443 = 1557 unused places.

The last digit is a shortcut. The visitor total ends in 3, and 8000 minus a number ending in 3 ends in 7. Only 1557 does.

6443 is the number who attend. 4525 subtracts only the morning visitors, 5032 subtracts only the afternoon visitors, and 14 443 adds the attendance to the capacity.

D

Write 2 1/4 as 2 5/20 and 3/5 as 12/20. Exchange one whole: 2 5/20 becomes 1 25/20. Now subtract to get 1 13/20.

The answer must be between 1 1/2 and 2 because you are taking a little more than one half from 2 1/4. That magnitude check rules out 1 7/20 and 2 2/5.

1 7/20 converts to twentieths but takes 12 - 5 without exchanging the whole correctly. 1 17/20 adds the fractional parts while reducing the whole number. 2 2/5 subtracts numerator digits without making equal-sized parts, and 1 3/5 copies the fraction being subtracted after taking away one whole.

E

The greatest common factor of 18 and 30 is 6. Divide both parts by 6: 18 : 30 becomes 3 : 5.

6 : 10 and 9 : 15 have the correct value but are not in simplest form. The instruction in the question matters.

5 : 3 reverses silver and gold. 6 : 5 comes from dividing the two parts by different numbers, so it changes the ratio.

B

The four screenings have 4 x 160 = 640 seats. Tickets sold total 126 + 148 + 95 + 131 = 500. Empty seats total 640 - 500 = 140.

A rough magnitude check also works: most screenings are nearly full, so the empty total should be much less than 640 but more than any one screening's gap. That supports 140.

500 is the attendance and 640 is the capacity. 34 is the empty count for the first screening only, and 65 is the empty count for the third screening only.

A

On a number line, numbers farther left are colder. The order is -7, then -2, then 0, then 4.

A magnitude check with negative numbers helps: -7 is colder than -2 because it is farther below zero. Rows starting with -2, 0 or 4 cannot be coldest first.

The final wrong row places 0 before -2. Zero is warmer than every negative temperature, so -2 must come first.

C

A quarter turn from north to east is 90 degrees. South-east is another 45 degrees clockwise, so the total turn is 90 + 45 = 135 degrees.

45 degrees counts only the turn from east to south-east, and 90 degrees stops at east. 180 degrees reaches south.

225 degrees is the turn from north to south-east in the opposite, anticlockwise direction.

D

Use a nearby multiple: 24 x 40 = 960. That is 24 too many, so take away one group. Therefore 24 x 39 = 936, and each volunteer gets 39 leaflets.

A rough size check puts the answer just below 40. That immediately removes 234 and 22 464.

40 forgets to adjust from 960. 234 divides by 4 instead of 24, 22 464 multiplies instead of dividing, and 36 uses the rough calculation 900 divided by 25 as an exact answer.

E

Line up the decimal points: 0.480 + 1.700 + 0.035 = 2.215 seconds.

For a magnitude check, 0.48 + 1.7 is 2.18 and the last clip adds only 0.035, so the answer must be just above 2.18. That singles out 2.215.

2.18 omits the last clip, 1.735 omits the first, and 2.53 reads 0.035 as 0.35. 0.685 reads 1.7 as 0.17, moving its decimal point.

E

The width is 18 divided by 6 = 3 m. The perimeter is 6 + 3 + 6 + 3 = 18 m.

A unit sanity check removes 18 square metres because that is an area, not a perimeter. The answer to a perimeter question needs a length unit.

3 m is the width, 9 m adds just one length and one width, 108 m multiplies the given area by the length, and 18 square metres simply repeats the area.

B

The top row has 5 shaded squares and the left column has 4. Their corner square is in both counts, so subtract it once: 5 + 4 - 1 = 8 shaded squares.

The fraction is 8/20. Divide top and bottom by 4 to simplify it to 2/5.

9/20 counts the corner twice. 8/20 is the correct amount but is not in simplest form. 1/4 counts only the left column and 1/5 treats one whole row as one square out of five.

A

In one hour she paints 18 divided by 3 = 6 m. In five hours she paints 5 x 6 = 30 m.

A rough magnitude check is quick: five hours is more than three but less than twice three, so the distance must be more than 18 m but less than 36 m. Only 30 m fits.

6 m is one hour's work, 12 m is only the extra two hours, and 18 m is the original three hours. 90 m multiplies by 5 without first dividing by 3.

C

The minibuses bring 4 x 16 = 64 performers. The cars bring 3 x 5 = 15. Add them: 64 + 15 = 79 performers.

Parity gives a quick check: 64 is even and 15 is odd, so their total must be odd. That removes 64 and 320.

15 counts only the cars and 64 counts only the minibuses. 35 gives all seven vehicles the five-person car capacity, while 320 multiplies 4, 16 and 5 and ignores the three cars.

D

Ten per cent of 80 pounds is 8 pounds and 5% is 4 pounds. The reduction is 12 pounds, so the new price is 80 - 12 = 68 pounds.

A magnitude check helps: a 15% reduction leaves 85% of the price, so the answer must lie between 64 pounds, which is 80%, and 72 pounds, which is 90%. Only 68 pounds does.

12 pounds is the saving, 72 pounds takes off only 10%, and 65 pounds subtracts 15 pounds instead of 15%. 92 pounds adds the saving instead of subtracting it.

E

A rhombus has all four sides equal. A general parallelogram needs only its opposite sides to be equal, so this is the property that separates them.

Opposite sides are parallel and opposite angles are equal in both shapes, so those statements do not separate them.

A rhombus has two pairs of parallel sides, not one. Some rhombuses have four right angles, but many do not, so four right angles is not true of every rhombus.

B

A prime number has exactly two factors, 1 and itself. Test primes up to the square root of 43: it is not divisible by 2, 3, 5 or 7, so 43 is prime.

Parity and last digits eliminate quickly: 42 and 48 are even, and 45 ends in 5. Also, 49 = 7 x 7.

Each wrong option therefore has a factor other than 1 and itself, while 43 does not.

A

From 14:35 to 15:35 is 60 minutes, and from 15:35 to 16:05 is 30 minutes. The whole session is 90 minutes. Subtract the 20-minute break: 90 - 20 = 70 minutes.

A time magnitude check puts the active time between one hour and one and a half hours, so 70 minutes is sensible.

90 minutes includes the break, 50 minutes subtracts the break twice, and 110 minutes adds it. 170 comes from subtracting clock displays as if they were ordinary base ten numbers.

C

If one quarter represents 18 children, the whole circle represents 4 x 18 = 72 children.

18 is the documentary group only, and 4 is the number of equal quarters. 54 is the other three quarters, not the whole group.

90 treats the 18 children as one fifth of the group even though the sector is stated to be one quarter.

D

The racks use 18 x 32 guides. Work out 18 x 30 = 540 and 18 x 2 = 36, giving 576. Then 684 - 576 = 108 guides remain.

The last digit is a shortcut: 684 minus a number ending in 6 must end in 8. Only 108 does.

576 is the number displayed, 652 subtracts 32 guides rather than 32 groups, and 716 adds 32. 18 is the number on one rack.

E

Use twentieths: 3/5 = 12/20 and 1/4 = 5/20. Add them to get 17/20 full.

3/20 multiplies the two fractions instead of adding them. 4/9 adds the tops and bottoms, which does not make equal-sized parts.

7/20 subtracts the added water. 7/10 treats the quarter as a quarter of the empty space rather than a quarter of the whole tank.

D

There are 5 + 3 = 8 parts, so one part is 96 divided by 8 = 12 pounds. The difference between the shares is 5 - 3 = 2 parts, which is 2 x 12 = 24 pounds.

12 pounds is one part, 36 pounds is the smaller share and 60 pounds is the larger share. The question asks for the difference, not either share.

96 pounds is the whole amount and comes from stopping before it is shared.

B

Angles in a triangle total 180 degrees, so the other two total 180 - 60 = 120 degrees. Their ratio has 3 parts, so one part is 40 degrees and two parts is 80 degrees. The largest angle is 80 degrees.

40 degrees is the smaller angle and 60 degrees is the angle already given. 120 degrees is the combined total of the two unknown angles.

180 degrees is the total for the whole triangle, not the size of one angle.

A

Dividing by 100 makes every digit worth one hundredth as much. The 6 moves from tens to tenths and the 3 moves from units to hundredths, giving 0.63.

A magnitude check says division by 100 must give a number much smaller than 63. That removes 63 and 6300 immediately.

6.3 divides by 10, 0.063 divides by 1000, and 6300 multiplies by 100 instead of dividing.

C

Both products contain groups of 32. The difference between 19 groups and 9 groups is 10 groups, so the answer is 32 x 10 = 320.

The last digit and magnitude help: ten groups of 32 must end in 0 and be a little over 300. That points straight to 320.

10 is only the difference between 19 and 9, while 32 is one group. 288 is 32 x 9, the smaller product, and 896 is 32 x (19 + 9), which adds instead of finding the difference.

D

One tonne is 1000 kg, so 4.2 tonnes is 4.2 x 1000 = 4200 kg.

A unit sanity check is enough: kilograms are smaller units than tonnes, so the number of kilograms must be much larger than 4.2.

4.2 kg keeps the number but changes the unit, 42 kg multiplies by 10 and 420 kg multiplies by 100. 0.0042 kg divides by 1000 instead of multiplying.

E

The increase is 30 - 24 = 6 pounds. Compare the increase with the original price: 6/24 = 1/4, and one quarter is 25%.

A magnitude check helps because 6 pounds is one quarter of 24 pounds, not a tiny 6% change and not most of the price.

20% compares the 6-pound increase with the new price of 30 pounds. 6% copies the number of pounds, 75% is the fraction of the new price represented by the old price, and 125% is the new price as a percentage of the old price.

B

For the first coordinate, start at -4, move right 9 to 5, then left 2 to 3. For the second coordinate, start at -1 and move up 6 to 5. The robot finishes at (3, 5).

(7, 5) forgets the final move left. (3, -7) moves down instead of up, and (-15, 5) treats both horizontal moves as moves left.

(5, 3) has the correct two final numbers but writes them in the wrong order. Coordinates always give the horizontal position first.

A

The recorded total is 6 x 14 = 84. Replacing 12 by 18 adds 6, so the correct total is 90. Divide by 6 to get a mean of 15.

1 is how much the mean rises, not the new mean. 14 is the old mean, and 90 is the corrected total.

20 adds the whole correction of 6 directly to the mean instead of sharing it across the six scores.

C

Eight lots of 19 make 152, and 157 - 152 = 5. So there are 19 complete bags and 5 beads left.

The remainder must be smaller than 8, so 18 bags and 13 left cannot be a finished division. It could make another bag.

Twenty complete bags would need 160 beads. Three beads left comes from subtracting 152 incorrectly, while 20 bags and 5 left counts the incomplete twentieth bag as complete without using its beads.

D

In the red to blue ratio, 3 parts equal 12, so one part is 4 and there are 2 x 4 = 8 red tents. In the blue to green ratio, 4 parts equal 12, so one part is 3 and there are 5 x 3 = 15 green tents.

Add all three colours: 8 + 12 + 15 = 35 tents.

8 and 15 are single colour totals. 23 adds red and green but leaves out blue, while 27 adds blue and green but leaves out red.

E

Convert 80 cm to 0.8 m. A triangle's area is half of base x height, so 1.2 x 0.8 = 0.96 and half of 0.96 is 0.48 square metres.

A unit sanity check says a small flag cannot have an area of 48 or 96 square metres. Those answers mix centimetres and metres.

0.96 square metres is the area of the surrounding rectangle and forgets to halve. 0.048 square metres divides by 10 once too many during the conversion.

D

Each hexagon has perimeter 6 x 5 = 30 m, so separately they total 60 m. The joined side was counted once for each hexagon, but neither copy is on the outside. Subtract 2 x 5 = 10 m to get 50 m.

30 m is the perimeter of one hexagon. 60 m leaves both joined edges on the outside, while 55 m subtracts the shared side only once.

10 m is just the total length removed from the two separate perimeters.

B

The lowest common denominator is 24. Convert 7/8 to 21/24 and 5/12 to 10/24. Then 21/24 - 10/24 = 11/24, which cannot be simplified.

2/24 changes the denominator but subtracts the original numerators. 1/4 treats 5/12 as if it were 5/8 before subtracting.

1/2 uses a rough estimate as an exact answer. 31/24 adds 21/24 and 10/24 instead of subtracting them.

A

Multiplying by 1000 makes every digit worth one thousand times as much. The 4 moves from tenths to hundreds, the 0 to tens and the 7 to units, giving 407.

0.00407 divides by 100, 0.407 leaves the number unchanged, 4.07 multiplies by 10 and 40.7 multiplies by 100.

Writing place-value columns before moving the digits prevents a zero in the middle from being lost.

C

In the units, 7 + 6 = 13, so write 3 and carry 1 ten. In the tens, the missing digit + 8 + 1 must end in 3. That total is 13, so the missing digit is 4. The hundreds then check: 4 + 2 + 1 = 7.

5 is the tempting answer if you forget the carried ten, because 5 + 8 ends in 3. 6 subtracts the carried ten in the wrong direction.

3 copies the tens digit of the answer, and 2 copies the hundreds digit of 286 instead of completing the column addition.

C

If 30% is used, 70% remains. Since 70% is 84 m, 10% is 84 divided by 7 = 12 m. Therefore 100% is 10 x 12 = 120 m.

A magnitude check says the original must be more than 84 m, but because 84 m is well over half, the original should be less than 168 m. Only 120 m fits.

25.2 m is 30% of 84 and 58.8 m is 70% of 84, both treating the remainder as the whole. 84 m ignores the used part, while 280 m wrongly treats 84 m as the 30% used.

A

The stage area is 9 x 6 = 54 square metres. Each mat covers 1 square metre, so 54 mats are needed.

15 adds the length and width instead of finding area. 30 is the perimeter, 2 x (9 + 6), rather than the area.

108 doubles the area by counting two mats per square metre, and 486 multiplies the area by the 9 m length again.

B

The six larger carriages have 6 x 72 = 432 seats. The other three have 3 x 64 = 192 seats. Total capacity is 432 + 192 = 624. Subtract the 37 empty seats: 624 - 37 = 587 passengers.

Parity is a quick check: the capacity is even and 37 is odd, so the passenger total must be odd. That rules out 624, 192 and 432 before the final subtraction.

192 and 432 are partial capacities, 624 is the full capacity, and 661 adds the empty seats instead of subtracting them.