IGCSE Mathematics Paper 2 (Extended) — non-calculator
Unit Assessment Mock 3 -- Sets, Percentages, Time, Money -- 40 marks in 45 minutes
45 minutes
40
4
45:00
0580
Instructions
Answer all questions in the spaces provided.
Show all working for calculations.
Give non-exact answers to 3 significant figures unless the question says otherwise.
Your answers will be automatically graded when you submit.
Question Navigation
Question 1 — Sets
Total: 10 marks
Information for parts (a)(i) to (a)(iii)
A year group has 64 students, so n(ξ) = 64. Set D is the students who study Drama and set E is the students who study Economics.
n(D) = 37 n(E) = 29 n(D ∩ E) = 14
The Venn diagram shows only the number in the overlap. The other three regions are deliberately blank — work each one out from the numbers above.
(a)(i)[2]
Find n(D ∩ E′).
Model Answer — (a)(i)
M1D ∩ E′ is the part of D that is outside E, so 37 − 14
A1 n(D ∩ E′) = 23
Check: 23 + 14 = 37 = n(D) ✓
⚠ If you missed marks here: if you wrote 14 you copied the only number on the diagram. 14 is the overlap, not D on its own. n(D) is the whole circle, so the part outside E is what is left after the overlap is taken away. Fill the region in on the diagram before you answer anything.
(a)(ii)[1]
Find n(D′).
Model Answer — (a)(ii)
B1 n(D′) = 64 − 37 = 27
The same answer the long way: Economics only (15) + neither (12) = 27 ✓
⚠ If you missed marks here:D′ means everything not inside circle D. That is the Economics-only region and the region outside both circles. Answering 15 means you stopped at the part of E and forgot the students who study neither.
(a)(iii)[2]
Find n((D ∪ E)′).
Model Answer — (a)(iii)
M1 n(D ∪ E) = 37 + 29 − 14 = 52, so the answer is 64 − 52
(equivalently: 23 + 14 + 15 = 52 inside the circles, and 64 − 52 is outside)
A1 n((D ∪ E)′) = 12
⚠ If you missed marks here: answering 64 is the commonest mistake of all — 64 is n(ξ), everybody. (D ∪ E)′ is only the students in neither circle. And adding 37 + 29 gives 66, which is more than the whole year group, because the 14 in the overlap has been counted twice. Take the overlap off once.
Information for parts (b)(i) to (b)(iii)
The Venn diagram below shows three sets A, B and C inside the universal set ξ. The eight regions are labelled I to VIII. No numbers are given — answer each part with the region label or labels only.
(b)(i)[1]
Write down the region that is A ∩ B ∩ C′.
Model Answer — (b)(i)
B1IV
In A and in B, but outside C.
⚠ If you missed marks here: if you chose VII you ignored the dash on C′. VII is inside all three circles, so it is A ∩ B ∩ C. Read a set expression one symbol at a time: in A, and in B, and not in C.
(b)(ii)[2]
Write down the two regions that together make up (A ∪ B)′.
Model Answer — (b)(ii)
M1A ∪ B is regions I, II, IV, V, VI and VII, so the complement is everything else
A1III and VIII
III is inside C only; VIII is inside none of the three.
⚠ If you missed marks here: giving VIII alone is the usual slip — it treats "outside A and B" as "outside everything". Region III is outside A and outside B too; it just happens to sit inside C, which the expression says nothing about.
(b)(iii)[2]
Write down the regions that contain the elements belonging to exactly two of the three sets.
Model Answer — (b)(iii)
M1 take each overlap of two circles, but not the middle where all three meet
A1IV, V and VI
⚠ If you missed marks here: including VII is the standard error. VII belongs to three sets, not two, so "exactly two" rules it out. The word exactly always means "and no more than that".
Question 2 — Percentages
Total: 10 marks
(a)[3]
A laptop is advertised at $240 before tax. Sales tax of 17.5% is added to this price.
Calculate the amount a customer pays for the laptop. You must show your working.
Model Answer — (a)
M1 split 17.5% into 10% + 5% + 2.5%: 10% of 240 = 24, 5% of 240 = 12, 2.5% of 240 = 6
M1 tax = 24 + 12 + 6 = $42
A1 total paid = 240 + 42 = 282, so $282
Check the other way: 240 × 1.175 = 240 + 42 = 282 ✓
⚠ If you missed marks here: answering $42 gives the tax, not the price paid — read the last line of the question again. On a non-calculator paper never reach for long multiplication by 17.5: find 10%, halve it for 5%, halve that for 2.5%, then add. Three easy halvings beat one hard sum.
(b)[3]
A train journey is scheduled to take 2 hours 30 minutes. One morning the train arrives 18 minutes late.
Calculate the delay as a percentage of the scheduled journey time.
Model Answer — (b)
M1 put both times into the same unit: 2 hours 30 minutes = 150 minutes
⚠ If you missed marks here: dividing by 2.30 — or by 2.5 — is the trap. A time written 2 h 30 min is not the number 2.30; a clock runs in sixties. Turn both quantities into minutes first and the percentage is then an ordinary fraction. Dividing by 168 (the late arrival time) is the other slip: the percentage is always measured against the original, which here is the scheduled 150 minutes.
Information for parts (c)(i) and (c)(ii)
In a town, 60% of the residents own a bicycle. Of the residents who own a bicycle, 35% use it every day.
(c)(i)[2]
Calculate the percentage of all the residents of the town who use a bicycle every day.
Model Answer — (c)(i)
M1 35% of 60%, i.e. 0.35 × 0.6 (or 35% of 60 = 21)
A121, so 21%
Sense check with 100 people: 60 own a bicycle, and 35% of 60 = 21 of them ride daily ✓
⚠ If you missed marks here: 35% is a percentage of the cyclists, not of the town, so you cannot simply write 35%, and you certainly cannot add 60 and 35. Percentages only combine by multiplying their decimal multipliers. Imagining 100 residents turns the whole thing into counting.
(c)(ii)[2]
2100 residents use a bicycle every day.
Calculate the total number of residents of the town.
Model Answer — (c)(ii)
M1 21% of the town is 2100, so 1% is 2100 ÷ 21 = 100
A1 100 × 100 = 10000 residents
Check forwards: 21% of 10 000 = 2100 ✓
⚠ If you missed marks here: this is a reverse percentage, so you divide. Working out 21% of 2100 goes the wrong way and gives a number smaller than the one you started with, which cannot be a town. Always finish a reverse percentage by going forwards again to check.
Question 3 — Time
Total: 10 marks
Information for parts (a)(i) and (a)(ii)
A school coach leaves school at 08:47 and reaches the museum at 11:12 on the same morning.
(a)(i)[2]
Find the length of the journey, in hours and minutes.
Model Answer — (a)(i)
M1 count up in stages: 08:47 → 09:00 is 13 minutes, 09:00 → 11:00 is 2 hours, 11:00 → 11:12 is 12 minutes
A1 13 + 12 = 25 minutes, so 2 hours 25 minutes
Check: 08:47 + 2 h = 10:47, and 10:47 + 25 min = 11:12 ✓
⚠ If you missed marks here: 3 hours 35 minutes, or 2 hours 65 minutes, both come from subtracting the columns as though a clock were base 10 — 11 − 8, then 12 − 47. There are 60 minutes in an hour, not 100, so column subtraction does not work on times. Count up to the next o’clock, then whole hours, then the minutes left over. It is slower to write and far faster to get right.
(a)(ii)[2]
The return journey takes 15 minutes longer than the outward journey. The coach leaves the museum at 15:50.
Find the time at which the coach arrives back at school.
Model Answer — (a)(ii)
M1 return journey = 2 h 25 min + 15 min = 2 hours 40 minutes
A1 15:50 + 2 h = 17:50, then + 40 min = 18:30
Check backwards: 18:30 − 2 h 40 min = 15:50 ✓
⚠ If you missed marks here: 17:90 is not a time. When the minutes pass 60, carry one hour: 50 + 40 = 90 minutes = 1 hour 30 minutes. Add the hours first and the minutes second and the carry is much harder to miss.
Information for parts (b)(i) and (b)(ii)
Ferries run from Harbour Point to Seal Island, calling at Gull Rock. Part of the timetable is shown. All times are on the same day.
Ferry A
Ferry B
Ferry C
Ferry D
Harbour Point (depart)
07:35
09:10
10:55
12:40
Gull Rock (arrive)
08:20
09:55
11:40
13:25
Gull Rock (depart)
08:35
10:10
11:55
13:40
Seal Island (arrive)
09:25
11:00
12:45
14:30
(b)(i)[2]
Mina must be at Seal Island by 12:30. She wants to leave Harbour Point as late as possible.
Write down the time at which she leaves Harbour Point.
Model Answer — (b)(i)
M1 start on the Seal Island row: Ferry C arrives 12:45, which is after 12:30, so C and D are both too late; the latest that works is Ferry B, arriving 11:00
A1 she leaves Harbour Point at 09:10
⚠ If you missed marks here: 10:55 means you chose Ferry C, which arrives at 12:45 — fifteen minutes too late. 11:00 means you read the right ferry but wrote down a time from the wrong row. Work the same way every time: find the row the condition is about (Seal Island arrive), pick the column, then read straight up that column to the row the question asks for.
(b)(ii)[2]
Find the total time Mina spends travelling on Ferry B, from Harbour Point to Seal Island, including the stop at Gull Rock.
Model Answer — (b)(ii)
M1 use only the Ferry B column: leaves 09:10, arrives Seal Island 11:00
A1 09:10 → 11:00 is 1 hour 50 minutes
Check by parts: 45 min sailing + 15 min stop + 50 min sailing = 110 minutes = 1 h 50 min ✓
⚠ If you missed marks here: 1 hour 35 minutes means you left the stop at Gull Rock out; the question says including it, and the simplest way to include it is to ignore the middle rows altogether and use the first and last times in the column. Slipping into the Ferry A or Ferry C column is the other common loss — put a finger on the column before you start.
(c)[2]
Tomas says that a journey lasting 2 hours 45 minutes can be written as "2.45 hours".
Explain why Tomas is wrong, and write 2 hours 45 minutes correctly as a number of hours.
Model Answer — (c)
B1 a decimal part of an hour is a fraction of 60 minutes, not of 100, so 45 minutes is 45/60 of an hour, and 0.45 of an hour would be only 27 minutes
B1 45 ÷ 60 = 0.75, so the journey is 2.75 hours
Check backwards: 0.75 × 60 = 45 minutes ✓
⚠ If you missed marks here: this is the same base-60 mistake as reading 11:12 − 08:47 down the columns, and it is the one that quietly ruins speed questions — dividing a distance by 2.45 instead of 2.75 is wrong by about 12%. To turn minutes into a decimal, divide by 60; to turn a decimal back into minutes, multiply by 60.
Question 4 — Money and finance
Total: 10 marks
(a)[4]
Leena is paid £8.40 for each of the first 35 hours she works in a week. Any hours after the first 35 are overtime, paid at time and a half.
One week Leena works 41 hours. Calculate her total pay for that week.
⚠ If you missed marks here: £344.40 comes from paying all 41 hours at the basic rate and forgetting the overtime uplift altogether; £516.60 comes from paying all 41 hours at time and a half. Only the hours beyond 35 are overtime, so split the week into two blocks and price each one separately.
Information for parts (b)(i) and (b)(ii)
An electricity company charges a standing charge of £14 each month, plus 18p for every unit of electricity used.
(b)(i)[2]
In March, Sam used 260 units. Calculate his bill for March.
Model Answer — (b)(i)
M1 cost of the units = 260 × 0.18 = £46.80 (18 × 26 = 468, so 260 units cost 4680p)
A1 bill = 14 + 46.80 = 60.80, so £60.80
⚠ If you missed marks here: an answer of £4694 means pence and pounds were mixed in one sum. Convert 18p to £0.18 the moment you start, or work entirely in pence and convert once at the end — never halfway through.
(b)(ii)[2]
In April, Sam’s bill was £59.00. Calculate the number of units he used in April.
Model Answer — (b)(ii)
M1 take the standing charge off first: 59.00 − 14 = £45 spent on units, then divide by 0.18
⚠ If you missed marks here: dividing £59 by 0.18 gives about 328 units and quietly charges Sam for the standing charge as though it were electricity. Undo the steps in reverse order: the standing charge was added last, so it comes off first.
(c)[2]
A shop sells shirts at £30 each and offers two deals.
Deal 1: buy two shirts and take 20% off the total. Deal 2: buy one shirt at the full price and get a second shirt at half price.
Kiran buys two shirts. Work out which deal is cheaper, and by how much.
⚠ If you missed marks here: "half price on the second shirt" sounds like 50% off, but it is 50% off one of the two shirts, which is 25% off the pair — and 25% beats 20%. Price the whole basket under each deal and compare the two totals; never compare the percentages themselves, because they are percentages of different things.
Self-Assessment
Tick marks earned, then click Calculate Grade.
0
40
0%
A* : 70%+
A : 60-69%
B : 50-59%
C : 40-49%
D : 30-39%
E : 20-29%
U : <20%
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