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IGCSE Mathematics Paper 2 (Extended) — non-calculator

Unit Assessment Mock 1 -- Sets, Percentages, Time, Money -- 40 marks in 45 minutes
45 minutes
40
4
45:00
0580

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Question 1 — Sets
Total: 10 marks
Information for the whole question
A chess club has 40 members, so n(ξ) = 40. Set A is the members who play online. Set B is the members who play in tournaments. The Venn diagram shows the number of members in three of the four regions. The fourth region has deliberately been left blank.
ξ A B 15 6 8
(a)(i) [2]
Find n(A′).
Model Answer — (a)(i)
M1 n(A) = 15 + 6 = 21, so n(A′) = 40 − 21
(equivalently: the blank region holds 40 − (15 + 6 + 8) = 11 members, and n(A′) = 8 + 11)
A1 n(A′) = 19
⚠ If you missed marks here: A′ is everything that is not inside circle A — that includes the region outside both circles, not just the part of B. You cannot read this one off the diagram; you have to work the regions.
(a)(ii) [2]
Find n((A ∪ B)′).
Model Answer — (a)(ii)
M1 n(A ∪ B) = 15 + 6 + 8 = 29
A1 n((A ∪ B)′) = 40 − 29 = 11
⚠ If you missed marks here: answering 40 means you gave n(ξ), the whole club. (A ∪ B)′ is the blank region only: the members in neither circle. Add up the three numbers shown, then subtract from 40.
(a)(iii) [1]
Find n(A ∩ B′).
Model Answer — (a)(iii)
B1 n(A ∩ B′) = 15
A ∩ B′ is "in A but not in B" — the left-hand crescent on its own.
⚠ If you missed marks here: giving 6 means you read the overlap. The dash on B′ flips B, so this is the part of A that the overlap is not in.
Information for the whole question
30 students were asked whether they take music (M) or sport (S) as an option. Some take neither. In the Venn diagram below, each of the four regions is labelled with how many students it contains. The letter x stands for a whole number.
ξ M S x + 3 x 2x − 1 4
(b)(i) [3]
Use n(ξ) = 30 to form an equation in x, and solve it.
Model Answer — (b)(i)
M1 adds all four regions: (x + 3) + x + (2x − 1) + 4
M1 4x + 6 = 30, so 4x = 24
A1 x = 6
Check: the regions are 9, 6, 11 and 4, and 9 + 6 + 11 + 4 = 30 ✓
⚠ If you missed marks here: the commonest slip is leaving the 4 out. Every member of ξ sits in exactly one of the four regions, including the one outside both circles, so all four go into the sum.
(b)(ii) [2]
Find n(S′).
Model Answer — (b)(ii)
M1 n(S) = x + (2x − 1) = 6 + 11 = 17
A1 n(S′) = 30 − 17 = 13
Check by regions: not in S means 9 (music only) + 4 (neither) = 13 ✓
⚠ If you missed marks here: writing 4 is reading the outside number straight off the diagram. S′ is everyone not in circle S — that is the music-only students as well as the 4 who take neither.
Question 2 — Percentages
Total: 10 marks
(a) [3]
A van is bought new. During its first year its value falls by 15%. At the end of that year the van is worth $10 200. Calculate the value of the van when it was new.
Model Answer — (a)
M1 the van is now worth 100% − 15% = 85% of its value when new, so 0.85 × (value when new) = 10 200
M1 10 200 ÷ 0.85, or 10 200 ÷ 85 × 100
A1 $12 000
Check forwards: 15% of 12 000 = 1800, and 12 000 − 1800 = 10 200 ✓
⚠ If you missed marks here: adding 15% of 10 200 gives 11 730, which is wrong. The 15% was taken off the original value, not off 10 200. A reverse percentage is always a division — and always check it by going forwards again.
(b) [3]
The number of passengers using a ferry fell from 480 one week to 372 the next week. Calculate the percentage decrease.
Model Answer — (b)
M1 480 − 372 = 108
M1 108 ÷ 480 × 100
A1 22.5%
By hand: 108 ÷ 480 = 27 ÷ 120 = 9 ÷ 40 = 0.225
⚠ If you missed marks here: dividing by 372 gives 29.0% and is the single most common error in the whole topic. Percentage change is always change ÷ ORIGINAL — the number you started from.
Information for the whole question
The population of a village is 3000. The population increases by 10% each year.
(c)(i) [2]
Find the population after 3 years.
Model Answer — (c)(i)
M1 3000 × 1.13, or year by year: 3300, then 3630
A1 3993
Year by year, 10% is easy by hand: 3000 → 3300 → 3630 → 3993
⚠ If you missed marks here: adding 10% of 3000 three times gives 3900 and is wrong. Each year the 10% is taken of the new population, so the increase itself grows. That is what compound means.
(c)(ii) [2]
Find the percentage increase in the population over the 3 years.
Model Answer — (c)(ii)
M1 3993 − 3000 = 993, then 993 ÷ 3000 × 100
A1 33.1%
Or read it straight from the multiplier: 1.13 = 1.331, which is a 33.1% increase.
⚠ If you missed marks here: answering 30% treats three years of 10% as 3 × 10%. It is not: 1.13 = 1.331, so the true increase is 33.1%. Percentages of different amounts can never simply be added.
Question 3 — Time
Total: 10 marks
(a)(i) [2]
A film starts at 14:50 and ends at 17:15. Find the length of the film in hours and minutes.
Model Answer — (a)(i)
M1 count on: 14:50 → 15:00 is 10 minutes, and 15:00 → 17:15 is 2 hours 15 minutes
A1 2 hours 25 minutes
Check: 14:50 + 2 h = 16:50, and 16:50 + 25 min = 17:15 ✓
⚠ If you missed marks here: if you got 3 hours 35 minutes you subtracted the columns as if a clock were base 10 — you did 17 − 14 and then tried 15 − 50. A clock has 60 minutes in an hour, not 100. Count up to the next o’clock first, then count the whole hours, then the minutes left.
(a)(ii) [3]
The cinema shows the film three times, one after another, with a gap of 20 minutes between the end of one showing and the start of the next. The first showing starts at 14:50. Find the time at which the third showing starts.
Model Answer — (a)(ii)
M1 one showing plus one gap = 2 h 25 min + 20 min = 2 hours 45 minutes
M1 two of these are needed to get from the first start to the third start: 2 × 2 h 45 min = 5 hours 30 minutes
A1 20:20
Check step by step: showing 1 ends 17:15, showing 2 starts 17:35 and ends 20:00, showing 3 starts 20:20 ✓
⚠ If you missed marks here: the usual slip is adding three gaps instead of two. Between the first start and the third start there are only two complete cycles. Draw the timeline if you are unsure — it costs ten seconds.
Information for the whole question
Ravi travels from Hillside to Northport. He takes a bus from Hillside to Marketgate, then a train from Marketgate to Northport. Part of the timetable is shown. All times are on the same morning.
Bus — Hillside (depart)07:3508:0508:55
Bus — Marketgate (arrive)08:1208:4209:32
Train — Marketgate (depart)08:2009:0509:50
Train — Northport (arrive)09:0409:4910:34
(b)(i) [3]
Ravi must arrive at Northport no later than 09:50. He wants to leave Hillside as late as possible. Write down the time of the bus he takes from Hillside, and find how long he waits at Marketgate.
Model Answer — (b)(i)
B1 the last train that arrives by 09:50 is the one arriving at 09:49, which leaves Marketgate at 09:05
M1 the latest bus that reaches Marketgate before 09:05 is the one arriving at 08:42
A1 bus at 08:05, and a wait of 23 minutes
The wait: 08:42 → 09:00 is 18 minutes, and 09:00 → 09:05 is 5 more, so 23 minutes.
⚠ If you missed marks here: the 08:55 bus is later, but it reaches Marketgate at 09:32 — after the 09:05 train has gone — so it only connects with the 09:50 train and lands at 10:34, far too late. Always work backwards from the deadline: fix the train first, and only then choose the bus. And read straight down one column.
(b)(ii) [2]
Find his total journey time from Hillside to Northport.
Model Answer — (b)(ii)
M1 08:05 to 09:49
A1 1 hour 44 minutes
Count on: 08:05 → 09:05 is 1 hour, and 09:05 → 09:49 is 44 minutes.
⚠ If you missed marks here: the journey time runs from when he leaves to when he arrives — the 23-minute wait is part of it, so do not subtract it. Adding the bus ride and the train ride only (37 + 44 = 81 minutes) leaves the wait out.
Question 4 — Money and finance
Total: 10 marks
(a) [4]
A shop sells rice in three sizes.

    Small: 400 g for £1.20
    Medium: 1.5 kg for £4.50, with the offer buy two, get a third free
    Large: 2.5 kg for £6.50

Work out which size gives the best value for money. You must show your working.
Model Answer — (a)
M1 a correct cost per kilogram for any one size
M1 uses the offer: three medium bags are 4.5 kg for £9.00
A1 Small £3.00/kg, Medium £2.00/kg, Large £2.60/kg
A1 Medium is the best value
By hand: 400 g for £1.20 is £1.20 × 2.5 = £3.00 per kg; £9.00 ÷ 4.5 = £2.00; £6.50 ÷ 2.5 = £2.60.
⚠ If you missed marks here: ignoring the offer makes Medium £4.50 ÷ 1.5 = £3.00 per kg, the same as Small, and Large then looks best. The offer is the whole question. Also, never compare the prices themselves — £1.20 is the cheapest price and the worst value. Reduce everything to one common amount first.
(b) [4]
Nina buys 25 lamps at £14 each. The delivery charge for the whole order is £50. She sells all 25 lamps at £20 each. Calculate her percentage profit.
Model Answer — (b)
M1 total cost = 25 × 14 + 50 = 350 + 50 = £400
M1 total income = 25 × 20 = £500, so the profit is £100
M1 100 ÷ 400 × 100
A1 25%
Check: 25% of £400 is £100 ✓
⚠ If you missed marks here: leaving the £50 delivery out gives 150 ÷ 350 × 100 = 42.9%. Delivery is money Nina paid out, so it is part of the cost. Percentage profit is always profit ÷ total cost, never profit ÷ selling price.
(c) [2]
Nina places another order of 25 lamps. Her total cost is again £400. She wants to make a percentage profit of 40% on her total cost. Calculate the price she must charge for each lamp.
Model Answer — (c)
M1 total income needed = 400 × 1.40 = £560
A1 £22.40
Check: 25 × £22.40 = £560, and £560 − £400 = £160, which is 40% of £400 ✓
⚠ If you missed marks here: the profit is 40% of the total cost, not 40% on each lamp’s own £14 price. Work out the total income first, then divide by 25 at the very end.

Self-Assessment

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IGCSE Mathematics 0580 — Paper 2 (Extended) — non-calculator — Unit Assessment Mock 1 — Sets, Percentages, Time, Money — 40 marks in 45 minutes
For examination preparation only. Not an official Cambridge Assessment paper.