Mathematics 0580/32 May/June 2021: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), May/June 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
Alex is building a house.
The materials cost 1 12 times the cost of the land.
The wages cost 1 14 times the cost of the land.
(a) Show that the ratio of costs, in its simplest form, is land : materials : wages = 4 : 6 : 5.
[2]
(b) The wages cost $47 500.
Show that the total cost of land, materials and wages is $142 500.
[2]
(c) Work out the cost of
(i) the land,
$ …… [2]
(ii) the materials.
$ …… [1]
(d) Alex borrows $28 000 for 6 years at a rate of 5.5% per year compound interest.
Calculate the amount he repays at the end of the 6 years.
Give your answer correct to the nearest dollar.
$ …… [3]
(e) When Alex sells the house, he makes a profit of 27% on the $142 500.
Calculate the selling price of the house.
$ …… [2]
Mark scheme
1(a) 1 1 B1
1 : 1.5 : 1.25 or 1 : 1 :1
2 4
Working shown leading to 4 : 6 : 5 M1
1(b) 47 500 ÷ 5 × (4 + 6 + 5) M2 M1 for 47 500 ÷ 5
1(c)(i) 38 000 2 M1 for 142 500 ÷ 15 [× 4] or
47 500 ÷ 5 [× 4] oe soi
1(c)(ii) 57 000 1 FT for 95 000 – their (c)(i)
1(d) 38 608 cao 3
6
5.5
M1 for 28 000 × 1 + oe
100
A1 for 38 607.5… or 38 607.6 or 38 607 or
38 610 or 38 600
B1 for their correctly rounded answer
1(e) 180 975 2 27
M1 for 142 500 × 1 + oe
100
or B1 for 38 475
The diagram shows four polygons on a 1 cm 2 grid.
y
11
10
9
A
8
7
6
5
4
C
3
2
1
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 x
–1
–2
–3
–4
B
–5
–6
–7
–8
–9
(a) Write down the mathematical name of the shaded polygon.
…… [1]
(b) Find the area of the shaded polygon.
…… cm 2 [2]
(c) Describe fully the single transformation that maps
(i) the shaded polygon onto polygon A,
…… [2]
(ii) the shaded polygon onto polygon B,
…… [3]
(iii) the shaded polygon onto polygon C.
…… [3]
(d) On the grid, draw the image of the shaded polygon after a reflection in the line y = 0 . [2]
Mark scheme
2(a) Pentagon 1
2(b) 12 2 B1 for 10 to 14
2(c)(i) Translation 2 B1 for each
7
4
2(c)(ii) Rotation 3 B1 for each
[centre] (0, 0) oe
180°
2(c)(iii) Enlargement 3 B1 for each
[centre] (4, 2)
[scale factor] 0.5 oe
2(d) Correct reflection 2 B1 for a correct reflection in x = 0 or in
(−2, −2), (−1, −4), (−2, −6), (−4, −6) y = k k ≠ 0 or for 4 correct points
(−6, −4)
Pierre travels from his home in Lyon to Singapore.
(a) He travels by train from Lyon to Paris.
The train leaves Lyon at 9.05 am and arrives in Paris at 1.30 pm.
(i) Write 1.30 pm in the 24-hour clock system.
…… [1]
(ii) Work out, in hours and minutes, the time the train journey takes.
…… h …… min [1]
(b) He then travels by plane from Paris to Singapore.
The plane leaves Paris at 16 35 on Thursday and arrives in Singapore 13 hours and 45 minutes later.
The local time in Singapore is 6 hours ahead of the local time in Paris.
Work out the day and time in Singapore when the plane arrives.
Day …… Time …… [3]
(c) The distance from Paris to Singapore is 10 736 kilometres.
Work out the average speed of the plane.
…… km/h [2]
(d) Pierre buys a watch for 400 Singapore dollars.
The exchange rate is 1 Singapore dollar = 0.658 euros.
Work out the cost of the watch in euros.
…… euros [1]
(e) Pierre stays at a hotel in Singapore for 5 nights.
The cost per night of the room is $170.
His total hotel bill is $975.40 .
Calculate how much Pierre spends on other hotel items.
$ …… [2]
7
Mark scheme
3(a)(i) 13 30 1
3(a)(ii) 4 [h] 25 [min] 1
3(b) Friday 3 B1 for Friday, as final answer
12 20 B2 for 12 20, as final answer
or B1 for [0]6 20 or 22 35 or 19h 45 min or
12 20 seen then spoilt
or M1 for
their arrival time of flight + 6 hours
3(c) 780.8 2 M1 for 10 736 ÷ time of flight
3(d) 263.2[0] cao 1
3(e) 125.4[0] cao 2 M1 for 975.4 – 5 × 170 or better
(a) Put a ring around the fraction that is equivalent to .
12
35 20 49 82 64
62 36 84 144 110
[1]
(b) Write these numbers in order, starting with the smallest.
7 8 2
0.6 58%
12 13 3
…… 1 …… 1 …… 1 …… 1 …… [2]
smallest
(c) Write 0.724 as a fraction in its simplest form.
…… [1]
(d) The mass, m grams, of a ball is 415 g, correct to the nearest 5 grams.
Complete the statement about the value of m.
…… G m 1 …… [2]
(e) Ruth uses three-quarters of a bag of flour to make one cake.
Work out the number of bags of flour she needs to buy to make 7 cakes.
…… [3]
(f) A tin of soup costs $t and a packet of biscuits costs $p.
(i) 3 tins of soup and 2 packets of biscuits cost $15.50 .
Complete the equation.
3t + 2p = …… [1]
(ii) 5 tins of soup and 4 packets of biscuits cost $28.50 .
Write down another equation in terms of t and p.
…… [1]
(iii) Solve the two simultaneous equations.
You must show all your working.
t = ……
p = …… [3]
18
Mark scheme
4(a) 49 1
84
4(b) 7 8 2 2 B1 for 4 in correct order
58% 0.6 or M1 for 0.583[...], [0.6], 0.58, 0.615[…]
12 13 3
or 0.61 or 0.62, 0.66[...] or 0.67 or 0.667
or 0.7 oe
4(c) 181 1
cao
250
4(d) 412.5 417.5 2 B1 for each
If 0 scored, SC1 for both correct but
reversed
4(e) 6 3 3
M1 for 7 × oe
4
1
A1 for 5.25 or 5
4
4(f)(i) 15.5[0] 1
4(f)(ii) 5t + 4p = 28.5[0] 1
4(f)(iii) For correct method to eliminate one M1 FT their two linear equations
variable
[t =] 2.5 A1
[p =] 4 A1 If 0 scored, SC1 for 2 values satisfying
one of the correct equations or their (f)(i)
or (f)(ii)
or SC1 if no working shown, but 2 correct
answers
(a) Complete the table of values for y = . x x -8 -6 -4 -3 -2 2 3 4 6 8
y -3 -6 6 3
[3]
18
(b) On the grid, draw the graph of y = for -8 G x G -2 and 2 G x G 8 . x y
10
8
6
4
2
0 x
–8 –6 –4 –2 2 4 6 8
–2
–4
–6
–8
– 10
[4]
(c) Write down the order of rotational symmetry of the graph.
…… [1]
(d) (i) On the grid, plot and join the points (-8, -3) and (6, 4). [2]
18
(ii) Write down the values of x where this line intersects the graph of y = . x
x = …… and x = …… [2]
(iii) Find the equation of this line in the form y = mx + c .
y = …… [2]
Mark scheme
5(a) −2.25 −4.5 −9 9 4.5 2.25 3 B2 for 4 or 5 correct
or B1 for 2 or 3 correct
5(b) Correct curve 4 B3FT for 9 or 10 points correctly plotted
or B2FT for 7 or 8 points correctly plotted
or B1FT for 5 or 6 points correctly plotted
5(c) 2 1
5(d)(i) (−8, −3) and (6, 4) plotted and joined in a 2 B1 for one point correctly plotted or both
ruled line correctly plotted but not joined, or ruled
5(d)(ii) −7.3 to −6.9 and 4.9 to 5.3 2 B1FT for each
5(d)(iii) 1 2 1
[y =] x + 1 oe final answer B1 for x + c (c ≠ +1) or
2 2
1
kx + 1 k ≠ 0 or
2
or B1FT for (their m)x + c
or kx + their intercept (k ≠ 0)
(a) The scale drawing shows the positions of house A and house B.
The scale is 1 centimetre represents 12 metres.
North
B
North
A
Scale: 1 cm to 12 m
(i) Work out the actual distance, in metres, from house A to house B.
…… m [2]
(ii) Measure the bearing of house A from house B.
…… [1]
(iii) Another house, C, is 102 metres from house B on a bearing of 157°.
On the scale drawing, mark the position of house C.
[3]
(b)
P 98 m Q
NOT TO
SCALE
67 m
R
S
The diagram shows a field PQRS.
PQ = 98 m, QR = 67 m and angle PQR = 90°.
There is a straight path from P to R.
Calculate the length of this path.
…… m [2]
Mark scheme
6(a)(i) 87.6 2 B1 for 7.1 to 7.5
6(a)(ii) 247 1
6(a)(iii) Point C correctly plotted 3 B2 for line from B 8.3 cm to 8.7 cm long
or M1 for 102 ÷ 12
and
B1 for bearing 155° to 159°
6(b) 119 or 118.7... 2 M1 for 982 + 672 or better
(a) The favourite sport of each of 135 boys is recorded in the table.
Favourite sport Frequency Pie chart sector angle
Soccer 54 144°
Hockey 45
Rugby 27
Other 9
(i) Complete the table.
[2]
(ii) Complete the pie chart to show these results.
The sector for soccer has been drawn for you.
Soccer
[2]
(iii) One of these boys is picked at random.
Find the probability that soccer is his favourite sport.
…… [1]
(b) 135 girls are asked if they like soccer (S) and if they like hockey (H).
n (S) = 53, n (H) = 68 and n (S , H) = 110 .
(i) Complete the Venn diagram.
S H
[3]
(ii) Write down n (S + H) .
…… [1]
Mark scheme
7(a)(i) 120 72 24 2 B1 for one correct angle
7(a)(ii) Correct pie chart 2 FT their table if angles add up to 360°
B1FT for one sector correctly drawn
7(a)(iii) 2 1
oe
5
7(b)(i) 3 B1 for 11
S H
B1 for 25
42 11 57
B1 for total in S equals 53 and total in
H equals 68 provided S ∩ H ≠ Ø
25
7(b)(ii) 11 1 FT their S ∩ H
(a)
C
NOT TO
36° SCALE
D
x°
A B
The diagram shows a triangle ABC and a line BD.
AB = BC and AC is parallel to BD.
(i) Angle ACB = 36°.
Write down the mathematical name for this type of angle.
…… [1]
(ii) Write down the mathematical name for triangle ABC.
…… [1]
(iii) Work out the value of x.
x = …… [2]
(iv) Find angle CBD.
Give a geometrical reason for your answer.
Angle CBD = …… because ……
…… [2]
(b)
P Q
NOT TO
SCALE
6.5 cm h
120°
T 6.5 cm R
8 cm
S
The diagram shows a quadrilateral, PQRS.
PQ is parallel to SR and SP is parallel to RQ.
TSR is a straight line.
SR = 8 cm, PS = ST = 6.5 cm and angle PST = 120°.
(i) Write down the mathematical name of quadrilateral PQRS.
…… [1]
(ii) Work out the perimeter of quadrilateral PQRS.
…… cm [1]
(iii) Find angle PSR.
Give a reason for your answer.
Angle PSR = …… because ……
…… [2]
(iv) PS and ST are two sides of a regular polygon.
Work out the number of sides of this regular polygon.
…… [1]
(v) Show that the height, h, of the quadrilateral PQRS is 5.63 cm, correct to 2 decimal places.
[2]
(vi) Work out the area of quadrilateral PQRS.
…… cm 2 [2]
Mark scheme
8(a)(i) Acute 1
8(a)(ii) Isosceles 1
8(a)(iii) 108 2 B1 for angle CAB = 36°
or M1 for 180 – 2 × 36 or 180 – 72 oe
8(a)(iv) 36 2 B1 for each
Alternate [angles]
8(b)(i) Parallelogram 1
8(b)(ii) 29 1
8(b)(iii) 60 2 B1 for each
Angles [on a straight] line [add up to] 180
8(b)(iv) 6 1
8(b)(v) h M1
sin 60 = or better
6.5
5.629 ... A1
8(b)(vi) 45.[0] or 45.03 to 45.04 2 M1 for 5.63 × 8 or 5.629…. × 8 oe
A sequence of patterns is made using rectangular blocks.
Pattern 1 Pattern 2 Pattern 3 Pattern 4
(a) Draw Pattern 4. [1]
(b) Complete the table.
Pattern number 1 2 3 4 5
Number of blocks 1 4 7
[2]
(c) Find an expression, in terms of n, for the number of blocks in Pattern n.
…… [2]
(d) Tara wants to make one pattern in this sequence.
She has 84 blocks.
Work out the largest pattern number she can make and the number of blocks remaining.
Pattern number ……
Number of blocks remaining …… [4]
Mark scheme
9(a) Correct pattern 4 1
9(b) 10 13 2 B1 for each
If 0 scored, SC1 for Pattern 5 three more
than their Pattern 4
9(c) 3n – 2 oe final answer 2 B1 for 3n + j (j ≠ −2) or kn – 2 (k ≠ 0 or 3)
or 3n – 2 oe seen then spoilt
9(d) 28 nfww 4 FT
2 B3 for 28 nfww as answer
or B3FT for their n correctly truncated
or B2 for 28.6 to 28.7
or B2FT for n =
(84 −their (b) ) correctly
their (a)
evaluated
or M1 for their (c) = 84
or 3 × 28 – 2 = 82
or for adding up in threes up to 82 or 85
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Mathematics 0580/32 for May/June 2021 is out of 104 marks, with 2 hours to answer it.
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