Mathematics 0580/32 October/November 2021: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), October/November 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) In a café at a train station, a cup of coffee costs $3.25 and a glass of cola costs $2.15 .
Gary buys 2 cups of coffee and 4 glasses of cola.
Work out how much change he receives from a $20 note.
$ …… [3]
(b) Roy spends $37.80 in the café on food and drink in the ratio food : drink = 7 : 2.
Work out how much he spends on food.
$ …… [2]
(c) The price of a $48 train ticket is increased by 12%.
Find the new price of the ticket.
$ …… [2]
(d) Here is part of the timetable for trains from Washby to Dunstley.
All trains take the same time to travel from Washby to Dunstley.
Washby 09 18 11 05
Dunstley 10 03 ……
Complete the timetable.
[2]
(e) On one day, Washby station sells 28 senior tickets, 192 adult tickets and some child tickets.
Senior tickets
42°
Complete the pie chart to show this information.
[3]
Mark scheme
1(a) 4.9[0] cao 3 M2 for 20 − (2 × 3.25 + 4 × 2.15) oe
or
M1 for 2 × 3.25 or 4 × 2.15
1(b) 29.4[0] cao 2 37.8
M1 for [× k] where k = 1, 2 or 7
7+2
1(c) 53.76 cao 2 12
M1 for 48 × 1 + oe
100
or B1 for 5.76
1(d) 11 50 2 B1 for 45 [min], 1 h 47 [min] or 107 [min]
1(e) Correct pie chart drawn 3 42
M2 for 192 × oe
28
or
42
M1 for oe
28
(a) 8 17 26 35 49 51 72
From this list of numbers, write down
(i) a multiple of 24,
…… [1]
(ii) a square number,
…… [1]
(iii) a cube number,
…… [1]
(iv) a prime number.
…… [1]
(b) Write 420 as a product of its prime factors.
…… [2]
(c) Find the lowest common multiple (LCM) of 30 and 84.
…… [2]
(d) By writing each number correct to 1 significant figure, show that an estimate for this calculation is 40.
9.875 + 18.305
+ 27.837
3.418
[2]
Mark scheme
2(a)(i) 72 1
2(a)(ii) 49 1
2(a)(iii) 8 1
2(a)(iv) 17 1
2(b) 22 × 3 × 5 × 7 2 B1 for 2, 2, 3, 5, 7
or M1 for correct factor tree/diagram/list/
table
2(c) 420 2 B1 for 420k as final answer
or M1 for
[30=] 2 × 3 × 5 and [84 =] 22 × 3 × 7
or for list of multiples of 30 and 84 with at
least 3 of each
or 2 correct factor trees or tables
or 2 × 2 × 3 × 5 × 7 oe
2(d) 10 + 20 M1
+ 30
3
30 A1 If 0 scored, SC1 for 3 correctly rounded
+ 30 [= 40] numbers or for all 4 correct but with any
3
trailing zeros
(a) Simone completes one lap of a 400 metre running track in 79 seconds.
Work out how long it will take her to run 6 km at the same rate.
Give your answer in minutes and seconds.
…… minutes …… seconds [4]
(b) The probability that she does not win a race is 0.94 .
Find the probability that she wins a race.
…… [1]
(c) Each day she records the number of laps she runs.
Here is her record for one week.
15 42 28 16 24 15 32
(i) Write down the mode.
…… [1]
(ii) Find the median.
…… [2]
(iii) Find the range.
…… [1]
(d) Wilfred records his times, in seconds, for each of 5 laps.
59 74 69 63 65
After running a 6th lap his mean time is 67 seconds.
Find his time for the 6th lap.
…… seconds [3]
Mark scheme
3(a) 19 [min] 45 [secs] 4 6000 79
M3 for × oe
400 60
or B2 for figs 1975
6000
or M2 for 79 × oe
400
or B1 for figs 1185
6000 400 79 79
or M1 for or or or
400 79 400 0.4
oe
3(b) 0.06 oe 1
3(c)(i) 15 1
3(c)(ii) 24 2 M1 for full list or 15 15 16 24 or
42 32 28 24
3(c)(iii) 27 1
3(d) 72 3 M2 for
6 × 67 – (59 + 74 + 69 + 63 + 65) oe
or
M1 for
(59 + 74 + 69 + 63 + 65 + x) ÷ 6 = 67 or
6 × 67 oe
(a)
A
D E
73° z° NOT TO
SCALE
x° 58° y°
F G
B C
In the diagram, ABC is a triangle.
Line DAE is parallel to line FBCG.
Find the value of x, the value of y and the value of z.
x = ……
y = ……
z = …… [3]
(b)
NOT TO
SCALE
Q R
32°
O u°
P
Points P, Q and R lie on a circle, centre O.
Find the value of u.
u = …… [2]
(c)
6.42 cm NOT TO
SCALE
72°
The diagram shows a sector of a circle with radius 6.42 cm and sector angle 72°.
Calculate the perimeter of this sector.
…… cm [3]
Mark scheme
4(a) 122 3 B1 for each
73
49 FT 122 – their 73
or their 122 – their 73
or (their 122) – 73
4(b) 58 2 M1 for 180 – 90 – 32 or 90 – 32
or angle PQR identified as 90
4(c) 20.9 or 20.90 to 20.91 3 72
M2 for × 2 × π × 6.42 + 2 × 6.42 oe
360
72
or M1 for × 2 × π × 6.42 oe
360
(a) Simplify.
5a - 3b + 7a + 2b
…… [2]
(b) Find the value of 8x - 3y when x = 5 and y =- 2 .
…… [2]
(c) Solve.
6x - 3 = 2x + 8
x = …… [2]
(d) P = 6t - 11
Make t the subject of this formula.
t = …… [2]
(e) Solve the simultaneous equations.
You must show all your working.
3x - 4y = 30
2x + 5y =- 3
x = ……
y = …… [4]
Mark scheme
5(a) 12a – b final answer 2 B1 for 12a or – b in final answer
or for correct answer spoilt
5(b) 46 2 M1 for 8 × 5 – 3 × −2
or B1 for 40 or [+] 6
5(c) 2.75 or 2 34 2 M1 for 6x – 2x = 3 + 8 or better
5(d) P + 11 2 P 11
[t =] oe final answer M1 for P + 11 = 6t or =t −
6 6 6
5(e) Correctly equating one set of coefficients M1
Correct method to eliminate one variable M1 Dependent on the coefficients being the
same for one of the variables
Correct consistent use of addition or
subtraction using their equations
[x =] 6 A1
[y =] −3 A1 If 0 scored, SC1 for two values that satisfy
one of the original equations
SC1 if no working shown, but 2 correct
answers given
(a) Write these in order, starting with the smallest.
11 17
0.5806 58%
19 29
…… 1 …… 1 …… 1 …… [2]
smallest
(b) Write 0.004 973 correct to
(i) 3 decimal places,
…… [1]
(ii) 2 significant figures.
…… [1]
(c) The height of a flag pole, h metres, is measured as 37.84 metres, correct to 2 decimal places.
Complete this statement about the value of h.
…… G h 1 …… [2]
(d) The population of Nigeria is 201 000 000, correct to 3 significant figures.
Write this population in standard form.
…… [1]
(e) The table shows the populations of some countries given in standard form, correct to
3 significant figures.
Country Population
Brazil 2.12 # 10 8
China 1.42 # 10 9
Eritrea 5.31 # 10 6
France 6.55 # 10 7
Maldives 4.52 # 10 5
New Zealand 4.79 # 10 6
Use the information in this table to find
(i) the country with the smallest population,
…… [1]
(ii) the country with the population that is nearest to 5 million,
…… [1]
(iii) the difference between the population of Brazil and the population of France,
…… [1]
(iv) the value of k, correct to 2 significant figures, where
the population of China = k # the population of Eritrea.
k = …… [2]
Mark scheme
6(a) 11 17 2 M1 for
58% 0.5806 [0.5806] [0].57… [0].586… [0].58
19 29
or B1 for 3 in the correct order
6(b)(i) 0.005 cao 1
6(b)(ii) 0.0050 cao 1
6(c) 37.835 37.845 2 B1 for each
If 0 scored, SC1 for both correct but
reversed
6(d) 2.01 × 108 1
6(e)(i) Maldives 1
6(e)(ii) New Zealand 1
6(e)(iii) 146 500 000 or 1.465 × 108 1
6(e)(iv) 270 cao 2 M1 for (1.42 × 109) ÷ (5.31 × 106) oe
or 267[. …] oe
(a)
15 m
NOT TO
15 m
SCALE
12 m
22 m
The diagram shows a shape made from a quarter circle and a trapezium.
Find the total area of this shape.
…… m 2 [4]
(b)
h cm
NOT TO
15.8 cm
SCALE
The diagram shows a rectangle.
The area of the rectangle is 387.1 cm 2 .
Find the value of h.
h = …… [2]
(c)
NOT TO
SCALE
15 cm
32 cm
18 cm
The diagram shows a right-angled triangular prism.
Find the volume of the prism.
…… cm 3 [3]
Mark scheme
7(a) 399 or 398.7… 4 15 +22
M3 for 152 × π × 14 + ×12 oe
2
or M2 for 152 × π × 14 oe
15 +22
or 152 × π and ×12 oe
2
15 +22
or M1 for 152 × π or ×12 oe
2
7(b) 24.5 2 M1 for 387.1 ÷ 15.8
7(c) 4320 3 M2 for 15 × 18 × 12 × 32 oe
or M1 for 15 × 18 × 12 oe
(a)
D NOT TO
SCALE
A 74.9 cm
21.4 cm
B 14.8 cm C E F
Right-angled triangles ABC and DEF are similar.
(i) Calculate EF.
EF = …… cm [2]
(ii) Calculate angle BCA.
Angle BCA = …… [2]
(b) The diagram shows two congruent rectangular tiles placed together.
H
NOT TO
32.5 cm SCALE
G
The width of each tile is 32.5 cm and GH = 84.5 cm .
Find the length of each tile.
…… cm [4]
(c) Town B is 72 km from town A on a bearing of 058°.
Town C is 60 km due east of town B.
(i) Using a scale of 1 cm to represent 12 km, complete the scale drawing to show the positions of town B and town C.
North
A
Scale: 1 cm to 12 km
[3]
(ii) Measure the bearing of town C from town A.
…… [1]
Mark scheme
8(a)(i) 51.8 2 EF 14.8
M1 for = oe or better
74.9 21.4
8(a)(ii) 46.2 or 46.24… 2 14.8
M1 for cos [ =] oe
21.4
8(b) 39 4 B3 for 78
1
or M3 for × 84.52 − 32.52 or better
2
or M2 for 84.52 − 32.52 or better
or M1 for [ ]2 + 32.52 = 84.52 or better
8(c)(i) Accurate scale drawing 3 B1 for accurate bearing at A of 058°
B1 for AB of length of 6 cm
B1 for BC of length of 5 cm in direction
east
8(c)(ii) Correct bearing 1 Strict FT on bearing of C from A
Triangles A, B and T are shown on the grid.
y
8
7
6
5
A
4
3
2
T
1
–2 –1 0 1 2 3 4 5 6 7 8 9 10 x
–1
–2 B
–3
–4
–5
(a) Describe fully the single transformation that maps triangle T onto triangle A.
…… [3]
(b) Describe fully the single transformation that maps triangle T onto triangle B.
…… [3]
5
(c) On the grid, draw the image of triangle T after a translation by the vector e o. [2]
-3
Mark scheme
9(a) Enlargement 3 B1 for each
[centre] (−1, −1)
[sf] 2
9(b) Rotation 3 B1 for each
[centre] (0, 0)
90 clockwise oe
9(c) Triangle at (6, 0), (6, –2) (9, –2) 2 5 k
B1 for either translation by or
k −3
(a) Complete the table of values for y = x 2 - 5x - 2 .
x -2 -1 0 1 2 3 4 5 6 y 4 -2 -8 -8 -2 4
[2]
(b) On the grid, draw the graph of y = x 2 - 5x - 2 for - 2 G x G 6 .
y
14
12
10
8
6
4
2
–2 –1 0 1 2 3 4 5 6 x
–2
–4
–6
–8
– 10
[4]
(c) On the grid, draw the line y = 2 . [1]
(d) Use your graph to solve the equation x 2 - 5x - 2 = 2 .
x = …… or x = …… [2]
Mark scheme
10(a) 12 −6 −6 2 B1 for 1 or 2 correct
10(b) Correct curve 4 B3FT for 8 or 9 points correctly plotted
or B2FT for 6 or 7 points correctly plotted
or B1FT for 4 or 5 points correctly plotted
10(c) Ruled line y = 2 drawn 1
10(d) −0.9 to −0.5 2 FT y = 2 and their curve
B1 for each
5.5 to 5.9
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On this page, free: the mark scheme for IGCSE Mathematics 0580/32, October/November 2021 (0580_w21_ms_32), and the question paper (0580_w21_qp_32), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/32 for October/November 2021 is out of 104 marks, with 2 hours to answer it.
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