Mathematics 0580/31 October/November 2020: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), October/November 2020. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
Sean is the manager of a museum.
(a) He buys a Chinese pot costing 1200 yuan.
The exchange rate is $1 = 6.4 yuan.
Work out the cost of this pot in dollars.
$ …… [1]
(b) Sean records the maximum and minimum temperatures, in °C, at the museum.
Some of the results for one week are shown in the table.
Day Mon Tue Wed Thu Fri Sat Sun
Maximum
8 12 15 14 11 7 4 temperature (°C)
Minimum
-5 -2 -4 -1 3 temperature (°C)
(i) Find the difference between the maximum temperature and the minimum temperature on
Wednesday.
…… °C [1]
(ii) The minimum temperature on Saturday was 2 °C higher than the minimum temperature on
Monday.
Find the minimum temperature on Saturday.
…… °C [1]
(iii) In this week the range of temperatures was 23 °C.
Find the minimum temperature on Sunday.
…… °C [1]
(c) These are the opening times for the museum.
Monday to Friday 09 00 to 17 00
Saturday and Sunday 10 00 to 16 00
During opening hours the museum has 4 security guards working.
Each guard works a maximum of 30 hours each week.
Work out the smallest number of guards needed each week.
…… [4]
(d) The entry price to the museum is $18.
This price is increased by 28%.
Find the increased entry price.
$ …… [2]
Mark scheme
1(a) 187.5[0] 1
1(b)(i) 19 1
1(b)(ii) −3 1
1(b)(iii) −8 1
1(c) 7 nfww 4 M1 for 8 × 5 + 6 × 2 oe
and
M2 for their 52 × 4 ÷ 30 oe
or M1 for their 52 × 4 oe
or their 52 ÷ 30 oe
1(d) 23.04 2 28
M1 for 18 × (1 + ) oe
100
or B1 for 5.04
(a) Jian has a fair spinner in the shape of a regular hexagon.
The spinner is numbered 2, 2, 3, 4, 4, 5.
Jian spins the spinner.
Find the probability that the spinner lands on
(i) an even number,
…… [1]
(ii) a number less than 6,
…… [1]
(iii) the number 1.
…… [1]
(b) Mei has two fair square spinners, A and B.
Spinner A is numbered 1, 2, 2, 4 and spinner B is numbered 3, 3, 4, 5.
Spinner A Spinner B
She spins both spinners and adds the two numbers.
(i) Complete the table to show all the possible outcomes.
B 3 3 4 5
A
1 4 4
2 5 5 6 7
2 5 5 6 7
4 7 7
[2]
(ii) Use the table to write down the probability that the total is
(a) 5,
…… [1]
(b) more than 5.
…… [1]
(c) Ning has a spinner numbered 1 to 6.
She spins it 50 times and her results are shown in the table.
Number on
Frequency spinner
1 15
2 12
3 9
4 5
5 2
6 7
(i) Write down the mode.
…… [1]
(ii) Find the median.
…… [1]
(iii) Work out the mean.
…… [3]
Mark scheme
2(a)(i) 2 1
oe
3
2(a)(ii) 1 1
2(a)(iii) 0 1
2(b)(i) 5 6 2 B1 for 2 or 3 correct, in correct places
8 9
in the correct places
2(b)(ii)(a) 5 1 FT their table
oe
16
2(b)(ii)(b) 9 1 FT their table
oe
16
2(c)(i) 1 1
2(c)(ii) 2 1
2(c)(iii) 2.76 3 M1 for 1 × 15 + 2 × 12 + 3 × 9 + 4 × 5 +
5 × 2 + 6 × 7 oe
M1dep for their 138 ÷ 50
(a)
8 15 18 33 39 41 51 57 60 81
From this list, write down
(i) a factor of 54,
…… [1]
(ii) a multiple of 19,
…… [1]
(iii) a prime number.
…… [1]
(b) Write down the reciprocal of 64.
…… [1]
(c) (i) Write 4.81 # 10 - 3 as an ordinary number.
…… [1]
(ii) Write 75 000 in standard form.
…… [1]
2
6.3 # 10
(iii) Calculate .
7 # 10 - 3
Write your answer in standard form.
…… [2]
(d) (i)
= {2, 4, 8, 16, 32, 64}
A = {square numbers}
B = {cube numbers}
Use this information to complete the Venn diagram.
A B
[2]
(ii) On this Venn diagram, shade the region P , Q .
P Q
[1]
Mark scheme
3(a)(i) 18 1
3(a)(ii) 57 1
3(a)(iii) 41 1
3(b) 1 1
64
3(c)(i) [0].00481 cao 1
3(c)(ii) 7.5 × 104 1
3(c)(iii) 9 × 104 2 B1 for figs 9
3(d)(i) 2 B1 for 4 or 5 numbers in the correct place
3(d)(ii) 1
(a) Simplify.
6a - 3b + 2a - 4b
…… [2]
(b) Expand.
5 (x - 3)
…… [1]
(c) Solve these equations. x
(i) = 18
3
x = …… [1]
(ii) 5x + 18 = 8
x = …… [2]
(iii) 12x - 3 = 4x + 21
x = …… [2]
(d) 6 10 # 6 x = 6 2
Find the value of x.
x = …… [1]
(e) The Fraser family and the Singh family go to the cinema.
The Fraser family buys 6 adult tickets and 2 child tickets for $124.
The Singh family buys 3 adult tickets and 5 child tickets for $100.
Find the price of an adult ticket and the price of a child ticket.
Adult ticket $ ……
Child ticket $ …… [5]
Mark scheme
4(a) 8a – 7b 2 B1 for 8a or –7b in final answer
or for 8a – 7b seen then spoilt
4(b) 5x – 15 1
4(c)(i) 54 1
4(c)(ii) −2 2 M1 for
18 8
5x = 8 – 18 or x + = or better oe
5 5
4(c)(iii) 3 2 M1 for 12x – 4x = 21 + 3 or better oe
4(d) −8 cao 1
4(e) 17.5[0] 5 B1 for 6a + 2c = 124 B1 for 3a + 5c = 100
9.5[0] oe
M1FT for a correct method to eliminate one
variable
A1 for 17.5[0]
A1 for 9.5[0]
If 0 scored after B0, B1 or B2, SC1 for two
values that satisfy one of the/their original
equations or family
(a) Write one hundred and twenty thousand and twenty in figures.
…… [1]
(b) Find the value of 3481.
…… [1]
(c)
(i) Write down the fraction of the rectangle that is shaded.
…… [1]
(ii) Find the percentage of the rectangle that is not shaded.
…… % [1]
(d) Write these numbers in order, starting with the smallest.
5 7
27% 0.268
17 29
…… 1 …… 1 …… 1 …… [2]
smallest
(e) Write 0.3728 correct to 1 decimal place.
…… [1]
(f) Write down the value of 19 0 .
…… [1]
(g) The height, h metres, of a tower is 128 m, correct to the nearest metre.
Complete the statement about the value of h.
…… G h 1 …… [2]
(h) Find the highest common factor (HCF) of 126 and 180.
…… [2]
(i) Write down an irrational number with a value between 6 and 7.
…… [1]
Mark scheme
5(a) 120 020 1
5(b) 59 1
5(c)(i) 5 1
8
5(c)(ii) 37.5 1
5(d) 7 5 2 B1 for 3 in the correct order
0.268 27% or M1 for .27 .29… [.268] .24…
29 17
5(e) 0.4 1
5(f) 1 1
5(g) 127.5 128.5 2 B1 for each
or SC1 for both correct but reversed
5(h) 18 2 B1 for an answer of 2 or 3 or 6 or 9 or
2 × 3 × 3 or 2 × 32 as final answer
or for [126 =] 2 × 3 × 3 × 7 or 2 × 32 × 7
and
[180 =] 2 × 2 × 3 × 3 × 5 or 22 × 32 × 5
or for complete correct list of factors for 126
and 180
5(i) Any irrational number between 6 and 7 1
NOT TO
SCALE
3 cm
4 cm 6 cm
The diagram shows a right-angled triangular prism.
(a) On the 1 cm 2 grid, complete the net of the prism.
One face has been drawn for you.
[3]
(b) Work out the surface area of the prism.
…… cm 2 [3]
(c) Work out the volume of the prism.
…… cm 3 [2]
Mark scheme
6(a) Correct net 3 B2 for 2 or 3 correct faces in the correct
place
or B1 for 1 correct face in the correct place
6(b) 84 3 M2 for 5 × 6 + 6 × 4 + 6 × 3 oe or better
or 6 × (5 + 4 + 3) oe or better
or 2( 12 × 3 × 4) oe or better
or M1 for one correct area
6(c) 36 2 M1 for 1 × 3 × 4 × 6 oe
2
(a)
NOT TO w° SCALE
118°
The diagram shows an isosceles triangle and a straight line.
Work out the value of w.
w = …… [2]
(b)
E
F
NOT TO
SCALE
A 31° x° B
y°
D C
ABCD is a rectangle.
AE is parallel to DBF.
Find the value of x and the value of y.
x = ……
y = …… [2]
(c)
B
NOT TO
SCALE
a° 53°
A C
A, B and C are points on a circle.
AC is a diameter of the circle.
Find the value of a.
a = …… [2]
(d)
NOT TO
SCALE
P
Two regular octagons and a square meet at point P.
Show, by calculation, that the three interior angles at P add up to 360°.
[3]
Mark scheme
7(a) 56 2 M1 for 180 – 118 oe
or 180 – 2 × their 62 oe
7(b) [x =] 31 2 B1 for each
[y =] 121 or M1 for their y = 90 + their x
7(c) 37 2 B1 for the angle ABC marked as 90
or M1 for 180 – (90 + 53) oe
7(d) 360 M2 360
180 – or (8 – 2) × 180 ÷ 8 M1 for or (8 – 2) × 180
8 8
135 + 135 + 90 [= 360] A1
y
6
5
4
3
D
2
C
1
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1
A
–2
–3
–4
B
–5
–6
(a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
…… [3]
(ii) triangle A onto triangle C,
…… [2]
(iii) triangle A onto triangle D.
…… [3]
(b) On the grid, draw the image of triangle A after a reflection in the line x =- 2 . [2]
15
Mark scheme
8(a)(i) Rotation 3 B1 for each
[centre] (2, −2)
90° [anticlockwise] oe
8(a)(ii) Translation 2 B1 for each
−4
3
8(a)(iii) Enlargement 3 B1 for each
[centre] (−2, −5)
[sf] 2
8(b) Correct reflection of triangle 2 B1 for correct reflection in lines x = k
points at (−3, 0) (−3, −2) (−6, −2) or y = −2
(a) Complete the table of values for y = . x x -5 -3 -2 -1 1 2 3 5 y -15 15
[3]
15
(b) On the grid, draw the graph of y = for - 5 G x G -1 and 1 G x G 5. x y
16
14
12
10
8
6
4
2
–5 –4 –3 –2 –1 0 1 2 3 4 5 x
–2
–4
–6
–8
– 10
– 12
– 14
– 16 [4]
(c) On the grid, draw the line y = 6 . [1]
15
(d) Use your graph to solve = 6. x
x = …… [1]
Mark scheme
9(a) −3 −5 −7.5 7.5 5 3 3 B2 for 4 or 5 correct
or B1 for 2 or 3 correct
9(b) Correct curve 4 B3FT for 7 or 8 points plotted correctly
or B2FT for 5 or 6 points plotted correctly
or B1FT for 3 or 4 points plotted correctly
9(c) Correct ruled line 1
9(d) 2.5 or 2.4 to 2.6 1 FT their line (y = k) and their curve
(a) These are the first four terms of a sequence.
8 15 22 29
(i) Write down the next term.
…… [1]
(ii) Write down the term to term rule for continuing this sequence.
…… [1]
(iii) Find an expression for the nth term.
…… [2]
(b) Find the next term in each of these sequences.
(i) 18, 21, 26, 33, 42, …
…… [1]
(ii) 18, 20, 24, 32, 48, …
…… [1]
(c) Find the first three terms of the sequence with nth term n 2 + 5n .
…… , …… , …… [2]
Mark scheme
10(a)(i) 36 1
10(a)(ii) add 7 oe 1
10(a)(iii) 7n + 1 oe final answer 2 B1 for 7n + j or kn + 1 (k ≠ 0) as final
answer, or for 7n + 1 seen then spoilt
10(b)(i) 53 1
10(b)(ii) 80 1
10(c) 6 14 24 2 B1 for 2 correct terms in the correct place
If 0 scored, SC1 for 0 6 14
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On this page, free: the mark scheme for IGCSE Mathematics 0580/31, October/November 2020 (0580_w20_ms_31), and the question paper (0580_w20_qp_31), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/31 for October/November 2020 is out of 104 marks, with 2 hours to answer it.
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