Mathematics 0580/32 May/June 2020: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), May/June 2020. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) Paul has a set of 8 cards, each with a number written on it.
The numbers on the cards are 1, 1, 2, 3, 3, 3, 4, 5.
One card is taken at random.
Write down the probability that the number on the card is
(i) 1,
…… [1]
(ii) an odd number,
…… [1]
(iii) a prime number,
…… [1]
(iv) a number less than 6.
…… [1]
(b) Dina has a set of 12 cards.
These are the numbers on the cards.
3 4 1 3 2 1 3 4 2 2 1 3
Work out
(i) the median,
…… [2]
(ii) the mode,
…… [1]
(iii) the mean,
…… [2]
(iv) the range.
…… [1]
(c) Helena has a different set of cards.
She takes one card at random and records the number shown.
She does this 50 times.
The results are shown in the table.
Number on card Frequency
1 8
2 11
3 10
4 9
5 12
Calculate the mean of her results.
…… [3]
Mark scheme
1(a)(i) 1 1
oe
4
1(a)(ii) 3 1
oe
4
1(a)(iii) 5 1
8
1(a)(iv) 1 1
1(b)(i) 2.5 2 M1 for ordering the numbers to the middle
two e.g. 1 1 1 2 2 2 3 or 2 3 3 3 3 4 4
or B1 for 2 and 3 identified
1(b)(ii) 3 1
1(b)(iii) 5 2 M1 for (1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 3
2.42 or 2.416 to 2.417 or 2 + 4 + 4) ÷ 12
12
1(b)(iv) 3 1
1(c) 3.12 3 M1 for
1 × 8 + 2 × 11 + 3 × 10 + 4 × 9 + 5 × 12 soi
156
M1dep for their 156 ÷ 50
(a) Jeremy goes on holiday.
He parks his car in the airport car park from
10 00 on Tuesday 17 July to 17 00 on Saturday 28 July.
The car park charges are shown below.
Monday to Friday $14 per day
Saturday and Sunday $8 per day
Part days are charged as full days
Find the total cost of parking his car.
$ …… [3]
(b) At the airport, Jeremy buys a ring for $53 and a watch for $65.
Work out how much change he receives from $120.
$ …… [2]
(c) The plane flies from Melbourne to Tokyo at an average speed of 783 km/h.
The distance from Melbourne to Tokyo is 8352 km.
The plane leaves Melbourne at 09 52 local time.
The local time in Tokyo is 2 hours behind the local time in Melbourne.
Find the local time in Tokyo when the plane arrives.
…… [4]
(d) In Tokyo, Jeremy buys a bracelet for 2050 yen.
The exchange rate is 1 yen = $0.0125 .
Calculate the price of the bracelet in dollars.
Give your answer correct to the nearest dollar.
$ …… [2]
(e) The plane ticket costs $680 plus a tax of 16%.
Find the total cost of this ticket.
$ …… [2]
Mark scheme
2(a) 150 3 M2 for 9 × 14 + 3 × 8 oe
or M1 for 9 × 14 or 3 × 8 oe
2(b) 2 2 M1 for 120 – (53 + 65) oe
2(c) 18 32 4 M1 for 8352 ÷ 783
A1 for 10 h 40 min
M1 for the correct adjustment of the 2 hours
2(d) 26 2 M1 for 2050 × 0.0125 soi 25.625
2(e) 788.8[0] 2 16
M1 for 680 × (1 + ) oe
100
Belle records the height, in centimetres, and the mass, in kilograms, of some goats.
Some of her results are shown in the scatter diagram.
36
35
34
Mass (kg)
33
32
31
30
20 25 30 35 40
Height (cm)
(a) The table shows four more results.
Height (cm) 23 30 36 38
Mass (kg) 31.2 33.5 34.6 34.8
Plot these points on the scatter diagram. [2]
(b) What type of correlation is shown in this scatter diagram?
…… [1]
(c) (i) Draw a line of best fit on the scatter diagram. [1]
(ii) Use your line of best fit to estimate the height of a goat with mass 32.5 kg.
…… cm [1]
(d) Work out the percentage of the 12 goats that have a height between 26 cm and 35 cm.
…… % [3]
Mark scheme
3(a) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted
3(b) Positive 1
3(c)(i) Ruled line of best fit 1
3(c)(ii) 25 to 27 1 FT their ruled line with positive gradient
3(d) 41.7 or 41.66 to 41.67 3 5
M2 for × 100
12
their 5
or M1 for × 100
12
or B1 for 5
Alexa, Ben and Chloe own a restaurant.
(a) Alexa records some temperatures.
Fridge 4 °C Cool box -3 °C Freezer -19 °C
(i) Find the difference in temperature between the fridge and the cool box.
…… °C [1]
(ii) Find the difference in temperature between the cool box and the freezer.
…… °C [1]
(iii) The temperature in the cold room is 5 °C lower than the fridge.
Find the temperature in the cold room.
…… °C [1]
(b) Alexa, Ben and Chloe share the profits from their restaurant in the ratio 2 : 6 : 7.
One year the restaurant makes a profit of $60 000.
Work out how much each receives.
Alexa = $ ……
Ben = $ ……
Chloe = $ …… [3]
(c) They invest $12 000 at a rate of n% per year simple interest.
At the end of 3 years the value of the investment is $12 900.
Find the value of n.
Mark scheme
4(a)(i) 7 1
4(a)(ii) 16 1
4(a)(iii) −1 1
4(b) 8000 3 B2 for one correct
24 000 60000
28 000 or M2 for ×k
2+6+7
60000
or M1 for
2+6+7
4(c) 2.5 3 12900 − 12000
M1 for
3
their 300
M1dep for [× 100]
12000
(a) T = 3a 2 b
Find the value of T when a = 4 and b = 5.
T = …… [2]
(b) (i) Multiply out the brackets. x (3 - 5x)
…… [2]
(ii) Factorise fully.
5x - 20x 2
…… [2]
(c)
NOT TO
SCALE
3a + b 4a - 5b
a + 2b
Find an expression for the perimeter of this triangle.
Give your answer in its simplest form.
…… [3]
Mark scheme
5(a) 240 2 M1 for 3 × 42 × 5 oe
5(b)(i) 3x – 5x2 final answer 2 B1 for 3x or – 5x2
5(b)(ii) 5x(1 – 4x) final answer 2 B1 for 5(x – 4x2) or x(5 – 20x)
5(c) 8a – 2b 3 M1 for 3a + b + 4a – 5b + a + 2b
B1 for 8a or – 2b
(a)
NOT TO
3 cm SCALE
2 cm
6 cm
The diagram shows a cuboid.
On the 1 cm2 grid, complete the net of the cuboid.
One face has been drawn for you.
[3]
(b) A cube has a surface area of 384 cm2.
Find the length of one of its sides.
…… cm [3]
(c)
4 cm
NOT TO
SCALE
12 cm
7 cm
The diagram shows a right-angled triangular prism.
Work out the volume of the prism.
…… cm3 [3]
Mark scheme
6(a) Correct ruled net of cuboid 3 B2 for 3 or 4 further correct faces drawn in
the correct places
or B1 for 1 or 2 further correct faces drawn in
the correct places
6(b) 8 3 M1 for 384 ÷ 6
M1dep for their 64
6(c) 168 3 M2 for (7 × 4 ÷ 2) × 12 oe
or M1 for (7 × 4 ÷ 2) or their area × 12
(a)
NOT TO
70° SCALE
x°
The diagram shows an isosceles triangle.
Find the value of x.
x = …… [2]
(b)
b° 32° NOT TO
50° SCALE
a° c°
The diagram shows two pairs of parallel lines.
Find the value of a, the value of b and the value of c.
a = ……
b = ……
c = …… [3]
(c)
23 cm NOT TO w cm SCALE
14 cm
The diagram shows a rectangle 14 cm by w cm.
The diagonal is 23 cm.
Calculate the value of w.
w = …… [3]
(d)
NOT TO
SCALE
O
The diagram shows a square with vertices on the circumference of a circle, centre O.
The radius of the circle is 6 cm.
Work out the shaded area.
…… cm2 [5]
Mark scheme
7(a) 55 2 M1 for 180 − 70
7(b) [a =] 32 3 B1 for each
[b =] 98
[c =] 82
7(c) 18.2 or 18.24 to 18.25 3 M2 for 232 − 142 or better
or M1 for 142 + […]2 = 232
7(d) 41.1 or 41.09 to 41.112 5 M1 for π × 62
M2 for 21 × 6 × 6 × 4
or M1 for 21 × 6 × 6
M1 for π × 62 − 21 × 6 × 6 × 4
y
6
5
4
3
B
2
A
1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x
-1
C
-2
-3
D
-4
-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 y =- 1. [2]
Mark scheme
8(a)(i) Rotation 3 B1 for each
[centre] (0, 0) oe
90° [anticlockwise] oe
8(a)(ii) Translation 2 B1 for each
−6
−3
8(a)(iii) Enlargement 3 B1 for each
[centre] (6, 4)
[sf] 3
8(b) Correct reflection 2 B1 for correct reflection in y = k
(2, −3), (2, −4), (5, −3)
(a) Complete the table of values for y = x 2 - 3x - 6 .
x -3 -2 -1 0 1 2 3 4 5 6 y 12 -2 -2 12
[3]
(b) On the grid, draw the graph of y = x 2 - 3x - 6 for - 3 G x G 6 .
y
14
12
10
8
6
4
2
-3 -2 -1 0 1 2 3 4 5 6 x
-2
-4
-6
-8
-10
[4]
(c) Write down the equation of the line of symmetry of the graph.
…… [1]
(d) Use your graph to solve the equation x 2 - 3x - 6 = 0 .
x = …… or x = …… [2]
Question 10 is printed on the next page.
Mark scheme
9(a) 4 –6 –8 –8 –6 4 3 B2 for 4 or 5 correct
or B1 for 2 or 3 correct
9(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
9(c) x = 1.5 1
9(d) −1.4 4.4 2 B1 for each
(a) Solve these equations.
(i) 5x =- 30
x = …… [1]
(ii) 4x - 2 = 28
x = …… [2]
(iii) 3(2x + 7) = 12
x = …… [3]
(b) Solve the simultaneous equations.
You must show all your working.
5x - 2y = 44
2x + 3y = 10
x = ……
y = …… [4]
Mark scheme
10(a)(i) −6 1
10(a)(ii) 7.5 or 7 12 2 M1 for 4x = 28 + 2 oe
10(a)(iii) −1.5 or −1 12 3 M1 for 6x + 21 [= 12] or 2x + 7 = 12 ÷ 3 or
better
M1 for their 6x = 12 – their 21
or 2x = their 4 – 7
10(b) Equating coefficients of one variable M1 Accept any correct method such as
by multiplying the equations by substitution e.g.
scalars e.g. M1 for rearranging one equation to make
15x – 6y = 132 either x or y the subject
4x + 6y = 20 M1 for substituting their rearranged equation
into the other equation
Adding or subtracting equations to M1 A1 A1 as in other method
eliminate one variable e.g.
19x = 152 If 0 scored, SC1 for two values that satisfy
one equation or SC1 for two correct answers
[x =] 8 A1 without any correct working
[y =] −2 A1
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On this page, free: the mark scheme for IGCSE Mathematics 0580/32, May/June 2020 (0580_s20_ms_32), and the question paper (0580_s20_qp_32), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/32 for May/June 2020 is out of 104 marks, with 2 hours to answer it.
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