Mathematics 0580/31 May/June 2023: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), May/June 2023. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) Write the number forty thousand and thirty-three in figures.
…… [1]
3
(b) Find the value of 729 .
…… [1]
7
(c) Find the reciprocal of .
9
Give your answer as a decimal, correct to 3 decimal places.
…… [2]
(d) Find the value of 6 5 ' 3 4 .
…… [2]
(e) Work out (- 9) # (- 7) ' (- 3) .
…… [1]
(f) Work out.
(i) 11 + 9 # 5 - 4
…… [1]
(ii) (11 + 9) # 5 - 4
…… [1]
5
(g) - 0.67 123 49 3.142
9
From this list, write down an irrational number.
…… [1]
(h) (i) Find the lowest common multiple (LCM) of 24 and 104.
…… [2]
(ii) Find the highest common factor (HCF) of 24 and 104.
…… [2]
Mark scheme
1(a) 40 033 1
1(b) 9 1
1(c) 1.286 cao 2 B1 for 9 or 1.29 or 1.285 or
7
1.285……
1(d) 96 2 B1 for 7776 or 81
1(e) −21 1
1(f)(i) 52 1
1(f)(ii) 96 1
1(g) √123 1
1(h)(i) 312 2 B1 for 312k as final answer
or M1 for [24 =] 2 × 2 × 2 × 3
or 23 × 3
and [104 =] 2 × 2 × 2 × 13 or
23 × 13
or 2 correct factor trees or tables
or a list of multiples of both 24
and 104 with at least 3 of each
or 2 × 2 × 2 × 3 × 13 oe
1(h)(ii) 8 2 B1 for 2 or 4 or 2 × 2 × 2 or 23
as final answer,
or for a complete list of factors
of 24 and 104
(a) Complete this statement.
The mathematical name of any polygon with 4 sides is a …… [1]
(b) Three of these shapes are shown on the grid.
y
8
7
6
5
A
4
3
2
1
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x
–1
–2
B
–3
–4
–5
–6
–7
–8
–9
Describe fully the single transformation that maps
(i) the shaded shape onto shape A
…… [3]
(ii) the shaded shape onto shape B.
…… [3]
(c) On the grid, draw the image of
9
(i) the shaded shape after a translation by the vector e o [2]
-6
(ii) the shaded shape after a reflection in the line y =- 1. [2]
Mark scheme
2(a) Quadrilateral 1
2(b)(i) Rotation 3 B1 for each
90° clockwise oe
(centre) (0, 0) oe
2(b)(ii) Enlargement 3 B1 for each
(scale factor) 12 oe
(centre) (7, −8) oe
2(c)(i) Correct translation 2 k
(4, 0), (7, −2), (7, −5), (3, −4) B1 for a translation of or
−6
9
k
2(c)(ii) Correct reflection 2 B1 for a reflection in y = k or in
(−2, −3), (−2, −6), (−5, −8), (−6, −4) x = −1
These are the test scores of 16 students.
15 26 9 45 36 20 41 39
40 23 32 18 41 34 37 31
(a) Complete the stem-and-leaf diagram.
0
1
2
3
4
Key: 1 5 represents 15
[2]
(b) Find the mode.
…… [1]
(c) Find the median.
…… [1]
(d) Find the range.
…… [1]
(e) Complete the bar chart for the test scores of the 16 students.
7
6
5
4
Number of students
3
2
1
0
0 to 9 10 to 19 20 to 29 30 to 39 40 to 49
Test score
[2]
(f) Work out the percentage of students with a test score of 40 or more.
…… % [1]
Mark scheme
3(a) 2 B1 for 3 fully correct rows
0 9 or for a fully correct unordered
stem-and-leaf diagram
1 5 8
2 0 3 6
3 1 2 4 6 7 9
4 0 1 1 5
3(b) 41 1
3(c) 33 1
3(d) 36 1
3(e) Correct bar chart 2 FT their stem-and-leaf diagram
B1FT for 3 correct or follow
through heights
3(f) 25 1 their k
FT × 100 from the bar
16
chart
or from their stem-and-leaf
diagram
(a) The diagram shows the net of a solid on a 1 cm 2 grid.
A N
B M
C L
D K
E J
F I
G H
(i) When the net is folded to make the solid, point C will join with point A.
Write down which other point will join with point A.
…… [1]
(ii) Calculate the total surface area of the solid.
…… cm2 [3]
(iii) Complete this statement.
The solid is a …… with the cross-section in the shape of a …… [2]
(iv) Draw a sketch of the solid.
[1]
(b)
NOT TO
SCALE
6 cm x cm
6 cm
The diagram shows a cuboid.
The volume of the cuboid is 540 cm 3 .
Calculate the value of x.
x = …… [2]
Mark scheme
4(a)(i) G 1
4(a)(ii) 180 3 M2 for
6×5+6×9+6×5+6×3+
2 × 12 × (9 + 3 ) × 4
or 6 × 22 + 2 × 12 × (9 + 3 ) × 4
oe or better
1
or M1 for [2 ×] (9 + 3) × 4 oe
2
or 6 × 5 + 6 × 9 + 6 × 5 + 6 × 3
or 22 × 6 oe
4(a)(iii) Prism trapezium 2 B1 for prism or trapezium
4(a)(iv) A recognisable attempt at a prism with 1
trapezium cross section
4(b) 15 2 M1 for 6 × 6 × x = 540 oe or
better
Antonio buys a restaurant for $240 000.
5
This is of the amount he has available to spend.
8
(a) Show that he has $144 000 left after buying the restaurant.
[2]
(b) Some of the $144 000 is spent on expenses.
Expenses are wages, equipment and supplies in the ratio
wages : equipment : supplies = 9 : 5 : 8.
The amount spent on wages is $45 000.
(i) Find the amount spent on
(a) equipment
$ …… [2]
(b) supplies.
$ …… [1]
(ii) Work out the amount Antonio has left now.
$ …… [2]
(c) Antonio borrows $25 400 for 6 years at a rate of 5% per year simple interest.
Calculate the total amount he repays at the end of the 6 years.
$ …… [3]
(d) In one week, the number of customers in the restaurant was 560.
In the next week, the number of customers in the restaurant was 656.
Calculate the percentage increase.
…… % [2]
Mark scheme
5(a) 240 000 ÷ 5 × 8 – 240 000 M2 M1 for 240 000 ÷ 5 × 8
3
or 240 000 ×
5
5(b)(i)(a) 25 000 2 M1 for 45 000 ÷ 9 oe
5(b)(i)(b) 40 000 1
5(b)(ii) 34 000 2 FT 99 000 – (their 25 000 +
their 40 000)
M1 for
144 000 – 45 000 –
(their 25 000 + their 40 000) oe
5(c) 33 020 3 B2 for 7620
or M2 for
25400 × 5 × 6
25 400 + oe
100
25400 × 5 × 6
or M1 for oe
100
5(d) 17.1 or 17.1[4…] 2 656 −560
M1 for [×100] oe
560
656
or ×100 [ −100] oe
560
656
or −1 [×100] oe
560
(a) Complete the table of values for y = 5 + 3x - x 2 .
x -2 -1 0 1 2 3 4 5 y 1 7 –5
[3]
(b) On the grid, draw the graph of y = 5 + 3x - x 2 for - 2 G x G 5.
y
12
11
10
9
8
7
6
5
4
3
2
1
–2 –1 0 1 2 3 4 5 x
–1
–2
–3
–4
–5
–6
[4]
(c) Write down the equation of the line of symmetry of the graph.
…… [1]
(d) (i) Complete the table of values for y = 2x + 1.
x -1 0 2 y
[2]
(ii) On the grid, draw the graph of y = 2x + 1 for - 2 G x G 5. [1]
(e) Write down the coordinates of the two points where the two graphs intersect.
( …… , …… ) and ( …… , …… ) [3]
Mark scheme
6(a) −5 5 7 5 1 3 B2 for 3 or 4 correct
or B1 for 1 or 2 correct
6(b) Correct and accurate curve 4 B3FT for 7 or 8 points correctly
plotted
or B2FT for 5 or 6 points
correctly plotted
or B1FT for 3 or 4 points
correctly plotted
6(c) x = 1.5 oe 1
6(d)(i) −1 1 5 2 B1 for 2 correct
6(d)(ii) Correct ruled line 1
6(e) (−1.7 to −1.4, −2.4 to −1.8) 3 FT their curve and their line
(2.4 to 2.7, 5.8 to 6.4) B2FT for 3 values correct
or B1FT for 2 values correct
7(a)(i)(a) Diameter 1
7(a)(i)(b) Tangent 1
(a)
D
F
NOT TO
E SCALE
O
C
B
28°
A
The diagram shows a circle, centre O, with points B, D and E on the circumference.
AOEF is a straight line.
The straight line AC touches the circle at B.
(i) Write down the mathematical name for
(a) line BOD
…… [1]
(b) line ABC.
…… [1]
(ii) Write down the two geometrical reasons why angle AOB is 62°.
and …… [2]
(iii) Give the geometrical reason why angle DOE is also 62°.
…… [1]
(iv) (a) Find angle DEB.
Angle DEB = …… [1]
(b) Find angle ODE.
Angle ODE = …… [2]
(c) Find angle BEF.
Angle BEF = …… [2]
(b) Write down two geometrical properties that show that a polygon is regular.
…… and …… [2]
(c) Work out the interior angle of a regular 10-sided polygon.
…… [2]
Mark scheme
7(a)(ii) Angle between tangent and radius = 90 2 B1 for each
Angles in a triangle add to 180
7(a)(iii) Opposite angles are equal 1
7(a)(iv)(a) 90 1
7(a)(iv)(b) 59 2 M1 for (180 – 62) ÷ 2 oe
7(a)(iv)(c) 149 2 B1 for OEB = 31
or B1FT for
180 – their a + their b
or 298 – (their a + their b)
7(b) Equal sides 2 B1 for each
Equal angles
7(c) 144 2 M1 for 180 – (360 ÷ 10) oe
(10 − 2) × 180
or oe
10
Two friends, Diego and Javier, meet at a swimming pool.
The travel graph shows Diego’s journey by bicycle from his home to the swimming pool.
Javier’s 10 home
9
8
7
Swimming pool 6
5
Distance from
Diego’s home
(km)
4
3
2
1
Diego’s 0 home 10 00 10 30 11 00 11 30 12 00 12 30 13 00
Time
(a) Calculate Diego’s speed for his journey from his home to the swimming pool.
Give your answer in kilometres per hour.
…… km/h [2]
(b) Diego stays at the swimming pool until 12 20.
(i) On the grid, draw the line representing the time he stays at the swimming pool. [1]
(ii) Work out how long, in hours and minutes, he is at the swimming pool.
…… h …… min [1]
(c) Javier leaves his home 15 minutes later than Diego.
He walks to the swimming pool at a constant speed of 6 km/h.
On the grid, show Javier’s journey from his home to the swimming pool.
[3]
(d) They both leave the swimming pool at 12 20 and return to their own homes, each at a constant speed.
Diego arrives home at 12 45.
Javier arrives home 5 minutes later than Diego.
Complete the travel graph. [2]
Mark scheme
8(a) 9 2 M1 for 6 ÷ 40 [× 60] oe
8(b)(i) Ruled straight line from 1
(10 40, 6) to (12 20, 6)
8(b)(ii) 1 [h] 40 [min] 1
8(c) Ruled straight line from (10 15, 10) 3 B1 for (10 15, 10) marked
to (10 55, 6) M1 for 4 ÷ 6 [× 60]
If 0 scored, then SC1
for straight line from (10 15, 0)
to (11 15, 6)
8(d) Ruled straight line from 2 FT
(their12 20, 6) to (12 45, 0) B1 for each
Ruled straight line from
(their 12 20, 6) to (12 50, 10)
(a) Maria spins a fair 7-sided spinner numbered 1 to 7.
2 3
1 4
7 5
6
4
Explain why the probability that the spinner lands on a prime number is .
7
[2]
(b) Maria spins the spinner a 2nd time.
1st spin 2nd spin
…… Prime
Prime
4
7
Not prime
…… Prime
Not prime
Not prime
(i) Complete the tree diagram. [2]
(ii) Work out the probability that the spinner lands on a prime number both times.
…… [2]
Mark scheme
9(a) Primes 2, 3, 5 and 7 and no others in the 2 B1 for each
explanation
There are 7 possible outcomes oe
9(b)(i) 4 2 B1 for 2, 3 or 4 correct
7 Prime
[ 47 ] Prime
3 Not Prime
7
4
7 Prime
3
7
Not Prime
3
7 Not Prime
9(b)(ii) 16 2 FT their tree diagram
oe
49
4 4
M1 for ×their
7 7
B
NOT TO
13.2 cm SCALE
4.5 cm
C
8.9 cm
A
The diagram shows a right-angled triangle, ABC, and a semicircle.
The radius of the semicircle is 4.5 cm.
AC = 8.9 cm and BC = 13.2 cm.
(a) Calculate the shaded area.
Give the units of your answer.
…… …… [5]
(b) Calculate AB.
AB = …… cm [2]
Mark scheme
10(a) 26.9 or 26.92 to 26.93….. 4 M3 for
0.5 × 8.9 × 13.2 – 0.5 × π × 4.52
oe
or M1 for 0.5 × 8.9 ×13.2
and M1 for 0.5 × π × 4.52
and M1 for subtraction of their
areas
cm2 1
10(b) 15.9 or 15.92[……] 2 M1 for 8.92 + 13.22 or better
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Mathematics 0580/31 for May/June 2023 is out of 104 marks, with 2 hours to answer it.
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