Mathematics 0580/31 May/June 2024: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), May/June 2024. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) The cost of a cinema ticket is $6.30 .
(i) Work out the total cost of 4 tickets.
$ …… [1]
(ii) The cinema sells 10 tickets for the price of 9 tickets.
A group of 10 people go to the cinema.
Work out how much each person must pay.
$ …… [2]
(b) The cinema has 650 seats.
(i) There are 26 seats in each row.
Work out the number of rows.
…… [1]
(ii) 84% of the seats are occupied.
Work out how many seats are not occupied.
…… [2]
(c) Suki buys a bag of popcorn and a bottle of water.
A bag of popcorn costs twice as much as a bottle of water.
She receives $3.55 change from $10.
Work out the cost of a bag of popcorn and the cost of a bottle of water.
Bag of popcorn $ ……
Bottle of water $ …… [3]
(d) (i) A film lasts for 155 minutes.
Write 155 minutes in hours and minutes.
…… hours …… minutes [1]
(ii) Another film starts at 14 45 and lasts for 2 hours and 20 minutes.
Work out the time that this film finishes.
…… [1]
(e) The table shows the hours that Trevor works in the cinema each week.
Monday No hours
Tuesday No hours
Wednesday 18 00 to 22 00
Thursday 18 00 to 22 00
Friday 12 00 to 17 30
Saturday 12 00 to 17 30
Sunday 13 00 to 18 00
Trevor is paid $11.50 per hour for the time he works before 18 00.
He is paid 30% more for the time he works after 18 00.
Work out how much Trevor is paid each week.
$ …… [4]
Mark scheme
1(a)(i) 25.2[0] 1
1(a)(ii) 5.67 2 M1 for 9 × 6.3[ ÷10] oe
1(b)(i) 25 1
1(b)(ii) 104 2 84
M1 for 650 × 1 − oe
100
or B1 for 546
1(c) 4.3[0] 2.15 3 B2 for 4.3[0] or 2.15 in correct place
or for both correct in the reverse order.
10 − 3.55
or M1 for [×k ] oe k = 1 or 2
3
1(d)(i) 2 [hours] 35 [minutes] 1
1(d)(ii) 1705 1
1(e) 303.6[0] 4 M3 for (4+4+5.5+5.5+5)×11.5
30
+ (4+4)× ( × 11.5 ) oe
100
OR
B2 for 59.8 (or 119.6) or 63.25 (or 126.5) or
57.5 or 184 or 276 or 27.6 seen
OR
M1 for 4 + 4 + 5.5 + 5.5 + 5 oe
or 4 + 4 oe and 5.5 + 5.5 + 5 oe
and
30
M1 for × 11.5 oe
100
30
or 1 + × 11.5 oe
100
(a) Chen asks some people if they prefer a beach, cruise, lake or mountain holiday.
The pie chart shows the results.
Mountain Beach
120° 135°
75°
30°
Lake
Cruise
(i) Find the fraction of people who prefer a mountain holiday.
Give your answer in its simplest form.
…… [2]
(ii) Find the percentage of people who prefer a beach holiday.
…… % [1]
(iii) Find the ratio of people who prefer each type of holiday in the form
beach : cruise : lake : mountain.
Give your answer in its simplest form.
…… : …… : …… : …… [2]
(iv) One person is chosen at random.
Find the probability that this person prefers a cruise or a lake holiday.
…… [2]
(v) 675 people prefer a beach holiday.
Show that the total number of people Chen asks is 1800.
[1]
(vi) (a) Complete the table.
Type of holiday Pie chart sector angle Frequency
Beach 135° 675
Cruise 30° 150
Lake 75°
Mountain 120°
[2]
(b) Complete the bar chart, including the scale on the frequency axis.
Frequency
0
Beach Cruise Lake Mountain
[3]
(b) Mr Gibb pays $2208 for a holiday.
Mr Shah pays 2050 euros for the same holiday.
The exchange rate is 1 euro = $1.15 .
Work out how much more, in euros, Mr Shah pays for the holiday than Mr Gibb.
…… euros [2]
Mark scheme
2(a)(i) 1 2 120
cao M1 for oe
3 360
2(a)(ii) 37.5 1
2(a)(iii) 9 : 2 : 5 : 8 cao 2 B1 for 135 : 30 : 75 : 120 or better
2(a)(iv) 105 2 75 + 30
oe M1 for oe
360 360
2(a)(v) 675 × 360 1
[ = 1800]
135
2(a)(vi)(a) 375 2 B1 for each
600
2(a)(vi)(b) A correct bar chart drawn with 3 B1 for an appropriate linear scale written
linear scale labelled. with at least 2 more numbers.
AND
B2FT their table for 4 bars drawn correctly
or
B1FT their table for two or three bars drawn
correctly
2(b) 130 2 2208 2050 ×1.15 − 2208
M1 for oe or oe
1.15 1.15
(a) Here is part of the timetable for trains from Hinton to Jarmouth.
All trains take the same time to travel from Hinton to Jarmouth.
Hinton 10 47 ……
Jarmouth 11 15 12 35
(i) Complete the timetable. [2]
(ii) Marge arrives at Hinton station exactly 20 minutes before the 10 47 train leaves.
12
11 1
10 2
9 3
8 4
7 5
6
Complete the clock diagram to show the time she arrives at Hinton station. [1]
(b) Each day, a bus leaves Texford to travel to Cranbrook every 45 minutes.
The first bus leaves Texford at 07 10.
The last bus leaves Texford at 22 10.
Work out the number of buses that travel from Texford to Cranbrook each day.
…… [3]
(c) The cost of a bus pass increases every year.
On 1st January 2022 a bus pass costs $50.
On 1st January 2023 the cost of the bus pass increases by 10%.
On 1st January 2024 the cost of the bus pass increases by 5%.
Calculate the cost of the bus pass on 1st January 2024.
$ …… [3]
(d) The Venn diagram shows information about the number of workers in a hotel who travel to work by bus (B) and train (T).
B T
31 9 85
107
(i) Work out the number of workers in the hotel.
…… [1]
(ii) Work out n (B , T ) .
…… [1]
(iii) Explain in words what the number 85 in the Venn diagram represents.
…… [1]
(iv) One of the workers is chosen at random.
Find the probability that this worker travels to work by bus and train.
…… [1]
(e) The hotel has single and double bedrooms in the ratio single | double = 3 | 8 .
There are 75 more double rooms than single rooms.
Work out the number of single rooms.
…… [2]
Mark scheme
3(a)(i) 12 07 2 B1 for 1 [hour] 20 [min] or 80[min]
or 28 [min] seen
3(a)(ii) 10 27 drawn correctly on clock 1
face.
3(b) 21 3 B2 for 20 as final answer
22 :10 − 07 :10
or M2 for × 60 oe
45
or M1 for ( 22 :10 − 07 :10 ) × 60 oe
3(c) 57.75 3 10 5
M2 for 50 × 1 + 1 + oe
100 100
or B2 for 1.155
10
or M1for 50 × 1 + oe
100
5
or 50 × 1 + oe
100
5
or their 55 × 1 + oe
100
10 5
or 1 + 1 + oe
100 100
3(d)(i) 232 1
3(d)(ii) 125 1
3(d)(iii) The number of workers who travel 1
to work by train but who do not
travel on a bus oe.
3(d)(iv) 9 1 FT their 3(d)(i) in denominator.
oe
232
3(e) 45 2 75
M1 for × k oe k = 1, 3, 8
8−3
The stem-and-leaf diagram shows the ages of the 16 workers in a shop on 1st January 2022.
2 3 5 7
3 4 6 6 6 9
4 1 1 7
5 0 7 7 8
6 1
Key: 2 5 represents 25
(a) (i) Work out the range.
…… [1]
(ii) Write down the mode.
…… [1]
(iii) Work out the median.
…… [1]
(iv) Work out the percentage of workers that are older than 40 but younger than 60.
…… % [2]
(b) On 1st January 2023 the shop has the same 16 workers.
Write down the range, the mode and the median on 1st January 2023.
Range ……
Mode ……
Median …… [2]
(c) On 1st January 2024 the oldest worker leaves.
His replacement is a new worker born on 12th November 1970.
There are no other changes to the workers.
Complete the stem-and-leaf diagram for 1st January 2024.
2 5 7 9
3 6 8 8 8
4
5
6
Key: 2 5 represents 25
[2]
(d) The shop owner is x years old.
x is a prime number. x + 2 is a square number. x - 2 is a multiple of 9.
Find the value of x.
x = …… [2]
Mark scheme
4(a)(i) 38 1
4(a)(ii) 36 1
4(a)(iii) 40 1
4(a)(iv) 43.75 2 7
M1 for
16
their 7
or correctly converted to a %.
16
4(b) 38 2 FT their (a)(i), (a)(ii) + 1, (a)(iii) + 1
37 B1FT for one or two correct
41
4(c) 2 B1 for 53 seen
2 [5 7 9] or for stem and leaf with no more than 2
errors or omissions.
3 [6 8 8 8]
4 1 3 3 9
5 2 3 9 9
6 0
4(d) 47 2 B1 for a final answer satisfying 2 of the 3
conditions.
(a)
H F I
NOT TO f°
105° SCALE
e° 52°
E G
The diagram shows a triangle EFG and a straight line HFI.
HFI is parallel to EG.
(i) Angle EFG = 105° .
Write down the mathematical name for this type of angle.
…… [1]
(ii) Work out the value of e.
Give a geometrical reason for your answer.
e = …… because ……
…… [2]
(iii) Find the value of f.
Give a geometrical reason for your answer.
f = …… because ……
…… [2]
(b) Calculate the interior angle of a regular 7-sided polygon.
Give your answer correct to 2 decimal places.
…… [3]
(c) The diagram shows a regular pentagon with sides 15 cm.
(2w) cm 5(x + 7) cm
NOT TO
SCALE
15 cm (w + x + y) cm
15 cm
Work out the values of w, x and y.
w = ……
x = ……
y = …… [5]
Mark scheme
5(a)(i) obtuse 1
5(a)(ii) 23 2 B1 for each
angles in a triangle add to 180
5(a)(iii) 52 2 B1 for each
alternate
5(b) 128.57 cao 3 B2 for 129 or 128.5 to 128.6
OR
M1 for 180 −
360
oe or
( 7 − 2 ) × 180 oe
7 7
B1 for their value seen, to at least 3dp,
rounded correctly to 2dp as final answer
5(c) 7.5 5 B1 for [ w =] 7.5
–4
11.5
B2 for [ x = ] − 4
or M1 for x + 7 = 3 or better
or 5 x = 15 − 5 × 7 or better
B2 for [ y =]11.5
or M2 for 15 − their w − their x correctly
evaluated
or M1 for their w + their x + y = 15
The diagram shows a point, P, three triangles, A, B and C, and part of triangle D on a 1 cm 2 grid.
y
10
9
D
8
7
6
5
4
3
A
2 a
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 x
–1
B
–2
–3
C
– 34
P
–5
–6
(a) On the grid, mark the image of point P after a reflection in the line y = 0 . [1]
(b) Use trigonometry to calculate angle a.
Angle a = …… [2]
(c) Describe fully the single transformation that maps
(i) triangle A onto triangle B
…… [3]
(ii) triangle A onto triangle C.
…… [2]
(d) Triangle A has been enlarged with centre (1, 0) to give triangle D.
The grid is only large enough to show one vertex and part of two of the sides of triangle D.
(i) Write down the scale factor of the enlargement.
…… [1]
(ii) Find the coordinates of the other two vertices of triangle D.
( …… , …… ) and ( …… , …… ) [2]
Mark scheme
6(a) P plotted at (13,4) 1
6(b) 36.9 or 36.86 to36.87 2 3
M1 for tan [ a =] oe
4
3 4
or sin [ a =] or cos [ a =] oe
5 5
6(c)(i) Rotation 3 B1 for each
[centre] (0,0)
90° clockwise
6(c)(ii) Translation 2 B1 for each
6
−5
6(d)(i) 7 1
6(d)(ii) (1,28), (29,7) 2 B1FT for each
(a) The scale drawing shows the position of a castle, C.
The scale is 1 centimetre represents 2 kilometres.
North
C
Scale: 1 cm to 2 km
Micah walks at 4.8 km/h for 3 hours on a bearing of 236° from C, to his house, H.
Mark the position of H on the scale drawing.
[3]
(b) A restaurant, R, is on a bearing of 083° from C.
(i) Work out the bearing of C from R.
…… [2]
(ii) The distance, d km, from R to C is 5 km, correct to the nearest kilometre.
Complete this statement about the value of d.
…… G d 1 …… [2]
(c) A model of the castle is made.
On the model, the length of one of the castle walls is 5 centimetres.
The actual length of the wall is 90 metres.
Find the scale of the model in the form 1 | n .
1 | …… [2]
(d) The castle has two kitchens with rectangular floors.
F G
B C
NOT TO
5.6 m 9.2 m SCALE
A 8.4 m D
E xm H
Rectangle ABCD is mathematically similar to rectangle EFGH.
Calculate the value of x.
x = …… [2]
(e) The castle has a cylindrical tower.
The tower has a radius of 2.4 m and a height of 25 m.
Calculate the curved surface area of the tower.
Give the units of your answer.
…… …… [3]
Question 8 is printed on the next page.
Mark scheme
7(a) H correctly marked 3 B2 for H 7.2 cm from C
7.2 cm from C on bearing 236° or M1 for 4.8×3
B1 for H on bearing 236 from C
7(b)(i) 263 2 M1 for 83 + 180 oe
or indicates correct angle on diagram
7(b)(ii) 4.5 5.5 2 B1 for each
If 0 scored SC1 for both correct but reversed
7(c) [1 : ] 1800 2 M1 for 5 : 9000 or 0.05:90
9000 90
or or
5 0.05
or B1 for answer figs 18
7(d) 13.8 2 9.2 5.6
M1 for = oe or better
x 8.4
7(e) 377 or 376.9 to 377.04 2 M1 for 2π × 2.4 × 25
m2 1
The table shows some values for y = x 2 - x - 3.
x -3 -2 -1 0 1 2 3 4 y -1 -1 9
(a) Complete the table. [3]
(b) On the grid, draw the graph of y = x 2 - x - 3 for - 3 G x G 4 . y
9
8
7
6
5
4
3
2
1
–3 –2 –1 0 1 2 3 4 x
–1
–2
–3
–4 [4]
(c) Write down the coordinates of the lowest point on the graph.
( …… , …… ) [1]
(d) Use your graph to solve the equation x 2 - x - 3 = 7 .
x = …… or x = …… [2]
Mark scheme
8(a) 9, 3, −3, −3, 3 3 B2 for 3 or 4 correct
or B1 for 1 or 2 correct
8(b) Completely correct curve 4 B3FT for 7 or 8 correctly plotted points
or B2FT for 5 or 6 correctly plotted points
or B1FT for 3 or 4 correctly plotted points
8(c) ( 0.5, k ) −3.6 k < −3 1
8(d) 3.7 −2.7 2 B1FT for each
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