Mathematics 0580/31 October/November 2023: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), October/November 2023. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) Write the number six and a half million in figures.
…… [1]
(b) Write 37 508 correct to the nearest thousand.
…… [1]
(c) 6 9 100 28 31 1000 32 36
From this list of numbers, write down
(i) a factor of 18
…… [1]
(ii) a multiple of 12
…… [1]
(iii) a square number
…… [1]
(iv) a prime number
…… [1]
(v) an irrational number.
…… [1]
(d) Put one pair of brackets in each statement to make it correct.
(i) 24 - 4 # 3 + 2 = 62 [1]
(ii) 24 - 4 # 3 + 2 = 4 [1]
3
(e) Write as a decimal.
4
…… [1]
3
(f) Work out of 126.
7
…… [1]
(g) Write down the value of the reciprocal of 0.5 .
…… [1]
2 1
(h) Without using a calculator, work out 5 - 2 .
3 5
You must show all your working and give your answer as a mixed number in its simplest form.
…… [3]
Mark scheme
1(a) 6 500 000 1
1(b) 38 000 1
1(c)(i) 6 or 9 1
1(c)(ii) 36 1
1(c)(iii) 9 or 36 1
1(c)(iv) 31 1
1(c)(v) 1000 1
1(d)(i) (24 − 4) × 3 + 2 = 62 1
1(d)(ii) 24 − 4 × (3 + 2) = 4 1
1(e) 0.75 1
1(f) 54 1
1(g) 2 1
1(h) 17 11 B1 Correct step for dealing with mixed
or 17 k
3 5 11k
numbers, allow e.g. or
3k 5k
85 33 M1 FT Correct method to find a common
and denominator
15 15
3 157 cao A1
Alternative methods
2 1 10 3
3 − B1, and M1, 3 157 cao
3 5 15 15
A1
10 3
5 and 2 M1, 3 157 cao B1 A1
15 15
10 3
and M1, 3 157 cao B1A1
15 15
(a) The diagram shows a circle.
NOT TO
SCALE
(i) The diameter of this circle is 168 mm.
Write down the radius of this circle.
…… mm [1]
(ii) On the diagram, draw a chord of this circle. [1]
(b) The scale drawing shows the position of ship A and the position of ship B.
The scale is 1 cm represents 6 km.
North
B
North
A
Scale : 1 cm to 6 km
Another ship, C, is 45 km from ship B on a bearing of 124°.
(i) On the scale drawing, mark the position of ship C. [2]
(ii) Find the actual distance of ship C from ship A.
…… km [2]
(c) (i) Show that the interior angle of a regular octagon is 135°.
[1]
(ii)
NOT TO
SCALE
Show that two regular octagons and a square meet at a point without any gaps.
[1]
(d)
E
F NOT TO
49°
SCALE
D
The diagram shows points D, E and F on the circumference of a circle.
DF is a diameter of the circle.
Find angle EDF.
Angle EDF = …… [2]
Mark scheme
2(a)(i) 84 1
2(a)(ii) Any chord 1
2(b)(i) Accurate position marked 2 B1 for accurate distance or accurate angle
2(b)(ii) 57 2 FT their diagram for 1 and 2 marks
B1 for 9.2 to 9.6 seen
or M1 for their length × 6
2(c)(i)
180 –
360
or
( 8 − 2 ) × 180 M1
8 8
2(c)(ii) 135 + 135 + 90 = 360 M1
2(d) 41 2 M1 for 180 – 90 – 49 oe
or angle DEF identified as 90°
(a) The bar chart shows the country in which each of 80 students live.
24
20
16
Frequency 12
8
4
0
Australia Brazil China India USA
Country
(i) How many of these students live in Brazil?
…… [1]
(ii) In which country do the largest number of these students live?
…… [1]
(iii) How many more of these students live in China than live in Australia?
…… [1]
(iv) Find the percentage of these students who live in the USA.
…… % [2]
(b) In Hobart, the temperature at 8 am was -3 °C and the temperature at 3 pm was 7 °C.
(i) Find the difference in the temperatures between 8 am and 3 pm.
…… °C [1]
(ii) The temperature at 10 pm was 12 °C lower than at 3 pm.
Find the temperature at 10 pm.
…… °C [1]
(c) The table shows the favourite language that each of 80 students studies.
Language Frequency
French 12
Spanish 26
English 42
Total 80
Complete the pie chart to show this information.
[4]
Mark scheme
3(a)(i) 9 1
3(a)(ii) India 1
3(a)(iii) 7 1
3(a)(iv) 23.75 2 19
M1 for [× 100]
80
3(b)(i) 10 1
3(b)(ii) −5 1
3(c) Correct pie chart 4 B3 for 2 correct sectors
or B2 for 1 correct sector or for 54°, 117°
and 189°
360 k
or M1 for or 4.5 or × 360
80 80
(k = 12, 26 or 42)
(a) The diagram shows a cuboid.
NOT TO
2 cm
SCALE
3 cm
5 cm
(i) On the 1cm 2 grid, complete the net of the cuboid.
One face has been drawn for you.
[3]
(ii) Calculate the surface area of the cuboid.
…… cm 2 [2]
(b) The diagram shows two solids: a cube and a right-angled triangular prism.
NOT TO
SCALE
4 cm
6 cm 9 cm x cm
Both solids have the same volume.
Calculate the value of x.
x = …… [4]
Mark scheme
4(a)(i) Fully correct net 3 B2 for 3 or 4 extra correct faces in the
correct places
or B1 for 1 or 2 extra correct faces in the
correct places
4(a)(ii) 62 2 M1 for [2 ×] (5 × 2 + 3 × 2 + 5 × 3) oe
4(b) 12 4 M3 for 18x = 216 oe or 216 ÷ 18 oe
OR
M1 for 63 or 6 × 6 × 6 or 216
1
M1 for × 4 × x × 9 oe or 18x
2
M1 for their 18x = 216 oe or better
A railway line has three stations, Town, Port and Cove.
Train A leaves Town for Cove and train B leaves Cove for Town.
Both trains stop at Port.
25
Cove B
Distance from 20
Town (km)
15
Port
10
5
A
Town 0
14 00 14 10 14 20 14 30 14 40 14 50
Time
(a) Write down the time that train B leaves Cove.
…… [1]
(b) Write down how long train A stops at Port.
…… min [1]
(c) How many more minutes does train A take to complete the whole journey than train B?
…… min [2]
(d) Write down the time that the two trains pass each other.
…… [1]
(e) Work out the average speed of train A between Town and Cove in kilometres per hour.
…… km/h [3]
Mark scheme
5(a) 14 10 1
5(b) 4 1
5(c) 2 2 B1 for 40 or 38
5(d) 14 25 1
5(e) 34.5 3 23
M2 for × 60 oe
40
23
or M1 for
their time
y
10
9
8
7
6
5
4
A
3
2
1
B
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 x
-1
C
-2
-3
-4
-5
-6
(a) Describe fully the single transformation that maps triangle A onto triangle B.
…… [2]
(b) Describe fully the single transformation that maps triangle A onto triangle C.
…… [3]
(c) On the grid, draw the image of triangle A after a reflection in the line y = 6 . [2]
Mark scheme
6(a) Translation 2 B1 for each
2
−3
6(b) Enlargement 3 B1 for each
(sf = ) 3
(centre = ) (4, 6)
6(c) Correct reflection 2 B1 for correct reflection in line y = k
points (1, 7), (1, 9), (5, 9)
(a) Simplify.
5a + 3b + 2a - 4b
…… [2]
(b) P = 8x + 3y
Find the value of x when P = 21 and y =-5.
x = …… [2]
(c) Make v the subject of the formula S = kv 2 .
v = …… [2]
(d) Multiply out and simplify.
(x - 3) (x + 5)
…… [2]
(e) Nasser has x marbles.
Selina has 15 more marbles than Nasser.
Hanif has 3 times as many marbles as Selina.
In total they have 150 marbles.
Find the value of x.
x = …… [5]
Mark scheme
7(a) 7a – b final answer 2 B1 for 7a or –b in final answer or 7a – b
seen then spoilt
7(b) 4.5 2 M1 for 21 = 8x + 3 × −5 oe or better
7(c) S 2 S
final answer M1 for v 2 = or S = k ×v
k k
7(d) x2 + 2x – 15 final answer 2 B1 for three correct terms from
x2 – 3x + 5x – 15
7(e) 18 5 B1 for x + 15 or 3 × their (x + 15) oe
M1 for
x + their (x + 15) + their (3( x + 15)) =
150 or better
M1 for 5x + 60 = 150 or better
or their linear equation simplified to
ax + b = 150
M1 for their [ax + b = c]
150 − b
solved to x =
a
y
L
6
5
4
3
2
1
-3 -2 -1 0 1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
- 10
(a) Find the equation of line L in the form y = mx + c .
y = …… [2]
(b) (i) On the grid, draw the line y = x . [1]
(ii) Write down the coordinates of the point where the line y = x intersects line L.
( …… , …… ) [1]
8
(c) (i) Complete the table of values for y = . x
x −5 −4 −3 −2 −1 1 2 3 4 5 y −1.6 −2.7 2.7 1.6
[3]
8
(ii) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5. x
y
8
7
6
5
4
3
2
1
0 x
-5 -4 -3 -2 -1 1 2 3 4 5
-1
-2
-3
-4
-5
-6
-7
-8
[4]
Mark scheme
8(a) [y =] 2x − 5 final answer 2 B1 for answer of 2x + c or mx – 5 (m ≠ 0)
8(b)(i) Correct ruled line 1
8(b)(ii) (5, 5) 1 FT their ruled y = x
8(c)(i) −2 −4 −8 8 4 2 3 B2 for 3, 4 or 5 correct
or B1 for 1 or 2 correct
8(c)(ii) 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
(a) Pure gold costs $42 per gram.
The fraction of pure gold in an object is measured in carats.
1
One carat means of the mass of an object is pure gold.
24
Henry buys a 9-carat gold bracelet weighing 16 g.
The price of the bracelet is $204.
Is the price of the bracelet more or less than the cost of the pure gold in it?
You must show your working.
[4]
(b) A clock made of metals has a mass of 1080 g.
The mass of each metal in the clock is in the ratio copper : zinc : other metals = 21 : 14 : 1.
Calculate the mass of copper in this clock.
…… g [2]
(c) There are 110 people in a group.
G = { people who own gold jewellery }
S = { people who own silver jewellery }
18 people own both gold jewellery and silver jewellery.
46 people own gold jewellery.
11 people own no gold jewellery and no silver jewellery.
G S
(i) Complete the Venn diagram. [2]
(ii) Write down n (G + S ) .
…… [1]
(iii) One of the 110 people is chosen at random.
Write down the probability that this person owns gold jewellery but not silver jewellery.
…… [1]
(d)
E F
Use set notation to describe the shaded region.
…… [1]
Mark scheme
9(a) Less 4 1
with working leading to 252 M3 for × 9 × 16 × 42 oe
24
or
M2 for three of these multiplied
or
M1 for any two of these multiplied
9(b) 630 2 1080
M1 for [× k] oe
21 + 14 + 1
where k =1,14 or 21 oe
9(c)(i) 2 B1 for two or three in the correct places
9(c)(ii) 18 1 FT their diagram
9(c)(iii) 28 1 FT their 28 from their diagram
oe
110
9(d) E F cao 1
(a)
U
P
21.4 cm
14.4 cm
9.6 cm NOT TO
SCALE
Q 12.8 cm R V W
Triangle PQR is mathematically similar to triangle UVW.
Calculate VW.
VW = …… cm [2]
(b) ABC is a right-angled triangle.
A
NOT TO
9.1 cm SCALE
3.5 cm
B C
Calculate BC.
BC = …… cm [3]
(c) DEF is a right-angled triangle.
D
8.4 cm NOT TO
SCALE
35°
E F
Calculate EF.
EF = ……cm [2]
(d) JKL is a right-angled triangle.
J 10 cm
L
NOT TO
8 cm SCALE
K
Calculate angle JKL.
Angle JKL = …… [2]
Mark scheme
10(a) 19.2 2 14.4 VW
M1 for = oe or better
9.6 12.8
10(b) 8.4 3 M2 for 9.12 – 3.52 oe or better
or M1 for […]2 + 3.52 = 9.12 oe or better
10(c) 6.88 to 6.881 2 [...]
M1 for cos35 = oe or better
8.4
or sin 55 =
[] oe or better
8.4
10(d) 51.3[4…] 2 10
M1 for tan[… =] oe or better
8
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Mathematics 0580/31 for October/November 2023 is out of 104 marks, with 2 hours to answer it.
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