Mathematics 0580/31 October/November 2024: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), October/November 2024. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) Write the number six million and thirty in figures.
…… [1]
(b) Write 7.896 correct to 2 decimal places.
…… [1]
(c)
8 24 25 36 39 41 48
From this list of numbers, write down
(i) a multiple of 16
…… [1]
(ii) a factor of 24
…… [1]
(iii) a cube number
…… [1]
(iv) a prime number.
…… [1]
(d) Put one pair of brackets into this calculation to make it correct.
10 - 12 ' 4 + 2 = 8
[1]
(e) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of
596 # 0.047
.
8.65
You must show all your working.
…… [2]
(f) Calculate (8 # 10 6) # (3 # 10 -2) .
Give your answer in standard form.
…… [2]
(g) 216 = 2 3 # 3 3
Write 2160 as a product of its prime factors.
…… [1]
Mark scheme
1(a) 6 000 030 1
1(b) 7.90 cao 1
1(c)(i) 48 1
1(c)(ii) 8 or 24 1
1(c)(iii) 8 1
1(c)(iv) 41 1
1(d) 10 – 12 ÷ (4 + 2) 1
1(e) 600 × 0.05 M1
9
10 A1 If 0 scored SC1 for 2 correct roundings
or for all correct but with any trailing
zeros
1(f) 2.4 × 105 2
B1 for correct value but not in standard
form
1(g) 24 × 33 × 5 1
(a) In the diagram, BCG is a triangle.
ABCD and EF are parallel lines.
NOT TO
G SCALE
z°
E y° F
38°
x° 69°
A B C D
(i) Find the value of x.
Give a geometrical reason for your answer.
x = …… because …… [2]
(ii) Find the value of y.
Give a geometrical reason for your answer.
y = …… because ……
…… [2]
(iii) Find the value of z.
z = …… [2]
(b)
X
NOT TO
SCALE
T
S O
Y
R
R, S and T are points on a circle, centre O.
Line XY touches the circle at T.
(i) Write down the mathematical name for the line XY.
…… [1]
(ii) Write down the mathematical name for the line SR.
…… [1]
(iii) Toby thinks shape RST is a right-angled triangle.
Give a geometrical reason why Toby is incorrect.
…… [1]
Mark scheme
2(a)(i) 38 2 B1 for each
Alternate [angles]
2(a)(ii) 69 2 B1 for each
Corresponding [angles]
2(a)(iii) 31 2 FT for their (a)(ii) – their (a)(i)
or their (a)(ii) – 38 or 69 – their (a)(i)
B1 for BCG = 111
or M1 for 180 – 69 oe
or for 180 – their (a)(ii) oe
or for 38 + 111 oe
2(b)(i) Tangent 1
2(b)(ii) Chord 1
2(b)(iii) None of the sides of the triangle is a 1
diameter of the circle oe
Jack does a survey about cycling.
(a) The bar chart shows the percentage of people in each age group who use a bicycle.
100%
80%
60%
Percentage of people
40%
20%
0%
0–9 10–19 20–29 30–39 40–49 50–59 60–69 70+
Age in years
(i) Write down the percentage of people aged 60 to 69 who use a bicycle.
…… % [1]
(ii) 980 people in the survey are in the 30–39 age group.
Work out how many of these people use a bicycle.
…… [2]
(b) Jack makes 18 cycling trips in one year.
Each cycling trip lasts 23 minutes.
Find the total time Jack spends cycling in this year.
Give your answer in hours and minutes.
…… h …… min [2]
(c) The table shows where 240 people cycle the most.
Pie chart
Number of people sector angle
Roads 84 126°
Cycle paths 72
Parks 48
Other 36
(i) Complete the table. [2]
(ii) Complete the pie chart to show this information.
Roads
126°
[2]
(d) A bicycle costs $720.
Carlo pays one-fifth of the cost as a deposit.
He pays the rest of the money in equal monthly payments of $16.
Work out how many monthly payments Carlo makes.
…… [3]
Mark scheme
3(a)(i) 30 1
3(a)(ii) 392 2 40
M1 for × 980 oe
100
3(b) 6 hours 54 mins 2 M1 for 18 × 23 oe
3(c)(i) 108 2 B1 for 1 correct angle in correct place
72 126
54 or M1 for [×k ] where k = 1, 72, 48
84
or 36
360
or for [×m] where m = 1, 72, 48 or 36
240
3(c)(ii) Correct pie chart 2 FT their table if angles add up to 360°
B1FT for one sector drawn correctly
3(d) 36 nfww 3 4
M2 for × 720 ÷ 16 oe
5
4 720
or M1 for × 720 or oe
5 5
or k ÷ 16 , k ≠ 720
(a) A parallelogram ABCD has sides 8 cm and 6 cm.
Lines AB and BC have been drawn.
By constructing triangle ACD, complete the parallelogram.
Use a ruler and compasses only and leave in your construction arcs.
A
6 cm
B 8 cm C
[2]
(b)
y
7
6
5
B
4
3
A
2
1
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x
–1
–2
–3
–4
–5
–6
(i) Describe fully the single transformation that maps shape A onto shape B.
…… [2]
(ii) On the grid, draw the image of shape A after a rotation, 90° anticlockwise, centre (5, 1). [2]
Mark scheme
4(a) Correct parallelogram 2
B1 for triangle constructed onto given
pair of lines with one correct and one
incorrect arc
or correct triangle with no arcs
or for no triangle but two correct arcs
only.
If 0 scored SC1 for triangle constructed
onto given pair of lines with arcs but
lines interchanged
4(b)(i) Translation 2 B1 for each
−6
2
4(b)(ii) Correct shape with coordinates 2 B1 for correct 90 clockwise rotation
(5, 1) (5, –3) (2, –3) (2, –1) (4, –1) (4, 1) about (5, 1)
or correct orientation, wrong centre
(a) The scatter diagram shows the distance travelled and the cost for each of 12 taxi journeys.
25
20
15
Cost ($)
10
5
0
0 2 4 6 8 10
Distance (km)
(i) ‘The scatter diagram shows positive correlation.’
Is this statement true or false?
Give a reason for your answer.
…… because ……
…… [1]
(ii) On one journey, the cost per kilometre travelled was much more expensive than on all of the other journeys.
Draw a ring around this point on the scatter diagram. [1]
(iii) Draw a line of best fit on the scatter diagram. [1]
(iv) Another journey is 8 km long.
Use your line of best fit to find an estimate for the cost of this journey.
$ …… [1]
(b) Arit, Luke and Marie share the cost of a taxi journey.
The cost is $26.40 .
(i) Calculate how much Arit pays if they share the cost equally.
$ …… [1]
(ii) They decide to share the cost in proportion to the distance they each travel in the taxi.
Arit travels 12 km, Luke travels 3 km and Marie travels 7.5 km.
(a) Write the ratio 12 : 3 : 7.5 in its simplest form.
…… : …… : …… [2]
(b) Calculate how much more Arit pays than if they share the cost equally.
$ …… [3]
(c) Jin invests some money from his taxi company.
He invests $18 600 at a rate of 1.7% per year compound interest.
Calculate the value of the investment at the end of 6 years.
Give your answer correct to the nearest dollar.
$ …… [3]
Mark scheme
5(a)(i) True and correct description of 1
correlation
e.g. as the distance increases the cost
increases
5(a)(ii) (1, 15) circled 1
5(a)(iii) Acceptable ruled line of best fit drawn 1
5(a)(iv) 16 to 19 1 If 0 scored, FT their straight line of best
fit with positive gradient
5(b)(i) 8.8[0] 1
5(b)(ii)(a) 8:2:5 2 M1 for any correct equivalent ratio
5(b)(ii)(b) 5.28 3 B2 for 14.08
26.40
or M1 for ×m
12 + 3 + 7.5
where m = 1, 3 ,7.5 or 12
or M1FT for
26.40
×k
(their 8 + their 2 + their 5)
where k = 1 or their 8 or their 2 or their 5
oe
5(c) 20 580 cao 3 B2 for answer 20 579.68[…] or 20
579.7[0] or 20 600[.00]
6
1.7
or M1 for 18 600 1 + oe
100
B1 for their answer correctly rounded
(a) This is a recipe to make ice cream for 6 people.
270 ml cream
270 ml milk
100 g sugar
4 egg yolks
Tom makes ice cream for 10 people.
(i) Work out how much milk he uses.
…… ml [2]
(ii) The mass of all the ingredients Tom uses is 1100 g.
After Tom heats the mixture, this mass reduces by 15%.
Find the mass of the mixture after heating.
…… g [2]
(iii) Tom lets the mixture cool to 5°C.
He then puts it into a freezer to cool to -18°C.
Find the difference in these temperatures.
…… °C [1]
(b) (i) In a factory, a machine fills 25 920 tubs of ice cream in 8 hours.
Work out the number of tubs the machine fills in 1 minute.
…… [1]
(ii) A pack of ice cream contains 6 tubs.
There are 120 packs on a tray.
There are 24 trays on a truck.
Work out how many tubs of ice cream are on the truck.
…… [1]
(c) Mario sells ice creams in five flavours.
The table shows the relative frequency of some of the ice cream flavours Mario sells.
Vanilla Chocolate Strawberry Coconut Banana
Relative
0.34 0.18 0.12 frequency
Mario sells three times as many chocolate ice creams as banana ice creams.
(i) Complete the table.
[3]
(ii) One week Mario sells 450 ice creams.
Find how many strawberry ice creams Mario expects to sell.
…… [1]
(iii) The probability that any customer is an adult is 0.7 .
First customer Second customer
Adult
0.7
Adult
0.7
…… Child
0.7 Adult
…… Child
…… Child
(a) Complete the tree diagram. [1]
(b) Find the probability that the first two customers are adults.
…… [2]
Mark scheme
6(a)(i) 450 2 270
M1 for [×10] oe
6
6(a)(ii) 935 2 15
M1 for 1100 × 1 − oe
100
or B1 for 165
6(a)(iii) 23 1
6(b)(i) 54 1
6(b)(ii) 17 280 1
6(c)(i) 0.27 oe 3 B2 for either 0.27 oe or 0.09 oe in any
0.09 oe position in the table
or M1 for 1 – ( 0.34 + 0.18 + 0.12) oe or
better
6(c)(ii) 81 1
6(c)(iii)(a) Correct complete tree diagram: 1
0.3
0.3
0.3
6(c)(iii)(b) [0].49 oe 2 M1 for [0].7 × [0].7 oe
(a)
NOT TO
10 cm SCALE
4 cm
7 cm
Find the perimeter of the triangle.
…… cm [1]
(b) The diagram shows a shape made from rectangles.
18.6 cm
4 cm
NOT TO
7 cm 7 cm SCALE
13.5 cm
Calculate the area of the shape.
…… cm2 [3]
(c) The diagram shows a right-angled triangle ABC.
B
NOT TO
27.2 cm SCALE
A 24 cm C
Calculate the area of the triangle.
…… cm2 [5]
(d) Calculate the volume of a sphere with diameter 5.25 cm.
4
[The volume, V, of a sphere with radius r is V = rr 3.]
3
…… cm3 [2]
Mark scheme
7(a) 21 1
7(b) 118.1 cao 3
M2 for 18.6 × 4 + (13.5 – 4) × (18.6 –7 –
7) oe
or 2 × 4 × 7 + 13.5 × (18.6 –7 –7) oe
or 18.6 × 13.5 – 2 ×7 × (13.5 – 4) oe
or 2×4×7+ (13.5–4)×(18.6–7–7)+ (18.6–
7–7)×4
oe
or B1 for 9.5 or 4.6 seen
7(c) 153.6 cao 5 B3 for 12.8
or M2 for 27.22 – 242 oe
or M1 for AB2 + 242 = 27.22 oe
AND
M1 for 0.5 × 24 × their AB oe
7(d) 75.8 or 75.76 to 75.78 2
3
4 5.25
M1 for ×π × oe
3 2
(a) The diagram shows the net of a solid.
10 cm
x cm NOT TO
SCALE x cm
(i) Write down the mathematical name of the solid.
…… [1]
(ii) Find the volume of the solid when x = 4 .
…… cm3 [2]
(iii) Write down an expression, in terms of x, for the volume of the solid.
…… cm3 [1]
(iv) Find the value of x when the volume of the solid is 360 cm3.
x = …… [2]
(b) (i) Complete the table of values for y = 2x 2 + x .
x 0 1 2 3 4 5 y 0 3 10
[2]
(ii) On the grid, draw the graph of y = 2x 2 + x for 0 G x G 5.
y
60
50
40
30
20
10
0
0 1 2 3 4 5 x
[3]
(iii) Use your graph to solve the equation 2x 2 + x = 30 for 0 G x G 5.
x = …… [1]
Mark scheme
8(a)(i) Cuboid 1
8(a)(ii) 160 2 M1 for 4 × 4 × 10 oe
8(a)(iii) 10x2 oe final answer 1
8(a)(iv) 6 nfww 2 M1 for 10x2 = 360 oe or better
or their (a)(iii) = 360 oe or better
or 360 ÷10
8(b)(i) 21, 36, 55 2 B1 for 2 correct
8(b)(ii) Correct smooth curve 3
B2FT for 5 or 6 points correctly plotted
or B1FT for 3 or 4 points correctly
plotted
8(b)(iii) 3.5 to 3.7 1 FT their value of x when y = 30
Samir leaves home at 2 pm.
He jogs 6 km to a café at a constant speed of 8 km per hour.
He stops to rest for 1 hour.
He then walks back home at a constant speed and arrives at 4.36 pm.
(a) On the grid, draw a travel graph to show Samir’s whole journey.
8
7
Café 6
Distance 5 from home
(km) 4
3
2
1
0
2 pm 2.30 pm 3 pm 3.30 pm 4 pm 4.30 pm 5 pm
Time
[3]
(b) Calculate Samir’s average speed for the whole journey.
…… km/h [3]
Mark scheme
9(a) Three correct ruled lines 3
B1 for a line from (2pm, 0) to (2 45, 6)
B1FT for a line from (their 2 45, their 6)
to
(their 2 45 + 1, their 6)
B1FT for a line from (their 2 45 + 1,
their 6)
to (4 36, 0)
9(b) 4.62 or 4.615… 3
12
M2 for × 60 oe
156
or M1 for 12 ÷ their time
(a) Solve.
4x - 7 = 3
x = …… [2]
(b) Simplify.
2
(i) `x 6j
…… [1]
(ii) `5x 3 y 4j # `2 x 2 y 2j
…… [2]
(c) Expand and simplify.
(i) 4a + 5 - 2 (a - 1)
…… [2]
(ii) (d + 7) (d - 3)
…… [2]
Mark scheme
10(a) 2.5 oe 2 7 3
M1 for 4x = 3 + 7 or for x − = oe
4 4
10(b)(i) x12 final answer 1
10(b)(ii) 10x5y6 final answer 2 B1 for two of 10, x5, y6 correct in final
answer
or for 10x5y6 seen then spoilt
10(c)(i) 2a + 7 final answer 2 B1 for 2a or + 7 seen in final answer
or for 2a + 7 seen then spoilt
10(c)(ii) d 2 + 4d – 21 final answer 2 B1 for d 2 + 7d – 3d – 21 with at least 3
terms correct
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Mathematics 0580/31 for October/November 2024 is out of 104 marks, with 2 hours to answer it.
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