Mathematics 0580/33 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) (i) Li has $20.
A box of cereal costs $2.29 .
Work out the maximum number of boxes of cereal that Li can buy.
…… [2]
(ii) Each box of cereal has mass 615 g.
Work out the total mass of 5 boxes of cereal.
Give your answer in kilograms.
…… kg [2]
(iii) The box of cereal is a cuboid.
The cuboid measures 25 cm by 20 cm by 5 cm.
Work out the volume of the cuboid.
…… cm 3 [1]
(b) A cereal bar is in a box.
The box is a cuboid measuring 6 cm by 3 cm by 1 cm.
6 cm NOT TO
SCALE
1 cm
3 cm
On the 1 cm 2 grid, complete a net of the cuboid.
One face has been drawn for you.
[3]
(c) The cereal contains fat, protein, carbohydrate and fibre.
The pie chart shows the information about the masses of fat and protein.
Fat
36° Protein
(i) Work out the percentage of the mass of the cereal that is fat.
…… % [1]
(ii) 60% of the mass of the cereal is carbohydrate.
Complete the pie chart.
[2]
(iii) Work out the mass of protein in 30 g of the cereal.
…… g [2]
Mark scheme
1(a)(i) 8 2 M1 for 20 ÷ 2.29
1(a)(ii) 3.075 2 M1 for 615 × 5
1(a)(iii) 2500 1
1(b) Fully correct net 3 B2 for 3 or 4 correct extra faces in correct
place
B1 for 1 or 2 correct extra faces in correct
place
1(c)(i) 10 1
1(c)(ii) Correct pie chart 2 B1 for 216º soi
1(c)(iii) 5.67 5.666 to 5.67 2
B1 for 68
OR
k
M1 FT for × 30 oe
360
(a) Write the number 845 024 in words.
…… [1]
(b) Write these numbers in order, starting with the smallest.
7 15
39% 0.388
18 40
…… 1 …… 1 …… 1 …… [2]
smallest
(c) Find the value of
(i) 45
…… [1]
(ii) 60
…… [1]
(iii) 16 # 49 .
…… [1]
(d) Solve.
6x + 5 = 29
x = …… [2]
(e) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of
2.7 # 42.4
.
8.6 - 4.3
You must show all your working.
…… [2]
(f) 3 5 # 3 x = 3 20
Find the value of x.
x = …… [1]
(g) Simplify (x 4) 3 .
…… [1]
(h) A boat to town A leaves a port every 16 minutes.
A boat to town B leaves the same port every 34 minutes.
Both boats leave the port at 07 30.
Work out the next time both boats leave the port together.
…… [3]
Mark scheme
2(a) Eight hundred and forty five thousand 1
and twenty four
2(b) 15 7 2
0.388 39%
40 18
B1 for 3 in the correct order
Or M1 for 0.389 or 0.3888 or 0.3889
and 0.39
and 0.375
2(c)(i) 1024 1
2(c)(ii) 1 1
2(c)(iii) 28 1
2(d) 4 2 5 29
M1 for 6x = 29 – 5 or x + = oe
6 6
2(e) 3× 40 M1
9 –4
24 A1 If 0 scored SC1 for 3 correct from 3, 40,
9 and 4 or for all correct but with trailing
zeros
2(f) 15 1
2(g) x12 1
2(h) 12 02 3
B2 for 272 or 4 h 32 mins
or M1 for 272k
or 2 × 2 × 2 × 2 × 17 oe
or [16 = ] 2 × 2 × 2 × 2 and [34 = ] 2 × 17
or 2 correct factor trees/tables of both 16
and 34
OR
M2 for listing times/multiples of both 16
and 34 to at least 1202 or 272
or M1 for listing at least the next 2 of
each or 1 full list
(a)
A wedding invitation is in the shape of a rectangle.
Draw the lines of symmetry on this rectangle. [2]
(b) There are 98 adults and 56 children at the wedding.
Find the fraction of people who are children.
Give your fraction in its simplest form.
…… [2]
(c) The wedding meal starts at 13 15 and lasts for 2 hours 50 minutes.
Find the time the meal ends.
…… [1]
(d) The probability that it will rain at the wedding is 0.12 .
Find the probability that it will not rain.
…… [1]
(e) (i) These are the ages of the staff at the wedding.
16 24 39 28 17 48 31 33 17 29 40 25
Complete the stem-and-leaf diagram.
1
2
3
4
Key: 1|6 represents 16
[2]
(ii) Find the range.
…… [1]
Mark scheme
3(a) 2 correct lines only 2 B1 for one correct line with no extras or
2 correct and 1 extra
3(b) 4 2 M1 for 98 + 56
cao
11
3(c) 16 05 1
3(d) 0.88 1
3(e)(i) 1 6 7 7 2 B1 for two or three rows correct or a fully
2 4 5 8 9 correct unordered stem-and-leaf diagram
3 1 3 9
4 0 8
3(e)(ii) 32 1 FT their (e)(i) dep. on an ordered table
(a) n = 15r + 20c
Find the value of r when n = 180 and c = 3.
r = …… [2]
(b) Factorise completely.
20p 2 q - 5p
…… [2]
(c) Apples cost 35 cents each and bananas cost 14 cents each.
Write down an expression for the total cost, in cents, of x apples and y bananas.
…… cents [2]
(d) Solve the simultaneous equations.
You must show all your working.
8x + 3y = 59
5x + 7y = 83
x = ……
y = …… [4]
Mark scheme
4(a) 8 2 M1 for 180 = 15r + 20 × 3 or better
4(b) 5p (4pq – 1) 2 B1 for 5 (4p2q – p) or p (20pq – 5)
or 5p (4pq – 1) seen then spoilt
4(c) 35x + 14y 2 B1 for 35x or 14y in final answer
or for 35x + 14y seen then spoilt
4(d) correctly equating one set of coefficients M1
correct method to eliminate one variable M1
x=4 A1
y=9 A1 If A0 scored SC1 for 2 values satisfying
one of the original equations
(a) Kurt owns some toy cars of different colours.
The pictogram shows the number of each colour.
Colour Number of toy cars
Red
Yellow
Green
Blue
White
Other
Key: = 8 cars
(i) Write down the colour of toy car that Kurt owns most of.
…… [1]
(ii) Find the number of yellow toy cars that Kurt owns.
…… [1]
(iii) Find how many more red toy cars than white toy cars Kurt owns.
…… [1]
(b) A toy car costs $12.40 in the USA and 11.50 euros in Spain.
The exchange rate is 1 euro = $1.12 .
Calculate the difference in the cost of the toy car in euros.
Give your answer correct to 2 decimal places.
…… euros [3]
(c) Leo owns some toy vehicles.
He owns 57 cars, 12 bicycles and 42 trucks.
Find the ratio of the number of cars : bicycles : trucks in its simplest form.
…… : …… : …… [2]
(d) Leo keeps his toy vehicles on a shelf.
(i) The shelf is in the shape of a right-angled triangle.
NOT TO
SCALE
0.75 m
ym
The area of the shelf is 0.3 m 2 .
Calculate the value of y.
y = …… [2]
(ii) The shelf is 1.35 metres from the floor.
Change 1.35 metres into centimetres.
…… cm [1]
Mark scheme
5(a)(i) Blue 1
5(a)(ii) 18 1
5(a)(iii) 20 1
5(b) 0.43 cao 3 B2 for 0.429 or 0.428[5…]
Or
12.4
M2 for 11.50 – oe
1.12
11.50 ×1.12 − 12.4
or oe
1.12
12.4
or M1 for soi by 11.07…
1.12
If 0 or M1 scored SC1 for correct
rounding to 2dp from their more accurate
answer
5(c) 19 : 4 : 14 cao 2 M1 for correct ratio not in its simplest
form
5(d)(i) 0.8 2 1
M1 for × y × 0.75 = 0.3 or better
2
5(d)(ii) 135 1
(a)
8m
NOT TO
SCALE
11 m
6m
15 m
The diagram shows a plan of Zak’s garden.
Find the perimeter of the garden.
…… m [2]
(b) Zak records the temperature in his garden each night for one week.
Sunday Monday Tuesday Wednesday Thursday Friday Saturday
4 °C 1 °C -2 °C 2 °C -5 °C 3 °C -4 °C
(i) Which night was coldest?
…… [1]
(ii) Find the difference in temperature between Friday night and Saturday night.
…… °C [1]
(c) Zak buys pea plants, bean plants and sunflower plants in the ratio peas : beans : sunflowers = 7 : 5 : 2.
He buys 45 bean plants.
Show that the total number of plants he buys is 126.
[2]
(d) Zak has a water barrel.
On Monday the barrel contains 120 litres of water.
On Friday the barrel contains 43.2 litres of water.
Calculate the percentage decrease of the water in the barrel.
…… % [2]
(e) Zak drives to a shop.
1
The journey takes 1 hours.
4
He drives at an average speed of 57 km/h.
Calculate the distance he drives.
…… km [2]
(f)
Machine hire charges
1st day $22.60
Each additional day $11.80
Zak pays $69.80 to hire a machine.
Calculate the number of days he hires it for.
…… days [3]
Mark scheme
6(a) 52 2 M1 for 15 – 8 and 11 – 6
or 2 × 11 + 2 × 15 oe
or 11 + 8 + (11 − 6 ) + (15 − 8 ) + 6 + 15 oe
6(b)(i) Thursday 1
6(b)(ii) 7 1
6(c) 45 ÷ 5 × (7 + 5 + 2) [=126] M2 M1 for 45 ÷ 5
6(d) 64 2 120 − 43.2
M1 for [×100]
120
43.2
or [100−] ×100
120
43.2
or 1 − [×100]
120
6(e) 71.25 2 M1 for their time × 57 oe
6(f) 5 nfww 3 69.80 – 22.60
M2 for oe
11.80
or M1 for 69.80 – 22.60
or 22.60 + 11.80 + 11.80 +. or better
(a)
Write down the mathematical name for this solid.
…… [1]
(b)
x
(i) Measure the size of angle x.
…… [1]
(ii) Write down the mathematical name for this type of angle.
…… [1]
(c)
A
NOT TO
SCALE
O
C
B
Points A, B and C lie on the circle, centre O.
AB = 11 cm and BC = 5 cm .
(i) Give a geometrical reason why angle ACB is 90°.
…… [1]
(ii) Calculate the circumference of the circle.
…… cm [2]
(iii) Show that AC is 9.8 cm, correct to 2 significant figures.
[3]
(d) The surface area of a sphere is 250 cm 2 .
Calculate the radius of the sphere.
[The surface area, A, of a sphere with radius r is A = 4rr 2 .]
…… cm [3]
Mark scheme
7(a) Cylinder 1
7(b)(i) 137 1
7(b)(ii) Obtuse 1
7(c)(i) Angle in a semicircle is 90º 1
7(c)(ii) 34. 6 or 34.55 to 34.562 2 M1 for 11 × π
7(c)(iii) 112 – 52 = AC2 M2 M1 for 52 +(…)2 = 112
96 = 9.79…or 9.80 A1
7(d) 4.46 or 4.460 … 3 250
M2 for
4π
250
or M1 for
4π
(a) (i) Complete the table of values for y = 4x - x 2 .
x -1 0 1 2 3 4 5 6
y -5 0 3 4 3 -5
[2]
(ii) On the grid, draw the graph of y = 4x - x 2 for -1 G x G 6 .
y
5
4
3
2
1
–1 0 1 2 3 4 5 6 x
–1
–2
–3
–4
–5
–6
–7
–8
–9
– 10
– 11
– 12
– 13
[4]
(iii) Use your graph to solve the equation 4x - x 2 = 1.
x = …… or x = …… [2]
(b) The line L is shown on the grid.
y
5
L
4
3
2
1
–2 –1 0 1 2 3 4 x
–1
–2
–3
–4
Find the equation of line L.
…… [3]
Question 9 is printed on the next page.
Mark scheme
8(a)(i) 0 –12 2 B1 for each
8(a)(ii) Correct curve 4 B3FT for 7 or 8 points correctly plotted
or B2FT for 5 or 6 points correctly
plotted
or B1 FT for 3 or 4 points correctly
plotted
8(a)(iii) 0.2 to 0.4 , 3.6 to 3.8 2 FT their curve
B1 for each
8(b) y = 1.5x – 1 oe final answer 3 B2 for 1.5x – 1 oe
or y = 1.5x + c oe
or y = mx – 1 oe m is their gradient m ≠0
or B1 for 1.5x + c
or mx – 1 where m is their gradient m ≠0
Shapes A, B and C are shown on the grid.
y
5
4
A
3
B
2
1
–5 –4 –3 –2 –1 0 1 2 3 4 5 x
–1
C
–2
–3
–4
–5
(a) Write down the mathematical name of shape A.
…… [1]
(b) Describe fully the single transformation that maps shape A onto shape B.
…… [3]
(c) Describe fully the single transformation that maps shape A onto shape C.
…… [2]
(d) Draw the image of shape A after a rotation, 90° clockwise, centre (0, 0). [2]
(e) Draw the image of shape A after a reflection in the line x = 1. [2]
Mark scheme
9(a) Trapezium 1
9(b) Enlargement 3 B1 for each
[SF] 0.5
[Centre] ( 2,1)
9(c) Translation 2 B1 for each
–7
–5
9(d) Correct rotation, vertices at 2 B1 for correct 90 anticlockwise rotation
(3, – 3) ( 3, –5) (4, –3)(4, –4) about the origin or correct orientation,
wrong centre
9(e) Correct reflection, Vertices at 2 B1 for reflection in x = k, or y = 1
(–3, 3) (–2, 4)(–1, 4) (–1, 3)
Checked your answers against these? Let AI mark the whole paper, on your own working.
Examiners follow the generic marking principles at the front of the scheme, then each question's points: method (M), accuracy (A) and independent (B) marks, error carried forward where the scheme allows it, and positive marking, so you're credited for what you got right.
Check your answers against it
Done this paper? Upload your script and CIE Buddy's AI marker marks it question by question against this exact scheme, puts the ticks on your own working and says what each lost mark needed.
Where can I find the 0580/33 October/November 2024 mark scheme?+
On this page, free: the mark scheme for IGCSE Mathematics 0580/33, October/November 2024 (0580_w24_ms_33), and the question paper (0580_w24_qp_33), to read or download, with each question's marking points written out underneath.
How many marks is 0580/33 out of?+
Mathematics 0580/33 for October/November 2024 is out of 104 marks, with 2 hours to answer it.
Can I get my 0580/33 answers marked?+
Yes. Upload your answers to 0580/33/O/N/24 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.