Mathematics 0580/33 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) Tom has a restaurant bill.
Soup $……
Pasta $ 13.30
Ice cream $ 4.80
Drinks $ 3.81
Total cost $ 25.40
(i) Complete the bill to show the cost of soup.
[2]
(ii) Find the cost of drinks as a percentage of the total cost.
…… % [1]
2
(b) (i) Work out of $2400.
5
$ …… [1]
(ii) Decrease $3450 by 18%.
$ …… [2]
(c) Amelia invests $14 000 at a rate of 1.6% per year compound interest.
Calculate the value of her investment at the end of 5 years.
Give your answer correct to the nearest dollar.
$ …… [3]
(d) This conversion graph can be used to change between dollars and Swiss francs.
200
160
120
Swiss francs
80
40
0
0 40 80 120 160 200
Dollars
(i) Use the graph to change
(a) $80 to Swiss francs
…… Swiss francs [1]
(b) 108 Swiss francs to dollars.
$ …… [1]
(ii) Explain how you can use the graph to change $360 to Swiss francs.
…… [1]
Mark scheme
1(a)(i) 3.49 2 M1 for
25.4[0] – (13.3[0] + 4.8[0] + 3.81) oe
1(a)(ii) 15 1
1(b)(i) 960 1
M1 for 3450 × 1 − 18 oe
1(b)(ii) 2829 2
100
or B1 for 621
1(c) 15156 cao 3 5
1.6
M1 for 14000 × 1 + oe
100
A1 for 15156.4…, or 15156 or 15160 or
15200
If A0 scored, SC1 for correctly rounding
their decimal answer to the nearest dollar
1(d)(i)(a) 72 1
1(d)(i)(b) 120 1
1(d)(ii) Correct explanation, using any correct 1
combination of values between 0 and 200
to reach 360 oe
(a) Bayside, Millwater and Westbridge are towns beside a lake.
The scale drawing shows the positions of Bayside (B) and Millwater (M).
The scale is 1 centimetre represents 2 kilometres.
North
B
M
Scale: 1 cm to 2 km
(i) Find the actual distance between Bayside and Millwater.
…… km [2]
(ii) Westbridge (W) is 17 km from Bayside on a bearing of 155°.
On the scale drawing, mark the position of Westbridge.
[2]
(b) (i) A boat travels from Bayside to Westbridge.
The table gives some information about its journey.
Bayside departs 10 50 arrives 11 36
Millwater departs 11 45
Westbridge arrives 13 07
Work out how long the boat takes to travel from Millwater to Westbridge.
Give your answer in hours and minutes.
…… h …… min [1]
(ii) The boat returns directly to Bayside.
It takes 1 hour 20 minutes to travel the 17 km.
Work out the average speed of this journey.
…… km/h [2]
(c) Here are the ticket prices for a boat trip from Bayside to Westbridge.
1 person Group of 6 people Group of 15 people
$9.80 $57.30 $138.75
(i) Calculate the cost per person for a group of 15 people.
$ …… [1]
(ii) A group of 24 people buy tickets for the boat trip from Bayside to Westbridge.
Calculate the least amount of money the group needs to pay.
$ …… [2]
1
Mark scheme
2(a)(i) 9 2 B1 for 4.5
or M1 for their 4.5 × 2
2(a)(ii) W correctly placed 2 B1 for correct bearing of 155° from B
or for correct distance of 8.5 cm from B
2(b)(i) 1 hour 22 mins 1
2(b)(ii) 12.75 2 M1 for 17 ÷ their time
2(c)(i) 9.25 1
2(c)(ii) 225.45 cao 2 M1 for 3 × 9.8[0] + 57.3 + 138.75 oe
or B1 for 9.55
3(a)(i)(a) 3 2 15
cao M1 for oe
16 80
3(a)(i)(b) 380 2 B1 for 500[g] or 120[g]
(a) Aneel has 80 tea bags, kg of sugar and 1 litre of milk.
2
To make a cup of tea he uses:
• 1 tea bag
• 8 grams of sugar
• 40 millilitres of milk.
(i) In the morning, Aneel makes 15 cups of tea.
Work out
(a) the fraction of the tea bags he uses, in its simplest form
…… [2]
(b) the mass of sugar, in grams, he has left.
…… g [2]
(ii) During the day, Aneel uses all of the milk to make cups of tea.
Work out the total number of cups of tea Aneel makes.
…… [1]
(b) Bobby, Carl and Davood share $6875 in the ratio Bobby : Carl : Davood = 6 : 8 : 11.
Calculate the amount of money they each receive.
Bobby $ ……
Carl $ ……
Davood $ …… [3]
32 # 34
(c) (i) Write as a power of 3.
36
…… [1]
(ii) Write the value of 2 - 4 as a decimal.
…… [1]
(d) Simplify.
(i) (b 5) 3
…… [1]
b4l
-2
(ii) m
…… [1]
(e) 30 = 2 # 3 # 5 84 = 2 2 # 3 # 7
Use this information to find the lowest common multiple (LCM) of 30 and 84.
…… [2]
2 5
(f) 7 16 23
9 4
Put a ring around the irrational number in this list. [1]
Mark scheme
3(a)(ii) 25 1
3(b) 1650 3 B2 for one correct answer in the correct
2200 place
3025 6875
or M1 for × k oe where k is 1,
6 + 8 + 11
6, 8 or 11
3(c)(i) 30 final answer 1
3(c)(ii) 0.0625 cao 1
3(d)(i) b15 1
3(d)(ii) m2 1
16
3(e) 420 2 B1 for 22 × 3 × 5 × 7 or 2 × 2 × 3 × 5 × 7
or for 2,2,3,5,7 as final answer
3(f) √7 1
(a) A company makes glass using silica, soda, lime and magnesia.
The table gives information about the proportions used.
Percentage of total mass Pie chart sector angle
Silica 75 270°
Soda 15
Lime and magnesia 10
(i) Complete the table.
[2]
(ii) Complete the pie chart to show this information.
270°
Silica
[1]
(iii) The masses of lime and magnesia used are in the ratio lime : magnesia = 3 : 2.
Find the percentage of the total mass of glass that is magnesia.
…… % [1]
(iv) The company uses 8.25 kg of soda to make some glass.
Work out how many kilograms of silica they use.
…… kg [2]
(b) The company uses the formula M = 2.5 # A # T to find the mass of a sheet of glass.
M is the mass in kilograms.
A is the area in square metres.
T is the thickness in millimetres.
Use the formula to calculate the mass of a rectangular sheet of glass that is 1.9 m long, 0.6 m wide and 8 mm thick.
…… kg [2]
(c) In one year, 130 000 000 tonnes of glass were produced worldwide.
Write this number in standard form.
…… [1]
(d) The company sets targets to recycle its waste materials.
The bar chart shows the target rate and the actual rate for some of its recycling.
Key:
Metal Target rate
Actual rate
Paper & cardboard
Glass
Plastic
Wood
0 10 20 30 40 50 60 70 80 90 100
Percentage recycling rate
(i) The target rate for recycling glass was 55%.
The actual rate for recycling glass was 70%.
Complete the bar chart. [2]
(ii) Which materials did the company recycle at more than double their target rate?
…… [2]
Mark scheme
4(a)(i) 54 2 B1 for each
36 360 270
If 0 scored M1 for or or 3.6
100 75
4(a)(ii) Correct pie chart 1 FT dep on their 54°and their 36° adding
to 90°
4(a)(iii) 4 1
4(a)(iv) 41.25 2
8.25 × 75
M1 for oe
15
4(b) 22.8 2
M1 for 1.9 × 0.6 [× 2.5] [× 8] oe soi
or B1 for figs 228 as answer
4(c) 1.3 × 108 1
4(d)(i) Correct bars drawn 2 B1 for shaded bar 55% or unshaded bar
70%
or both bars of correct length
4(d)(ii) Plastic 2 B1 for 1 correct and none incorrect or 2
Wood correct and 1 incorrect
(a) Zena records the number of letters she posts on each of 12 days.
3 7 3 8 7 1 0 6 5 1 7 2
(i) Write down the mode.
…… [1]
(ii) Find the median.
…… [2]
(b) Zena posts 6 parcels.
• The lightest parcel has a mass of 4.6 kg.
• The heaviest parcel has a mass of 6.2 kg.
• The other 4 parcels have a mean mass of 5.01 kg.
Calculate the mean mass of the 6 parcels.
…… kg [3]
(c) Zena pays 105 euros to post a parcel.
The exchange rate is $1 = 0.84 euros.
Work out the cost in dollars to post the parcel.
$ …… [1]
(d) The cost to post a box increases from $22.68 to $44.
Work out the percentage increase in the cost.
…… % [2]
(e) The diagram shows a parcel in the shape of a cuboid.
NOT TO
SCALE
3 cm
2 cm
6 cm
(i) Complete the net of the parcel on the 1 cm 2 grid.
Two faces have been drawn for you.
[2]
(ii) Find the volume of the parcel.
…… cm 3 [1]
Mark scheme
5(a)(i) 7 1
5(a)(ii) 4 2 M1 for an ordered list of at least the first
7 or last 7 values
or B1 for 3 and 5 both identified
5(b) 5.14 3 M2 for (4 × 5.01 + 4.6 + 6.2) ÷ 6 oe
or M1 for 4 × 5.01 + 4.6 + 6.2
or B1 for 20.04
5(c) 125 1
5(d) 94 or 94.00… 2 44 − 22.68
M1 for [×100]
22.68
or 44 − 1 [×100]
22.68
44
or ×100 [– 100]
22.68
5(e)(i) Fully correct net 2 B1 for 2 or 3 correct extra faces in correct
places
5(e)(ii) 36 nfww 1
(a)
P Q
114° 3y° NOT TO
SCALE
y°
S R
114°
T
In the diagram, PST is a straight line.
(i) Give the geometrical reason why the lines PQ and SR are parallel.
…… [1]
(ii) Write down the mathematical name for the shape PQRS.
…… [1]
(iii) Find the value of y.
y = …… [2]
(b) y
7
6
C
5
4
3
2
1
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 x
-1
-2
B A
-3
-4
-5
-6
(i) Describe fully the single transformation that maps triangle A onto triangle B.
…… [3]
(ii) Describe fully the single transformation that maps triangle A onto triangle C.
…… [2]
(iii) On the grid, enlarge triangle A by scale factor 3, centre (4, - 5). [2]
Mark scheme
6(a)(i) TSR and SPQ (or TPQ) are 1
corresponding angles oe
6(a)(ii) Trapezium 1
6(a)(iii) 45 2
B1 for [angle PSR=] 66
or M1 for y + 3y = 180 or 114 + 66 + 3y
+ y = 360
6(b)(i) Rotation 3 B1 for each
90° clockwise oe
(centre) (0, 0) oe
6(b)(ii) Translation 2 B1 for each
3
8
6(b)(iii) Triangle at (–2, 1), (7, 1), (–2, 4) 2 B1 for enlargement SF 3 in wrong
position
These are the first four diagrams in a sequence.
The diagrams are made using dots and lines.
Diagram 1 Diagram 2 Diagram 3 Diagram 4
(a) Complete the table.
Diagram 1 2 3 4
Number of small squares 2 4 6
Number of dots 6 9 12
Number of lines 7 12 17
[2]
(b) Complete this statement.
A diagram in this sequence cannot have 51 small squares because ……
…… [1]
(c) An expression for the number of dots in Diagram n is 3n + 3.
Which diagram has 249 dots?
…… [2]
(d) (i) Find an expression, in terms of n, for the number of lines in Diagram n.
…… [2]
(ii) Find the number of lines in Diagram 41.
…… [1]
Mark scheme
7(a) 8 2 B1 for 2 correct in correct position in
15 table
22
7(b) 51 is an odd number oe 1
7(c) 82 2 M1 for 3n + 3 = 249 or 3(n + 1) = 249 or
better
7(d)(i) 5n + 2 oe final answer 2 B1 for 5n + j or kn + 2 k ≠ 0 as final
answer or for 5n + 2 oe seen then spoilt
7(d)(ii) 207 1 FT dep on their(d)(i) in the form an + b
with a ≠ 0
(a) Expand and simplify.
(i) 4 (x + 3) + 2 (x - 1)
…… [2]
(ii) (m - 6) (m - 4)
…… [2]
(b) Make t the subject of the formula p = 4t + 3 .
t = …… [2]
(c) In this part, all measurements are in centimetres.
4x - 15
2x + 1 NOT TO
SCALE
x
The perimeter of this triangle is 49 cm.
Work out the value of x.
x = …… [3]
Mark scheme
8(a)(i) 6x + 10 final answer 2 B1 for 4x + 12 or 2x – 2
or for 6x or 10 in the final answer
or for 6x + 10 seen then spoilt
8(a)(ii) m2 – 10m + 24 final answer 2 B1 for m2 – 6m – 4m + 24 with at least
three terms correct
8(b) p−3 2 p 3
oe final answer M1 for p – 3 = 4t or =t+
4 4 4
8(c) 9 3 M2 for 4x + 2x + x = 49 + 15 – 1 or
better
or M1 for 4x – 15 + 2x + 1 + x [=49] oe
(a)
C
NOT TO
SCALE
9.6 cm 18 cm
A O B
The diagram shows a semicircle with diameter AB.
O is the midpoint of AB and C is a point on the circumference.
(i) Calculate the area of triangle ABC.
…… cm 2 [2]
(ii) Show that AB = 20.4 cm.
[2]
(iii) Calculate the shaded area.
…… cm 2 [2]
(b) The diagram shows two right-angled triangles, PQR and XYZ.
Y
NOT TO
46° SCALE
Q
26 cm
51°
P R X 34 cm Z
Calculate the difference in the heights RQ and XY.
…… cm [4]
Mark scheme
9(a)(i) 86.4 2 M1 for ½ × 9.6 × 18 oe
9(a)(ii) M2 M1 for 9.62 + 182
9.62 + 182 leading to 20.4
9(a)(iii) 77[.0] or 77.02 to 77.05 2 2
20.4
M1 for [½ ×] π × soi
2
9(b) 12.6 or 12.62 to 12.63 4 34
M3 for – 26 × sin 51 oe
tan46
or
RQ
M1 for sin 51 = or better oe
26
34
M1 for tan 46 = or better oe
XY
y
NOT TO
SCALE
x
(–1, 0) (3, 0)
The sketch shows the graph of y = x 2 - 2x - 3.
The graph crosses the x-axis at ( -1, 0) and (3, 0).
(a) Find the equation of the line of symmetry of the graph.
…… [1]
(b) (i) The point A with coordinates (6, k) lies on the graph.
Show that the value of k is 21.
[1]
(ii) The point B with coordinates (p, 21) also lies on the graph.
Find the value of p.
p = …… [1]
(c) Write down the y-coordinate of the point where the graph crosses the y-axis.
…… [1]
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.
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Mathematics 0580/33 for October/November 2023 is out of 104 marks, with 2 hours to answer it.
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