Mathematics 0580/32 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) The bar chart shows the number of goals scored by a team in each of 5 months.
22
20
18
16
14
12
Frequency
10
8
6
4
2
0
Sept Oct Nov Dec Jan Feb
Month
(i) In February, 12 goals are scored.
Complete the bar chart. [1]
(ii) How many more goals were scored in January than in October?
…… [1]
(b) Find the range of the number of goals scored.
…… [1]
(c) (i) The team shop is open from 09 00 to 17 15 on Monday to Friday only.
Work out how long the shop is open each week.
Give your answer in hours and minutes.
……h ……min [3]
(ii) Brunobuysashirtfor$36andascarffor$12.25.
He pays with a $50 note.
Work out how much change he receives.
$ …… [2]
(d)
Ticket prices
Adult $35
Child $20
Senior $25
(i) Calculatethecostof150adulttickets,70childticketsand30seniortickets.
$ …… [3]
(ii) Calculate the percentage of these tickets that are senior tickets.
…… % [2]
(e) A game starts at 15 00.
The team plays for 90 minutes.
There is also a break of 15 minutes.
Find the time the game ends.
…… [2]
Mark scheme
1(a)(i) Bar to 12 1
1(a)(ii) 11 1
1(b) 14 1
1(c)(i) 41 [h] 15 [min] 3 1
B2 for 41.25 or 41 or 40 hr 75 [mins]
4
1
or B1 for 8.25 or 8 or 8 h 15 [min] or
4
495 [min]
or M1 for 7.25 × 5 oe or 9.25 × 5 oe
OR
SC2 for 57 [h] 45 [min]
1(c)(ii) 1.75 2 M1 for 50 – (36 + 12.25) oe
or B1 for 48.25
1(d)(i) 7400 3 M2 for 35 × 150 + 20 × 70 + 25 × 30 oe
or M1 for two of 35 × 150, 20 × 70 or 25 × 30
oe
1(d)(ii) 12 2 30
M1 for × 100 oe
150 + 70 + 30
1(e) 16 45 or 4.45 pm 2 M1 for 15 00 + 90 [min] + 15 [min] oe
(a) (i)
Write down the mathematical name for this polygon.
…… [1]
(ii)
Write down the mathematical name for this quadrilateral.
…… [1]
(iii)
(a) Write down the mathematical name for this type of angle.
…… [1]
(b) Measure the size of this angle.
…… [1]
(b)
Draw the lines of symmetry on this rectangle. [2]
(c) Acuboidmeasures6cmby3cmby2cm.
(i) Work out the volume of the cuboid.
…… cm 3 [1]
(ii) Draw a net of the cuboid on the 1 cm 2 grid.
One face has been drawn for you.
[3]
Mark scheme
2(a)(i) Pentagon 1
2(a)(ii) Trapezium 1
2(a)(iii)(a) Obtuse 1
2(a)(iii)(b) 123 1
2(b) 2 correct lines 2 B1 for 1 correct and 0 extra
or 2 correct and 1 extra
2(c)(i) 36 nfww 1
2(c)(ii) Fully correct net 3 B2 for 3 or 4 correct extra faces in correct place
or B1 for 1 or 2 correct extra faces in correct
place
(a) Write the number fourteen thousand and ninety-seven in figures.
…… [1]
(b) Write down a common multiple of 17 and 5.
…… [1]
(c) Write 0.25 as a percentage.
…… % [1]
(d) Find the value of
(i) 75
…… [1]
(ii) 80 .
…… [1]
5
(e) Ranjit buys some plants and sells of them.
11
He sells 190 plants.
Work out how many plants he buys.
…… [2]
(f) Factorise completely.
15x 3 y - 3x
…… [2]
(g) Make n the subject of the formula V = 3n + t .
n = …… [2]
(h) 7 15 ' 7 x = 7 9
Find the value of x.
x = …… [1]
Mark scheme
3(a) 14 097 1
3(b) Any correct multiple i.e. 85k 1
3(c) 25 1
3(d)(i) 16 807 1
3(d)(ii) 1 1
3(e) 418 2 M1 for 190 ÷ 5 soi by 38
3(f) 3x(5x2y – 1) final answer 2 B1 for 3(5x3y – x) or for x(15x2y – 3)
or correct answer spoilt
3(g) V −t 2 V t
oe final answer M1 for V – t =3n or =n+
3 3 3
3(h) 6 1
(a) Complete the table of values for y = x 2 - 4x - 2 .
x -2 -1 0 1 2 3 4 5
y 3 -2 -5 -5 -2 3
[2]
(b) On the grid, draw the graph of y = x 2 - 4x - 2 for - 2 G x G 5.
y
10
9
8
7
6
5
4
3
2
1
-2 -1 0 1 2 3 4 5 x
-1
-2
-3
-4
-5
-6
[4]
(c) Use your graph to solve the equation x 2 - 4x - 2 = 0 .
x = …… or x = …… [2]
Mark scheme
4(a) 10 –6 2 B1 for each
4(b) Correct curve 4 B3FT for 7 or 8 points correctly plotted
or B2FT for 5 or 6 points correctly plotted
or B1FT for 3 or 4 points correctly plotted
4(c) –0.6 to –0.3, 4.3 to 4.6 2 FT their curve
B1 for each
Heidi records the colour of each of 500 cars crossing a bridge.
The pie chart shows some of this information.
Grey
Red
Other
(a) How many cars are red?
…… [1]
(b) 35carsaregrey.
Show, by calculation, that the sector angle for grey is 25.2°.
[1]
(c) 175 cars are white and 150 cars are black.
Complete the pie chart to show this information.
[2]
(d) Find the probability that a car chosen at random is not grey.
Give your answer as a fraction in its simplest form.
…… [2]
(e) Another320carscrossthebridge.
Howmanyofthese320carsareexpectedtobewhite?
…… [2]
(f) Heidi also records the number of people in each car crossing the bridge for one hour.
Number of people Frequency
1 20
2 6
3 0
4 15
5 8
6 12
Calculate the mean.
…… [3]
Mark scheme
5(a) 125 1
5(b) 35 M1
× 360
500
5(c) Correct pie chart 2 B1 for 126º or 108º
5(d) 93 2 500 – 35 360 – 25.2
cao M1 for oe or oe
100 500 360
7
If 0 scored, then SC1 for final answer of
100
5(e) 112 2 175 126
M1 for × 320 oe or × 320 oe
500 360
5(f) 21 3 M1 for (1 × 20) + (2 × 6) + [3 × 0] + (4 × 15) +
3.34 or 3.344… or 3
61 (5 × 8) + (6 × 12)
M1dep for
their Σ fx ÷ ( 20 + 6 + [0] + 15 + 8 +12) oe
(a) Simplify. a + 4a - 3a
…… [1]
(b) Simplify.
8b - 4 # 7b
…… [1]
(c)
4x + 3 x+7
3x - 9 NOT TO
SCALE
9x + 8
7x + 3
The perimeter of this shape is equal to the perimeter of a square.
Findanexpressionforthelengthofonesideofthesquare.
Give your answer in its simplest form.
…… [4]
(d) Victoriabuys5cupsofteaand4cakesfor$15.69.
Isabellabuys3cupsofteaand7cakesfor$17.97.
Write down a pair of simultaneous equations and solve them to find the cost of one cup of tea and the cost of one cake.
You must show all your working.
Tea $ ……
Cake $ …… [6]
Mark scheme
6(a) 2a final answer 1
6(b) – 20b final answer 1
6(c) 6x + 3 final answer 4 24 x +12
B3 for seen or 6x + 3 seen then
4
spoilt
24 x + k kx +12
or B2 for 24x + 12 or or seen
4 4
k≠0
or M2 for
3x – 9 + 4 x + 3 + x + 7 + 9 x + 8 + 7 x + 3
oe
4
or M1 for
3x – 9 + 4x + 3 + x + 7 + 9x + 8 + 7x + 3 oe
or B1 for 24x + k or kx + 12 seen k≠0
6(d) 5t + 4c = 15.69 oe B1
3t + 7c = 17.97 oe B1
correctly equating one set of M1
coefficients
correct method to eliminate one M1
variable
t = 1.65 A1
c = 1.86 A1 If A0 scored, SC1 for 2 values satisfying one of
the original equations
or if no working shown, but 2 correct answers
given
Elize, Lily and Marco start a business.
(a) Elize invests $5000.
Lily invests $8000.
Marcoinvests$3000.
After one year they make a profit of $40 000.
They share this profit in the ratio of their investments.
Work out how much they each receive.
Elize $ ……
Lily $ ……
Marco $ …… [3]
(b) (i) Lily buys 20 rolls of ribbon.
8arered,6areblue,4areyellowand2arepink.
A roll of ribbon is chosen at random.
On the probability scale, draw an arrow ( ) to show the probability that this roll is
(a) yellow
0 0.5 1
[1]
(b) not red
0 0.5 1
[1]
(c) green.
0 0.5 1
[1]
(ii) The length, l m, of a roll of ribbon is 120 m, correct to the nearest metre.
Complete this statement about the value of l.
…… G l 1 …… [2]
(c) Elize buys some picture frames.
The frames cost $5.80 each in New York and 4.50 euros each in Paris.
Theexchangerateis1euro=$1.37.
Calculate the difference in the cost in euros.
Give your answer correct to 2 decimal places.
……euros [3]
(d) Elize buys a framed picture.
(i)
18 cm
NOT TO
18 cm SCALE
The picture is a circle with diameter 18 cm.
The frame is a square of side length 18 cm.
Calculate the shaded area.
…… cm 2 [3]
(ii) Elize buys the framed picture for $12.50 .
She sells the framed picture for $20.25 .
Calculate the percentage profit.
…… % [2]
Mark scheme
7(a) 12 500, 20 000, 7500 3 B2 for 12 500 or 7500 in correct place
40000
or M1 for × k where k = 1, 5, 8 or 3
5+8+3
7(b)(i)(a) Arrow at 0.2 1
7(b)(i)(b) Arrow at 0.6 1
7(b)(i)(c) Arrow at 0 1
7(b)(ii) 119.5 120.5 2 B1 for each or both correct but reversed
7(c) 0.27 3 B2 for 0.266…
or
5.80 5.80
M2 for 4.50 – oe or −4.50 oe
1.37 1.37
5.80
or M1 for soi by 4.23…
1.37
If 0 or 1 scored, SC1 for correct rounding to 2dp
from their more accurate answer
7(d)(i) 69.5 or 69.49 to 69.531 3 M2 for 182 – 92 × π oe
or M1 for 92 × π oe
7(d)(ii) 62 2 20.25 − 12.50
M1 for [× 100] oe
12.50
20.25
or × 100 [– 100] oe
12.50
20.25
or –1 [× 100] oe
12.50
(a) In triangle RST, RT = 7 cm and ST = 4 cm.
(i) Using a ruler and compasses only, construct triangle RST.
Leave in your construction arcs.
The line RS has been drawn for you.
R S
[2]
(ii) Measure the distance from S to the midpoint of RT.
Give your answer in millimetres.
…… mm [1]
(b) Town A is 8.5 cm from town B on a map.
The scale of the map is 1 : 50 000.
Calculate the actual distance from town A to town B.
Give your answer in kilometres.
…… km [2]
(c)
E
x° NOT TO
SCALE
118°
A B C D
The diagram shows triangle BCE and a straight line ABCD.
BE = CE and angle DCE = 118°.
Find the value of x.
x = …… [2]
(d)
A
NOT TO
8.9 cm SCALE
4.8 cm
C B
The diagram shows a right-angled triangle ABC.
Show that BC is 7.5 cm, correct to 2 significant figures.
[3]
Question 9 is printed on the next page.
Mark scheme
8(a)(i) Correct triangle with correct arcs 2 B1 for correct triangle with incorrect or no arcs
or for two correct arcs
If 0 scored, SC1 for triangle with arcs but lines
interchanged
8(a)(ii) 52 1 FT their complete triangle
8(b) 4.25 2 B1 for figs 425 as answer or 1 cm = 0.5 km seen
or M1 for 8.5 × 50 000 oe
8(c) 56 2 M1 for 180 – 2 × (180 – 118) oe
or B1 for [angle] ECB or EBC = 62
8(d) 8.92 – 4.82 M2 M1 for 4.82 + BC2 = 8.92
8.92 − 4.82 = 7.49… A1
or 56.17 = 7.49…
Triangles A, B and C are shown on the grid.
y
6
5
C
4
B
3
2
1
A
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x
-1
-2
-3
-4
-5
-6
-7
(a) Describe fully the single transformation that maps triangle A onto triangle B.
…… [3]
(b) Describe fully the single transformation that maps triangle A onto triangle C.
…… [3]
6
(c) On the grid, translate triangle A by the vector e o. [2]
-4
(d) On the grid, reflect triangle A in the line y =- 2 . [2]
Mark scheme
9(a) Rotation 3 B1 for each
(Centre) (0, 0)
90º clockwise
9(b) Enlargement 3 B1 for each
(Scale factor) 1.5
(Centre) (–1, –7)
9(c) Correct translation 2 k 6
Vertices (2, –3), (2, –5), (5, –3) B1 for translation by or
–4 k
9(d) Correct reflection 2 B1 for reflection in x = –2 or y = k
Vertices at (–4, –3), (–4, –5),
(–1, –5)
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Mathematics 0580/32 for October/November 2023 is out of 104 marks, with 2 hours to answer it.
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