Mathematics 0580/43 October/November 2024: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 4 (Extended), October/November 2024. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
Dinari sells fruit and vegetables.
(a) One day the mass of fruit and vegetables he sells is in the ratio fruit : vegetables = 9 : 8.
He sells 48 kg of vegetables.
Find the mass of the fruit he sells.
…… kg [2]
(b) On another day he receives $280 for the fruit and vegetables he sells.
The $280 is in the ratio fruit : vegetables = (c + 3) : (c - 1) .
Find the amount he receives from selling the fruit.
$ …… [3]
(c) In one week Dinari buys fruit and vegetables for $1620.
He sells the fruit and vegetables for $1750.
Calculate his percentage profit.
…… % [2]
(d) In another week Dinari sells fruit and vegetables for $1738.
He makes a profit of 10%.
Calculate the amount he paid for the fruit and vegetables in that week.
$ …… [2]
Mark scheme
1(a) 54 2 48
M1 for
8
1(b) 142 3 B2 for 2c = 278 or better
or M1 for c + 3 + c – 1 = 280
OR
B2 for 2x = 276 or better
or M1 for c + 3 – (c – 1) = 4
1(c) 8.02 or 8.024 to 8.025 2 1750 − 1620
M1 for [×100]
1620
1750
or for ×100[−100]
1620
1(d) 1580 2 100 + 10
M1 for [...]× =1738 oe or better
100
(a) A is the point (3, 7) and B is the point (-1, 5).
(i) Find the coordinates of the midpoint of the line AB.
( …… , …… ) [2]
(ii) Write AB as a column vector.
f p [1]
(iii) AC = 3BA
Find the coordinates of C.
( …… , …… ) [2]
(b) y
7
6
5
4
Q
3
2 P
1
–2 –1 0 1 2 3 4 5 6 7 8 x
–1
–2
(i) Rotate shape P through 180° about the point (4, 1). [2]
(ii) Reflect shape P in the line y = x + 2 . [2]
(iii) Describe fully the single transformation that maps shape P onto shape Q.
…… [3]
Mark scheme
2(a)(i) (1, 6) 2 B1 for each
2(a)(ii) −4 1
−2
2(a)(iii) (15, 13) 2 FT their (a)(ii)
12 −12
M1 for or seen
6 −6
or for –1 + 16 and 5 + 8 seen
2(b)(i) Image at (4, 1), (5, –1), (7, –1), (7, 1) 2 B1 for rotation 180° but incorrect
position
2(b)(ii) Image at (1, 3), (–1, 3), (–1, 6), (1, 5) 2 B1 for correct orientation but incorrect
position
or for drawing line y = x + 2
2(b)(iii) Enlargement 3 B1 for each
[centre] (3, 3)
1
[factor] −
2
(a) Ed invests $500 in an account paying r % per year simple interest.
At the end of 14 years the total amount in Ed’s account is $675.
Find the value of r.
r = …… [3]
(b) Eva invests $400 at a rate of 2.2% per year compound interest.
Calculate the total interest earned at the end of 11 years.
$ …… [3]
(c) Erin invests $700 at a rate of p% per month compound interest.
At the end of 21 years the value of Erin’s investment is $1074, correct to the nearest dollar.
Calculate the value of p.
p = …… [3]
Mark scheme
3(a) 2.5 3 500 × r ×14
M2 for = 675 − 500 oe
100
500 × r ×14
or M1 for or for 675 – 500
100
3(b) 108.18 3 B2 for 508.18... or 508.2 or 508
11
100 + 2.2
or M1 for 400 × oe or
100
better
3(c) 0.17[0] or 0.1700... 3 1074 1074
M2 for either (12×21) or 252 or
700 700
better
or M1 for 700 × [...](12×21 = 1074 oe
If 0 scored SC1 answer 2.06 or 2.059...
(a) A box contains 50 cuboids.
Each cuboid has a mass of 135 g.
The total mass of the cuboids and the box is 7 kg.
Calculate the mass of the box.
Give your answer in grams.
…… g [2]
(b) A solid cube of side 4 cm is fixed to the base inside an empty cube of side 6 cm.
Water is poured into the larger cube until it reaches the top of the smaller cube.
Calculate the amount of water poured into the larger cube.
…… cm 3 [2]
(c)
4 cm NOT TO
SCALE
20 cm
The diagram shows a solid triangular prism of length 20 cm.
The cross-section is an equilateral triangle with side length 4 cm.
The prism is made of wood with a density of 0.85 g/cm 3 .
Calculate the mass of the prism.
[Density = mass ÷ volume]
…… g [4]
(d)
NOT TO
SCALE
24 cm
10 cm
The diagram shows a solid cone with base radius 10 cm and height 24 cm.
(i) Show that the total surface area of the cone is 1131 cm 2 , correct to the nearest cm 2 .
[The curved surface area of a cone with base radius r and slant height l is A = rrl .]
[4]
(ii) The total surface area of the cone is painted.
(a) The cost to paint the cone is $1.71 .
Calculate the cost to paint 1 cm 2 of the cone.
Give your answer in cents.
…… cents [1]
(b) One tin of paint has enough paint to cover 2.5 m 2 .
Calculate the number of these cones that can be painted completely using one tin of paint.
…… [2]
Mark scheme
4(a) 250 2 B1 for 6750
or M1 for 7000 – 50 × 135
or for 7 – 50 × 0.135
4(b) 80 2 M1 for 6 × 6 × 4 or for 43 oe
OR
M1 for (6 × 6) – (4 × 4) oe
4(c) 118 or 117.7 to 117.8 4 1
M3 for × 4 × 4 × sin 60 × 20 × 0.85 oe
2
OR
1
M1 for × 4 × 4 × sin 60 or
2
1
× 4 × 42 − 22 oe
2
M1 for 20 × their area of triangle
M1 dep for 0.85 × their volume,
dependent on previous M1
If 0 scored SC1 for height = 3.46...
4(d)(i) π × 242 + 102 ×10 + π ×102 M3
or
( )
2 × π ×10 M2 for π × 242 + 102 ×10 or
2
π × 242 + 102 × + π × 102
2 × π × 26
( )2 × π ×10
2
π × 242 + 102 ×
2 × π × 26
or M1 for 242 + 102 or π × 102
1130.9 to 1131.1... A1 Must see at least 5 sf
4(d)(ii)(a) 0.151 or 0.1511 to 0.1512... 1
4(d)(ii)(b) 22 2 B1 for figs 22[1…]
2.5 × 1002
or M1 for
1131
(a) Naomi runs 100 m in 15 seconds.
Calculate Naomi’s average speed in kilometres per hour.
…… km/h [2]
(b) Olav runs for 45 minutes at a speed of 9.5 km/h.
He then runs 8.1 km at a speed of 7.5 km/h.
Calculate Olav’s average speed for the whole run.
…… km/h [3]
(c) A train has length p metres.
The train passes through a station of length q metres.
The speed of the train is v kilometres per hour.
Find an expression for the time the train takes to completely pass through the station.
Give your answer in seconds, in terms of p, q and v.
…… s [3]
24u 10
Mark scheme
5(a) 24 2 100or 0.1
M1 for
time
or B1 for figs 24
5(b) 8.32 or 8.319 to 8.320 3 45
M1 for 9.5 × oe
60
8.1
M1 for
7.5
5(c) 18( p + q) 3 ( p + q)
oe final answer M1 for [k ×] for some k ≠ 0
5v v
1000
M1 for v × oe soi
3600
(a) Simplify # .
5y 3u
…… [2]
(b) Expand and simplify (x - 1) (x + 2) (x + 3) .
…… [3]
(c) Solve the equation 2x 2 + x - 5 = 0 .
You must show all your working and give your answers correct to 2 decimal places.
x = …… or x = …… [4]
Mark scheme
6(a) 16 2 240u
final answer M1 for or better
y 15uy
6(b) x 3 + 4 x 2 + x − 6 final answer 3 B2 for correct unsimplified expansion of
three brackets
or for simplified four-term expression of
correct form with 3 terms correct in final
answer
or B1 for correct expansion of two given
brackets with at least 3 terms out of 4
correct
6(c) −1 ± 12 − 4(2)(−5) M2 M1 for 12 − 4(2)(−5) or better
2(2) −1 + p −1 − p
or for or
2(2) 2(2)
–1.85, 1.35 A2 A1 for each
or –1.851 to –1.850 and 1.350 to 1.351
or –1.9 and 1.4 or –1.35 and 1.85
(a) (i)
13 cm
NOT TO
8 cm SCALE
9 cm
Calculate the area of the trapezium.
…… cm 2 [2]
(ii)
( y + 4) cm
NOT TO
( y + 2) cm SCALE
( y + 1) cm
The area of this trapezium is 264 cm 2 .
(a) Show that 2y 2 + 9y - 518 = 0 .
[3]
y = …… [3]
(b)
NOT TO
SCALE
8 cm
75°
The diagram shows a sector of a circle with radius 8 cm and angle 75°.
Find the perimeter of the sector.
…… cm [3]
(c)
A B
NOT TO
SCALE
5 cm
P Q
O
The diagram shows a shape ABQP made from three straight lines and an arc of a sector of a circle.
The sector has centre O and angle 90°.
POQ is a straight line and AP = PO = OQ = QB = 5 cm.
Find the area of ABQP.
Give your answer in the form a + k r .
…… cm 2 [4]
Mark scheme
7(a)(i) 88 2 1
M1 for (9 + 13) × 8 oe
2
7(a)(ii)(a) 1 M1
( y + 4 + y + 1) × ( y + 2) [= 264]
2
or
1
× 3 × ( y + 2) + ( y + 1) × ( y + 2) [= 264]
2
2 y 2 + 5 y + 4 y + 10 B1
Leading to 2 y 2 + 9 y − 518 = 0 A1 No errors or omissions
7(a)(ii)(b) (2 y + 37)( y − 14) B2 B1 for (2 y + a)( y + b)
where ab = –518 or a + 2b = 9
or 2 y( y − 14) + 37( y − 14)
or y(2 y + 37) − 14(2 y + 37)
14 B1
7(b) 26.5 or 26.47... 3 10π
B2 for 10.5 or 10.47… or
3
OR
75
M2 for 8 + 8 + × 2π8
360
75
or M1 for × 2π8
360
7(c) 25 4
25 + π
90
2 M2 for × π × ( (52 + 52 ) )2
360
or M1 for [radius 2 = ] 52 + 52
1
M1 for [triangle area = ] [2×] × 5 × 5 oe
2
Guillaume measures the speed of each of 100 cars.
The results are shown in the table.
Speed (v km/h) 30 1 v G 40 40 1 v G 45 45 1 v G 50 50 1 v G 70
Frequency 15 20 35 30
(a) Guillaume draws a pie chart for this data.
Calculate the angle for the interval 45 1 v G 50 .
…… [2]
(b) Calculate an estimate of the mean speed.
…… km/h [4]
(c) Complete the histogram to show the data in the table.
8
7
6
5
Frequency density 4
3
2
1
0
30 40 50 60 70 v
Speed (km / h)
[3]
Mark scheme
8(a) 126 2 35
M1 for × 360
100
8(b) 48.375 4
M1 for mid-values 35, 42.5, 47.5, 60 soi
M1 for 15 × 35 + 20 × 42.5 + 35 × 47.5 +
30 × 60
Σfx
M1 dep dep on second M1
100
8(c) Correct histogram with correct widths 3 B1 for each column
and heights 1.5, .... 7, 1.5
If 0 scored, SC1 for freq. densities 1.5,
...7, 1.5 seen
15 35 30
or , ,
10 5 20
A bag contains 5 white balls and 3 black balls.
(a) (i) Marwan picks a ball from the bag at random and then replaces it.
Find the probability that the ball is white.
…… [1]
(ii) Naomi picks a ball from the bag at random and then replaces it.
She repeats this 120 times.
Find the number of times the ball is expected to be white.
…… [1]
(b) Oscar picks a ball from the bag at random.
He replaces it and then picks a second ball from the bag at random.
(i) Find the probability that the balls are the same colour.
…… [3]
(ii) Find the probability that the balls are not the same colour.
…… [1]
(c) Priya picks 3 of the 8 balls from the bag at random without replacement.
Find the probability that she picks two white balls and one black ball.
…… [3]
Mark scheme
9(a)(i) 5 1
oe
8
9(a)(ii) 75 1 FT their (a)(i)
9(b)(i) 17 3 5 5 3 3
oe M2 for × + ×
32 8 8 8 8
5 5 3 3
or M1 for × or ×
8 8 8 8
9(b)(ii) 15 1 FT their (b)(i)
oe
32
9(c) 15 3 5 4 3
oe M2 for × × × k , k = 1 or 2 or 3 oe
28 8 7 6
5 4 3
M1 for and and or showing the
8 7 6
three possible combinations oe
225
If 0 scored SC1 for oe
512
y
B NOT TO
SCALE
A
O x
The diagram shows a sketch of the graph of y = 3 + 2x - x 2 .
A is the point (-1, 0) and B is the point (2, 3).
(a) Find the derivative of 3 + 2x - x 2 .
…… [2]
(b) (i) Show that the equation of the tangent at A is y = 4x + 4 .
[3]
(ii) The line L is perpendicular to the line y = 4x + 4 .
The line L passes through the point B.
Find the equation of the line L.
Give your answer in the form y = mx + c .
y = …… [3]
(c) Find the coordinates of the maximum point on the graph of y = 3 + 2x - x 2 .
( …… , …… ) [3]
1
Mark scheme
10(a) 2 – 2x 2 B1 for k – 2x or 2 – kx or 3 + 2 – 2x
10(b)(i) Gradient (m) = correct substitution of –1 M1
into their (a) 2 – 2(–1)
0 = their m × –1 + c M1 Dep on previous M1
or
y [– 0] = their m(x – –1) oe
c = 4 and leading to y = 4x + 4 A1
10(b)(ii) 1 7 3 1
− x + oe M1 for −
4 2 4
M1 for 3 = their m × 2 + c or better
or y – 3 = their m(x – 2) or better
10(c) (1, 4) 3 B2 for x = 1
or M1 for their (a) = 0
M1 for substituting their 1 into y = 3 + 2x
– x2
OR
B2 for x = 1
or M2 for 4 – (x – 1)2
or M1 for (x – 1)2
f (x) = 2x + 5 g (x) = 1 - 2x h (x) = , x ! -1 j (x) = 2 x x+1
(a) Find g(-3).
…… [1]
(b) Find f (x) g (x) + fg (x) + 1.
Give your answer in its simplest form.
…… [4]
(c) Find g -1 (x) .
g -1 (x) = …… [2]
(d) Find hh(1).
…… [2]
1
(e) Simplify - h (x) . f (x)
Give your answer as a single fraction in its simplest form.
…… [3]
1
(f) Find x when j (x) = .
32
x = …… [1]
(g) Find x when j -1 (x) = 0 .
x = …… [1]
Mark scheme
11(a) 7 1
11(b) −4 x 2 − 12 x + 13 final answer 4 B1 for (2x + 5)(1 – 2x)
B1 for 2x – 4x2 + 5 – 10x oe
B1 for 2(1 – 2x) + 5
11(c) 1− x 2 M1 for
oe final answer
2 y 1
x = 1 − 2 y or 2 x = 1 − y or = −x
2 2
11(d) 2 2
oe
3 1 1
M1 for h or oe
2 1
+1
x +1
11(e) −x − 4 −x − 4 3 M1 for x + 1 − (2 x + 5) oe
or or
(2 x + 5)( x + 1) 2x + 7 x + 5
2
x+4
− M1 for common denominator
2x + 7 x + 5
2
(2 x + 5)( x + 1) seen
final answer
11(f) –5 1
11(g) 1 1
D
A NOT TO
SCALE
20°
E
8.7 cm
119° 10.9 cm
B
11.4 cm
C
ABCD is a quadrilateral and E is a point on CD.
AB = 8.7 cm, BC = 11.4 cm and CE = 10.9 cm.
Angle ADE = 90°, angle ABC = 119° and angle CAE = 20°.
(a) Show that AC = 17.37 cm, correct to 2 decimal places.
[3]
(b) Angle AEC is obtuse.
Calculate angle ACE.
Angle ACE = …… [4]
(c) Calculate the perimeter of quadrilateral ABCD.
…… cm [3]
Mark scheme
12(a) 8.72 + 11.42 − 2 × 8.7 ×11.4cos119 M2 M1 for 8.72 + 11.42 − 2 × 8.7 ×11.4cos119
A1 for 301.8...
17.372 to 17.373 A1
12(b) 13.[0] or 13.02 to 13.03 4 17.37sin 20
M2 for sinE =
10.9
10.9 17.37
or M1 for = oe
sin 20 sin E
M1 for ACE = 180 – 20 – their obtuse
AEC oe
12(c) 40.9 or 40.91 to 40.94 3 M1 for a correct implicit trig statement
for AD
AD
e.g. sin(their acute ACE ) = oe
17.37
M1 for a correct implicit statement for
CD
CD
e.g. cos(their acute ACE ) = oe
17.37
or CD2 = 17.372 – (theirAD)2
or for a correct statement for ED
eg tan(180 – their obtuse AEC) =
theirAD
ED
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On this page, free: the mark scheme for IGCSE Mathematics 0580/43, October/November 2024 (0580_w24_ms_43), and the question paper (0580_w24_qp_43), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/43 for October/November 2024 is out of 130 marks, with 2 hours 30 minutes to answer it.
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