Mathematics 0580/32 February/March 2024: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), February/March 2024. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) l
P
Draw a line through point P that is perpendicular to line l. [1]
(b) Write down the mathematical names for two different quadrilaterals with
• two lines of symmetry and
• rotational symmetry of order two.
…… and …… [2]
(c) The diagram shows a quadrilateral on a 1 cm2 grid.
Find the area of this quadrilateral.
…… cm2 [1]
(d)
H
G x°
F 143°
103°
NOT TO
SCALE
82°
E y°
D
The diagram shows a quadrilateral DEFG and a straight line FGH.
(i) Angle DEF = 82° .
Write down the mathematical name for this type of angle.
…… [1]
(ii) Work out the value of x.
Give a geometrical reason for your answer.
x = …… because ……
…… [2]
(iii) Work out the value of y.
Give a geometrical reason for your answer.
y = …… because ……
…… [2]
Mark scheme
1(a) Ruled line drawn through P, 1
perpendicular to l.
1(b) rectangle rhombus 2 B1 for each
1(c) 11 1
1(d)(i) acute 1
1(d)(ii) 37 1
Angles on a straight line add to 180 1
1(d)(iii) 32 1
Angles in a quadrilateral add to 360 1
(a)
Fuel Fuel
Garage A Garage B
$1.41 per litre $1.50 per litre
(i) Tiya buys 55 litres of fuel from garage A.
Work out the change she receives from $100.
$ …… [2]
(ii) Work out how much cheaper it is to buy 20 litres of fuel from garage A than from garage B.
$ …… [2]
(iii) These are the amounts that 6 people spend on fuel at garage A.
$63 $84.50 $72.23 $46 $54.10 $80
Calculate the mean number of litres that they buy.
…… litres [3]
(iv) The cost of fuel at garage B increases from $1.50 to $1.53 .
Calculate the percentage increase.
…… % [2]
2
(b) The fuel tank of a car is full.
5
It takes 39 more litres of fuel to fill the tank.
Work out the number of litres of fuel in a full tank.
…… litres [3]
(c) (i) Use 1 litre = 0.22 gallons to complete this conversion graph.
30
25
20
Gallons 15
10
5
0
0 10 20 30 40 50 60 70 80 90 100
Litres
[2]
(ii) Use 1 litre = 0.22 gallons to complete this statement.
1 gallon = …… litres. [1]
(d) A cylindrical tank for storing fuel has radius 1.5 metres and height 8 metres.
Calculate the volume of the tank in litres.
…… litres [3]
Mark scheme
2(a)(i) 22.45 2 M1 for 100 − 55 ×1.41 oe
or B1 for 77.55
2(a)(ii) 1.8[0] 2 M1 for (1.50 − 1.41) × 20 oe
or B1 for 30 and 28.2[0] seen
2(a)(iii) 47.3 or 47.26… 3 M2 for
63 + 84.5 + 72.23 + 46 + 54.10 + 80
oe
6 × 1.41
or M1 for
63 + 84.5 + 72.23 + 46 + 54.10 + 80
oe
1.41
63 + 84.5 + 72.23 + 46 + 54.10 + 80
or oe
6
2(a)(iv) 2 2 1.53 − 1.50
M1 for × [100] oe
1.50
1.53
or ×100[ −100] oe
1.50
1.53
or − 1 [×100] oe
1.50
2(b) 65 3 5
M2 for 39 × oe
3
3
or M1 for 39 is equivalent to or for
5
39
3
5
if 0 scored then SC1 for 39 × oe
2
2(c)(i) A straight line through (0,0) and (100,22) 2
B1 for a straight line drawn through the
origin
or for 2 correct points plotted
2(c)(ii) 4.55 or 4.545… 1
2(d) 56500, 56600 or 56540 to 56560…. 3 M2 for π × 1.52 ×8×1000 oe
or π × 1502 ×800÷1000 oe
or M1 for π × 1.52 ×8 oe
or π × 1502 ×800 oe
or B1 for final answer figs 565 to 566
If 0 scored, SC1:
for their volume in m3 × 1000
or for their volume in cm3 ÷ 1000
or for stating clearly 1m3 =1000l
or 1000 cm3 =1l
(a) In triangle DEF, DE = 6 cm and DF = 4.8 cm .
Using a ruler and compasses only, construct triangle DEF.
Leave in your construction arcs.
The line EF has been drawn for you.
E F
[2]
(b)
A B
C
T
D
F G
E
(i) Write down the letter of the triangle that is congruent to triangle T.
…… [1]
(ii) Write down the letter of the triangle that is similar but not congruent to triangle T.
…… [1]
(c)
NOT TO
SCALE h
62° 62°
7 cm
The diagram shows an isosceles triangle.
(i) Show that the perpendicular height, h, is 6.58 cm, correct to 3 significant figures.
[3]
(ii) Calculate the area of the triangle.
Give the units of your answer.
…… …… [3]
(iii) Kalpit tries to arrange some of these triangles to make a regular polygon with centre O.
O
NOT TO
SCALE
7 cm 7 cm
62° 62°
7 cm
Show that Kalpit cannot make a regular polygon.
[3]
Mark scheme
3(a) Correct triangle drawn with construction 2 B1 for correct triangle drawn with
arcs. incorrect or no arcs
or for 2 correct arcs drawn
If 0 scored, SC1 for reversed triangle
with arcs.
3(b)(i) G 1
3(b)(ii) F 1
3(c)(i) 7 M2 h
[h=] tan 62 oe M1 for tan62 = oe
2 7
2
6.582 to 6.583 A1
3(c)(ii) 23[.0] or 23.03 to 23.04… 2 1
M1 for × 7 × 6.58 oe
2
cm2 1
3(c)(iii) 360 M2 M1 for 180 − 2 × 62 oe
180 − 2 × 62
6.4… which is not integer oe A1
(a) A shop sells 58 televisions in one week.
The bar chart shows the number of televisions that the shop sells on five of the days.
16
14
12
10
Number of
8 televisions
6
4
2
0
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
(i) Write down the number of televisions that the shop sells on Monday.
…… [1]
(ii) Find the fraction of the televisions that the shop sells on Sunday.
…… [1]
(iii) The number of televisions that the shop sells on the other two days is in the ratio
Wednesday : Friday = 2 : 3.
Complete the bar chart.
[4]
(iv) Write down the mode.
…… [1]
(b) A television has a price of $550.
This price is reduced by 4%.
Calculate the new price of this television.
$ …… [2]
(c) The scatter diagram shows the prices of different sized televisions.
Price
Television size
Write down the type of correlation shown in the scatter diagram.
…… [1]
(d) Hemang buys two televisions.
The probability that a television is faulty is 0.02 .
1st television 2nd television faulty
faulty
0.02
not faulty
faulty
not faulty
not faulty
(i) Complete the tree diagram. [2]
(ii) Find the probability that Hemang buys two faulty televisions.
…… [2]
(iii) The shop sells 4150 televisions in one year.
Calculate the expected number of faulty televisions.
…… [1]
Mark scheme
4(a)(i) 3 1
4(a)(ii) 11 1
cao
58
4(a)(iii) Completely correct bar chart 4 B3 for a bar height 8 drawn for
Wednesday or a bar height 12 drawn for
Friday.
or
58 − 3 − 4 − 4 − 16 − 11
M2 for ×k ,
2+3
k = 1,2 or 3
or
M1 for 58 − 3 − 4 − 4 −16 −11 oe
If 0 scored SC1 for 2 bars drawn
correctly from their identified values in
working
4(a)(iv) Saturday 1
4(b) 528 2 4
M1 for 550 × 1 − oe
100
or B1 for 22
4(c) Positive 1
4(d)(i) 0.02 2 B1 for 0.98 correctly placed once on tree
0.98 or for 0.02 correctly placed twice on tree.
0.98 0.02
0.98 oe
4(d)(ii) 0.0004 oe 2 M1 for 0.02 × 0.02
4(d)(iii) 83 1
(a) (i) Complete the table of values for y =- x 2 + 5x + 7 .
x -1 0 1 2 3 4 5 6 y 11 11 1
[3]
(ii) On the grid, draw the graph of y =- x 2 + 5x + 7 for - 1 G x G 6 .
y
14
13
12
11
10
9
8
7
6
5
4
3
2
1
–1 0 1 2 3 4 5 6 x
[4]
(iii) (a) Write down the equation of the line of symmetry of the graph.
…… [1]
(b) The points (-8, -97) and (t, -97) also lie on the graph of y =- x 2 + 5x + 7 .
Use symmetry to find the value of t.
t = …… [1]
(b) Write down the gradient of the line y = 9x - 4 .
…… [1]
(c) Write down the equation of a line parallel to y =-5x + 19 .
y = …… [1]
(d) y
7
6
L
5
4
3
2
1
–4 –3 –2 –1 0 1 2 3 4 x
–1
–2
–3
Find the equation of line L in the form y = mx + c .
y = …… [2]
(e) Make x the subject of the formula y = mx + c .
x = …… [2]
Mark scheme
5(a)(i) 1, 7, 13, 13, 7 3 B2 for 3 or 4 correct
or B1 for 1 or 2 correct
5(a)(ii) Completely correct curve 4 B3FT for 7 or 8 correctly plotted points
or
B2FT for 5 or 6 correctly plotted points
or
B1FT for 3 or 4 correctly plotted points
5(a)(iii)(a) x = 2.5 oe 1
5(a)(iii)(b) 13 1
5(b) 9 1
5(c) y = −5x + k where k ≠ 19 1
5(d) [ y = ] − x + 2 final answer 2 B1 for [ y = ] − x + c
or [ y = ] mx + 2 where m is their gradient
5(e) y −c 2 M1 for a correct first step
[ x =] oe final answer
y c
m y − c = mx or = x+
m m
(a) Town S is 44 km from town R on a bearing of 117°.
(i) Using a scale of 1 cm represents 8 km, mark the position of town S.
North
R
Scale: 1 cm to 8 km
[2]
(ii) Anvi cycles the 44 km from R to S.
She leaves R at 13 15 and cycles at a speed of 12 km/h.
Work out the time she arrives at S.
…… [3]
(b) A tower has a height of 16 metres.
When Jai makes a scale drawing of the tower it has a height of 20 cm.
Work out the scale Jai uses, giving your answer in the form 1 : n.
1 : …… [2]
(c) X, Y and Z are three towns.
Z
North NOT TO
9.7 km SCALE
X
6 km
Y
X is on a bearing of 288° from Y.
Z is on a bearing of 018° from Y.
(i) Show that angle XYZ is 90°.
[2]
(ii) XY = 6 km and YZ = 9.7 km .
Calculate XZ.
XZ = …… km [2]
Mark scheme
6(a)(i) The position of S correctly marked on the 2 B1 for S on bearing 117° from R
diagram B1 for S 5.5 cm from R
6(a)(ii) 16 55 3 B2 for 3 [h] 40 [min]
44
or M1 for
12
6(b) [1:]80 2 M1 for 20:1600 or 0.2:16 or better
1600 16
or or
20 0.2
or B1 for answer figs 8
6(c)(i) 360 − 288 + 18 oe M2 M1 for 360 − 288 or 288 −18
If 0 scored SC1 for 72 and 18 correctly
marked on the diagram
6(c)(ii) 11.4 or 11.40 to 11.41 2 M1 for 62 + 9.7 2 or better
(a) P = 3a + 5
Find the value of P when a = 2 .
P = …… [1]
(b) Solve these equations.
(i) 7x =-42
x = …… [1]
(ii) 9 (8x - 7) = 72
x = …… [3]
(c) 5 8 # 5 k = 5 -24
Find the value of k.
k = …… [1]
(d) Solve the simultaneous equations.
-6x - y = 13
8x + y =- 51
x = ……
y = …… [2]
(e) n is an integer where n 2- 3 and n G 1.
Write down all the possible values of n.
…… [2]
(f) A boy walks for 35 minutes at x metres per minute.
He then runs for t minutes at 160 metres per minute.
Write down an expression, in terms of x and t, for the total distance, in metres, the boy travels.
…… m [2]
(g)
NOT TO x–2 SCALE
x+5
Find an expression for the area of this rectangle.
Give your answer in the form x 2 + ax + b .
…… [3]
Question 8 is printed on the next page.
Mark scheme
7(a) 11 1
7(b)(i) −6 1
7(b)(ii) 1.875 oe 3 M1 for a correct first step
e.g. 8x − 7 = 8 or 72x − 63 = 72
M1FT for a correct second step
e.g. 8x = 15 or 72x = 135
7(c) −32 1
7(d) [ x = ] −19 [ y =]101 2 B1 for [ x = ] −19
B1 for [ y = ]101
7(e) −2, −1, 0, 1 2 B1 for 3 correct and no extras
or 4 correct and one extra
7(f) 35x + 160t final answer 2 B1 for 35x or 160t seen in final answer
or 35x + 160t seen and spoilt
7(g) x 2 + 3x − 10 final answer 3 B2 for x 2 + 5x − 2 x − 10 with at least 3
terms correct
or B1 for ( x + 5 )( x − 2 ) oe
(a) 120 people teach in a university mathematics department.
Some information is shown in the table.
Lecturers Professors Total
Part-time 11
Full-time
Total 120
One fifth of the people are professors.
30% of the people are part-time.
Work out the number of full-time lecturers.
…… [4]
(b) % = {children in a school}
F = {children who like fruit}
V = {children who like vegetables}
24 children like vegetables but do not like fruit.
8 children do not like fruit and do not like vegetables. n (F + V ) = 9 n (F ) = 3 # n (V )
F V
(i) Complete the Venn diagram. [3]
(ii) Work out n (F , V ) .
…… [1]
Mark scheme
8(a) 71 nfww 4 B3 for 13 and 84 or for 25 and 96
OR
B1 for 24 or 96
B1 for 36 or 84
8(b)(i) 3 If answer incorrect can score a maximum
V of 2 from:
F
B1 for 24 and 8 correctly placed
90 9 24
B1 for 9 correctly placed
8 B1FT for their n(F)= 3×their n(V)
8(b)(ii) 123 1 B1FT for their n(F V)
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Mathematics 0580/32 for February/March 2024 is out of 104 marks, with 2 hours to answer it.
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