Mathematics 0580/32 February/March 2022: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), February/March 2022. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) One day, Mahika records the number of teachers and students who cycle to school.
Tally Frequency
Teachers ||||
Students |||| |||| |||| |||| |||
(i) Complete the frequency column in the table. [1]
(ii) Work out the percentage of people who cycle that are students.
…… % [2]
(b) Mahika records how 120 students from Year 1 and Year 2 travel to school.
Each student walks, cycles or travels by bus.
• 48 students are in Year 1.
• 77 students walk.
• 5 students in Year 2 cycle.
• 36 students travel by bus.
4
• of the students who travel by bus are in Year 1.
9
(i) Complete the table.
Walk Cycle Bus Total
Year 1
Year 2
Total 120
[3]
(ii) One of the 120 students is chosen at random.
Work out the probability that this student does not travel by bus to school.
…… [2]
(c) There have been 24 complaints about one of the buses.
The complaints are:
• The bus is late.
• The price is too high.
• The bus is crowded.
(i) Complete the table.
Pie chart
Complaint Frequency sector angle
Late 10
Price 6
Crowded 8
[2]
(ii) Complete the pie chart.
[2]
Mark scheme
1(a)(i) 5 23 1
1(a)(ii) 82.1 or 82.14… 2 FT their (a)(i)
their 23
M1 for [×100] soi
their 5 + their 23
1(b)(i) 30 2 16 48 3 B2 for 9 or 10 correct
47 5 20 72 or B1 for 5, 6, 7 or 8 correct
77 7 36 [120]
1(b)(ii) 7 2 120 − 36
oe M1 for oe
10 120
or B1 for 84
or for their77 +their 7
1(c)(i) 150, 90, 120 2 B1 for one correct sector angle
360
or M1 for × k k =1, 6, 8 or 10
24
1(c)(ii) Correct pie chart drawn 2 FT their table if angles add up to 360
B1FT for one sector correctly drawn
(a) Calculate the interior angle of a regular pentagon.
…… [2]
(b) The diagram shows three congruent regular pentagons and a triangle.
y°
NOT TO
SCALE
x°
(i) Work out the value of x.
Give a geometrical reason for your answer.
x = …… because ……
…… [2]
(ii) Work out the value of y.
Give a geometrical reason for your answer.
y = …… because ……
…… [3]
(iii) Find the ratio x : y.
Give your answer in its simplest form.
…… : …… [1]
Mark scheme
2(a) 108 2
M1 for 180 −
360
or
( 5 − 2 ) × 180 oe
5 5
2(b)(i) 36 2 B1 for each
Angles [at a] point [add to] 360
2(b)(ii) 72 2 FT their (b)(i)
180 − their ( b )( i )
M1 for
2
Angles [in a] triangle add to 180 1
or
Base angles [of an] isosceles
triangle are equal
2(b)(iii) 1:2 1 FT their (b)(i): their (b)(ii) provided there
has been some simplification
3(a)(i)(a) Trapezium 1
3(a)(i)(b) 28 2 M1 for a complete method from counting
squares e.g. 8 + 16 + 4
(10 + 4 ) oe
or ×4
2
cm2 1
(a) The diagram shows three quadrilaterals, A, B and C, on a 1cm 2 grid. y
11
10
9
8
B
7 w
6
5
4
3
A
2
C
1
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 x
–1
–2
–3
–4
(i) (a) Write down the mathematical name for quadrilateral B.
…… [1]
(b) Work out the area of quadrilateral B.
Give the units of your answer.
…… …… [3]
(ii) Measure angle w.
Angle w = …… [1]
(iii) Describe fully the single transformation that maps
(a) quadrilateral A onto quadrilateral B,
…… [3]
(b) quadrilateral A onto quadrilateral C.
…… [3]
(b) The diagram shows a parallelogram and a line AB on a 1cm 2 grid.
A B
On the grid, complete a triangle, ABC, that has the same area as the parallelogram.
[2]
Mark scheme
3(a)(ii) 117 1
3(a)(iii)(a) Enlargement 3 B1 for each
[centre] ( 2, −2 )
[scale factor] 2
3(a)(iii)(b) Rotation 3 B1 for each
[centre] ( − 2, 4)
90° clockwise oe
3(b) A correct triangle drawn 2 B1 for 18[cm2] soi
4(a)(i)(a) Radius 1
4(a)(i)(b) Chord 1
(a)
Y
Z
O
X
X, Y and Z lie on a circle, centre O.
(i) Write down the mathematical name of the line
(a) OX,
…… [1]
(b) YZ.
…… [1]
(ii) Measure the length of OX.
…… cm [1]
(b) Another circle has a radius of 18 cm.
Calculate the circumference of this circle.
…… cm [2]
(c) In this part, all angles are in degrees.
NOT TO
B
SCALE
A 18x - 4y
O
C
9x + 3y
X
D
Y
A, B, C and D lie on a circle, centre O, diameter AC.
XY is a tangent to the circle at D.
(i) Use the information in the diagram to complete these two simultaneous equations.
9x + 3y = ……
18x - 4y = ……
[2]
(ii) Solve your simultaneous equations.
You must show all your working.
x = ……
y = …… [3]
Mark scheme
4(a)(ii) 3.5 1
4(b) 113 or 113.09… to 113.112 2 M1 for 2 × 18 × π oe
4(c)(i) 90 2 B1 for each
90
4(c)(ii) For correctly eliminating one M1 M1FT their two linear equations
variable
[ x =] 7 A1
[ y =] 9 A1 If M0 scored, SC1 for 2 values satisfying one
of their original equations
If no working shown, SC1 for two correct
answers given
(a) A closed box, in the shape of a cuboid, has length 5 cm, width 4 cm and height 2 cm.
(i) Draw a net of the box on the 1cm 2 grid.
[3]
(ii) A container is a cube with volume 1m 3 .
Work out the maximum number of these boxes that can be packed into this container.
…… [3]
(b) A shop sells three different sized boxes of rice.
The boxes all have the same cost per kilogram.
NOT TO
SCALE
Box A Box B Box C
80 rupees $3.50
750 g 1.35 kg
(i) Work out the cost in rupees of box B.
…… rupees [2]
(ii) $1 = 64 rupees.
Calculate the mass of box C.
Give your answer in kilograms.
…… kg [3]
(c) Change 75cm 3 into litres.
Give your answer in standard form.
…… litres [2]
Mark scheme
5(a)(i) Correct ruled net 3 B2 for 4 or 5 correct rectangles drawn in
correct positions relative to each other
or
B1 for one correct face drawn
5(a)(ii) 25 000 3 100 × 100 × 100
M2 for oe
2× 4×5
or M1 for 100 × 100 × 100
or 0.02×0.04×0.05
or 2×4×5
or 50, 25, 20
If 0 scored, SC1 for final answer figs 25
5(b)(i) 144 2 figs135 1.35 80 750
M1 for or or or
750 figs750 750 80
oe
or B1 for 1350 or 0.75[0]
5(b)(ii) 2.1 3 3.5 ×64 × figs75
M2 for oe
80
80
or M1 for 3.5× 64 or
64
5(c) 7.5 × 10−2 cao 2 75
M1 for oe
1000
If 0 scored, SC1 for correctly converting
their number to standard form, provided their
number is <1
6(a)(i)(a) 1 1
oe
9
6(a)(i)(b) 7 1
oe
9
(a)
6 5
6 7
5
3 5
8
2
The diagram shows a fair 9-sided spinner.
The numbers on the spinner are 2, 3, 5, 5, 5, 6, 6, 7 and 8.
(i) The spinner is spun once.
Write down the probability that the spinner lands on
(a) the number 8,
…… [1]
(b) a number less than 7.
…… [1]
(ii) The spinner is spun 135 times.
Work out the expected number of times the spinner lands on the number 6.
…… [1]
(b) Hitesh throws a dice 80 times.
The results are shown in the table.
Number thrown Frequency
1 15
2 16
3 14
4 11
5 9
6 15
(i) Write down the mode.
…… [1]
(ii) Work out the range.
…… [1]
(iii) Work out the median.
…… [1]
(iv) Calculate the mean.
…… [3]
(a) 1 mile = 1.609344 kilometres
Change 6 miles into metres.
Give your answer correct to the nearest metre.
…… m [3]
(b) (i) The bearing of a boat from a harbour is 322°.
Work out the bearing of the harbour from the boat.
…… [2]
(ii) The boat is 12 km from the harbour.
At 2.30 pm the boat starts to sail to the harbour.
The speed of the boat is 5 km/h.
Work out the time the boat arrives at the harbour.
…… [3]
(c) The scale drawing shows the positions of Shakti’s house, S, and Mairi’s house, M, on a map.
The scale is 1 cm represents 4 km.
North
S
North
M
Scale: 1 cm to 4 km
(i) Measure the bearing of M from S.
…… [1]
(ii)
North
S
Scale: 1 cm to 5 km
This scale drawing shows another map with Shakti’s house, S, marked on it.
The scale of this map is 1 cm represents 5 km.
Mark the position of Mairi’s house, M, on this map.
[4]
Mark scheme
7(a) 9656 cao 3 M2 for 6 × 1.609344 × 1000
or
M1 for 6 ×1.609344
or
B1 for final answer figs 9654 to 9660
If 0 scored, SC1 for their decimal answer
correctly rounded to nearest integer
7(b)(i) 142 2 M1 for 322 −180 oe
or a clear diagram with both 322 or 38
marked and the reverse bearing to be found
7(b)(ii) 4.54 pm or 16 54 3 12
M1 for soi
5
A1 for 2 h 24 [mins]
7(c)(i) 107 1
7(c)(ii) The position of M correctly marked 4 B1 for SM = 9[cm] soi
on the diagram
1
M1 for their SM ×4 ×
5
B1 for 7.2[cm] soi
or for bearing of M drawn at 107°
(a) (i) Complete the table of values for y = x 2 + 6x - 160 .
x -20 -15 -10 -5 0 5 10 15 y 120 -120 -165 -160 -105
[3]
(ii) On the grid, draw the graph of y = x 2 + 6x - 160 for - 20 G x G 15.
y
200
150
100
50
– 20 – 15 – 10 –5 0 5 10 15 x
– 50
– 100
– 150
– 200
[4]
(iii) (a) Write down the equation of the line of symmetry of the graph.
…… [1]
(b) Find the coordinates of the lowest point on the graph.
( …… , ……) [1]
(iv) Use your graph to solve the equation x 2 + 6x - 160 = 0 .
x = …… or x = …… [2]
(b) Rearrange the formula y = mx + c to make x the subject.
x = …… [2]
Mark scheme
8(a)(i) −25 0 155 3 B1 for each
8(a)(ii) Completely correct curve 4 B3FT for 7 or 8 correctly plotted points
B2FT for 5 or 6 correctly plotted points
B1FT for 3 or 4 correctly plotted points
8(a)(iii)(a) x = −3 oe 1
8(a)(iii)(b) ( − 3, k) oe 1 FT their graph
where −180 k < −165
8(a)(iv) 10 −16 2 B1 FT for each
8(b) y−c 2 M1 for correct first step
[ x =] oe final answer
y c
m y − c = mx or = x+
m m
Tarak has two fields.
He grows wheat, barley and corn in his fields.
(a)
P S
NOT TO
174 m SCALE
126 m
53°
Q 120 m R
The diagram shows Tarak’s two triangular fields, PQR and PRS.
Angle RPS = 90° and angle PRS = 53°.
PQ = 174 m, QR = 120 m and PR = 126 m.
(i) Show that angle PRQ = 90°.
[2]
(ii) Calculate the area of the quadrilateral PQRS.
Give your answer correct to 4 significant figures.
…… m2 [5]
(b) (i) The mass, m tonnes, of wheat grown in 2021 is 4.3 tonnes, correct to 1 decimal place.
Complete this statement about the value of m.
…… G m 1 …… [2]
(ii) In 2020, 2.6 tonnes of barley is grown.
In 2021, 3.25 tonnes of barley is grown.
Show that the percentage increase in barley grown from 2020 to 2021 is 25%.
[1]
(iii) In 2019, 2.4 tonnes of corn is grown.
In 2020, 20% more corn is grown than in 2019.
In 2021, 20% less corn is grown than in 2020.
Calculate the amount of corn grown in 2021.
…… tonnes [3]
Mark scheme
9(a)(i) Complete method shown and 2 M1 for correct Pythagoras
evaluated e.g. 1202 + 1262 = 1742
9(a)(ii) 18 090 cao 5 B4 for 18 081 to 18 094.1
OR
M2 for 126 × tan53
x
or M1 for tan53 =
126
and
1
M1 for × 120 × 126
2
1
or × 126 × theirPS
2
1
or × 126 × (120 + theirPS ) oe
2
If 0 scored, SC1 for evidence of rounding
their answer to 4sf
9(b)(i) 4.25 4.35 2 B1 for each
If 0 scored, SC1 for answers correct but
reversed
9(b)(ii) Complete method seen 1 3.25 − 2.6
e.g. × 100 [ = 25]
2.6
9(b)(iii) 2.304 3 100 + 20 100 − 20
M2 for 2.4 × × oe
100 100
100 + 20
or M1 for 2.4 × oe
100
100 − 20 100 + 20
or B1 for and used
100 100
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On this page, free: the mark scheme for IGCSE Mathematics 0580/32, February/March 2022 (0580_m22_ms_32), and the question paper (0580_m22_qp_32), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/32 for February/March 2022 is out of 104 marks, with 2 hours to answer it.
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