Mathematics 0580/32 October/November 2022: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), October/November 2022. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
(a) 2 18 27 29 39 49 80 92
From this list of numbers, write down
(i) a multiple of 8,
(ii) a factor of 46,
(iii) a square number,
(iv) a cube number,
(v) a prime number�
(b) Write 0�003 857 correct to
(i) 3 decimal places,
(ii) 3 significant figures�
(c) Anna invests $16 000 at a rate of 3�8% per year compound interest�
Calculate the value of her investment at the end of 5 years�
(d) (i) Write 48 as the product of its prime factors�
(ii) Find the lowest common multiple (LCM) of 48 and 126�
(e) The mass of a truck, m tonnes, is 28�5 tonnes, correct to 1 decimal place�
Complete this statement about the value of m�
Mark scheme
1(a)(i) 80 1
1(a)(ii) 2 1
1(a)(iii) 49 1
1(a)(iv) 27 1
1(a)(v) 2 or 29 1
1(b)(i) 0.004 cao 1
1(b)(ii) 0.00386 cao 1
1(c) 19 300 or 19 280 2 3.8 5
or 19 279.98 to 19 279.99 M1 for 16 000 × (1 + ) oe
100
1(d)(i) 2 × 2 × 2 × 2 × 3 or 24 × 3 2 B1 for 2, 2, 2, 2, 3
or M1 for a correct factor tree / diagram /
list / table
1(d)(ii) 1008 2 B1 for 1008k as final answer
or M1 for 2 × 2 × 2 × 2 × 3 × 3 × 7 oe
or 2, 2, 2, 2, 3, 3, 7
or for [126=] 2×3×3×7 or 2, 3, 3, 7
or [126=] 6×21 and [48=] 6×8 or 6, 21 and
6, 8
or correct factor tree / diagram / list / table
for 126
or a list of consecutive multiples of both 48
and 126 with at least 3 of each
1(e) 28.45 28.55 2 B1 for each
If 0 scored, SC1 for both correct but
reversed
(a)
a
(i) Measure the size of angle a�
(ii) Write down the mathematical name of this type of angle�
(b) The scale drawing shows the positions of town B and town C�
The scale is 1 cm represents 8 km�
North
B
Scale: 1 cm to 8 km
C
(i) Work out the actual distance between town B and town C�
(ii) Measure the bearing of town C from town B�
(c)
47° x° NOT TO
SCALE
y°
The diagram shows two parallel lines and a straight line crossing them�
Find the value of x and the value of y�
(d) A triangle has angles 119°, 31° and d °�
Explain why this triangle is scalene�
You must show your working�
(e) Find the size of one interior angle of a regular 15-sided polygon�
(f) One of the angles in a parallelogram is 64°�
Find the other three angles in this parallelogram�
Mark scheme
2(a)(i) 76 1
2(a)(ii) Acute 1
2(b)(i) 45.6 2 B1 for 5.7 cm
or M1 for their 5.7 × 8
2(b)(ii) 124 1
2(c) 133 2 B1 for each
47
2(d) 30 and 2 M1 for 180 – 119 – 31 oe
all three angles different oe
2(e) 156 2
M1 for 180 −
360
oe or
(15 −2 ) × 180 oe
15 15
2(f) 64, 116, 116 3 B1 for 64 as an answer
B1 for 116 seen
or M1 for (360 – 2 × 64) ÷ 2 oe
24 people own a car�
(a) Ranjit asks each of these 24 people the colour of their car�
The bar chart shows some of these results�
8
7
6
5
Frequency
4
3
2
1
0
Black Blue Red Green White
Colour
(i) Complete the bar chart by drawing the bar for the colour red�
[2]
(ii) Write down the mode�
(iii) How many more people have a green car than have a blue car?
(b) The table shows the size, in litres, of each of the 24 car engines�
Engine size (litres) 0�8 1�2 1�5 1�8 2�4
Frequency 7 4 5 6 2
Calculate the mean�
(c) Ranjit also asks each of the 24 people what type of car they have�
The pie chart shows some of these results�
Electric
60°
105°
Hybrid
(i) Work out the number of hybrid cars�
(ii) The rest of the cars are either petrol or diesel�
There are 8 petrol cars�
Complete the pie chart to show this information�
[2]
Mark scheme
3(a)(i) Bar at 6 with correct width 2 M1 for 24 – 6 – 2 – 7 – 3 oe
3(a)(ii) Green 1 FT their bar chart
3(a)(iii) 5 1
3(b) 1.4[0] or 1.395 to 1.396 3 M1 for
0.8×7 + 1.2×4 + 1.5×5 + 1.8×6 + 2.4×2 oe
M1dep for their 33.5 ÷ 24
3(c)(i) 7 2 105
M1 for × 24 oe
360
3(c)(ii) Correct sector with line at 120° 2 B1 for 120 soi
Mr and Mrs Perez and their 3 children go on holiday to Tokyo�
(a) The holiday costs $3800 for an adult and $2400 for a child�
8% tax is then added to the cost of the holiday�
Find the total cost of the holiday, including tax, for the Perez family�
(b) The plane takes 11 hours 40 minutes to fly from Los Angeles to Tokyo�
The plane leaves on Wednesday at 10 35 local time�
The local time in Tokyo is 17 hours ahead of the local time in Los Angeles�
(i) Find the day and local time in Tokyo when the plane arrives�
(ii) The distance the plane flies is 8820 km�
Calculate the average speed of the plane�
(c) The diagram shows a conversion graph between dollars and Japanese yen�
4500
4000
3500
3000
2500
Yen
2000
1500
1000
500
0
0 5 10 15 20 25 30 35 40
Dollars
A watch costs $100�
Find the cost of this watch in yen�
(d) The family go to a restaurant�
The total cost of the food and drinks is $154�
The ratio cost of food : cost of drinks = 21 : 4�
Work out the cost of drinks�
Mark scheme
4(a) 15 984 cao 4 8
M3 for (2×3800 + 3×2400) × (1+ ) oe
100
8
or M2 for [2×]3800 × (1+ ) oe
100
8
or [3×]2400 × (1+ ) oe
100
8
or (2 × 3800 + 3 × 2400) × oe
100
or M1 for 2 × 3800 + 3 × 2400 oe
8
or [k×]3800 × oe
100
8
or [k×]2400 × oe
100
where k is any integer
8
If 0 scored, SC1 for j × (1+ )
100
where j is any value
4(b)(i) Thursday and 15 15 or 3 15 pm 3 B1 for Thursday as final answer
B2 for 15 15 as final answer
or B1 for 22 15, [0]3 35, 28h 40, 39 15
If 0 scored, SC1 for 10 35 + 11 40 + 17
4(b)(ii) 756 2 M1 for 8820 ÷ their time
4(c) 11 000 or 10 875 to 11 125 2 B1 for 10 000 to 12 000 as answer
or M1 for 110 × 100
or for a valid method
e.g. look up ‘40’ × 2.5
4(d) 24.64 cao 2 154
M1 for × k where k is 1, 4 or 21 oe
21 + 4
(a) Apples cost $a per kilogram and bananas cost $b per kilogram�
Lee buys 6 kg of apples and 8 kg of bananas�
Write down an expression, in terms of a and b, for the total cost, in dollars, of the apples and the bananas�
(b) Cara is one year older than twice Asher’s age�
Brice is 22 years older than Asher�
The total of their three ages is 167�
Find the age of each person�
(c) Solve the simultaneous equations�
You must show all your working�
3x + 2y = 21
2x - 5y = 33
Mark scheme
5(a) 6a + 8b or 2(3a +4b) 2 B1 for 6a or 8b in final answer
final answer or correct answer seen then spoilt
5(b) 36 4 B3 for [Asher]36 or [Brice]58 or [Cara]73
58
73 OR
M2 for a correct equation which would lead
to 4a + 23 = 167
or for (167 – 23) ÷ 4 oe
or B1 for 2a + 1 or a + 22 seen
or (167 – 23) oe
M1 for 4a = 144 or for rearranging their
equation to ka = j
5(c) Correctly equating one set of M1
coefficients
Correct method to eliminate one M1 Dependent on the coefficients being the
variable same for one of the variables
Correct consistent use of addition or
subtraction using their equations
[x =] 9 A1
[y =] −3 A1 If M0 scored, SC1 for 2 values satisfying
one of the original equations
The diagram shows four flags, F, A, B and C, on a grid�
y
8
7
A
6
5
4
3
F
2
1
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 x
–1
B
–2
–3
–4
–5
–6
C
–7
–8
(a) Describe fully the single transformation that maps
(i) flag F onto flag A,
(ii) flag F onto flag B,
(iii) flag F onto flag C�
3
(b) On the grid, draw the image of flag F after a translation by the vector e o� [2]
-4
Mark scheme
6(a)(i) Enlargement 3 B1 for each
(–5, 1)
3
6(a)(ii) Rotation 3 B1 for each
(0, 0)
90° [anti-clockwise]
6(a)(iii) Reflection 2 B1 for each
y = −2
6(b) Flag with outline at (1, –3), (1, –2), 2 k
(1, –1), (2, –1) and (2, –2) B1 for correct translation
−4
3
or
k
(a)
NOT TO
2 cm A
4 cm B SCALE
12 cm
The area of rectangle A is equal to the area of rectangle B�
Work out which rectangle has the greater perimeter and by how much�
(b) A circle has an area of 150 cm 2 �
Calculate the radius of this circle�
(c)
NOT TO
SCALE
16 cm 16 cm
12 cm
An isosceles triangle has base 12 cm and sides 16 cm�
Find the area of this triangle�
Mark scheme
7(a) A 8 4 B2 for [length =] 6
or M1 for [area A =] 2 × 12
M1 for 2 × (2 + 12) oe
or 2 × (4 + 24 ÷ 4) oe
7(b) 6.91 or 6.909… 3 150
M2 for
π
or M1 for [r2 = ] 150 ÷ π
7(c) 89.0 or 88.98 to 89 5 2
12
M4 for 12 × 12 × 162 − oe
2
OR
B3 for [height =] 14.8 or 14.83… or 220
or 2 55
or M2 for 162 − (122 )2 oe or better
or M1 for [...]2 + (122 )2 = 162 oe
M1dep for 12 × 12 × their 14.8 oe
(a) (i) Complete the table of values for y = x 2 + 2x - 4 �
x −5 −4 −3 −2 −1 0 1 2 3 y 11 −1 −1 11
[3]
(ii) On the grid, draw the graph of y = x 2 + 2x - 4 for - 5 G x G 3�
y
12
11
10
9
8
7
6
5
4
3
2
1
–5 –4 –3 –2 –1 0 1 2 3 x
–1
–2
–3
–4
–5
–6
[4]
(iii) Write down the equation of the line of symmetry of the graph�
(iv) Use your graph to solve the equation x 2 + 2x - 4 = 0 �
(b) A line L has an equation of y = 5x + 7 �
Write down the equation of the line parallel to L that passes through (0, −2).
1
Mark scheme
8(a)(i) 4 –4 –5 –4 4 3 B2 for 3 or 4 correct
B1 for 1 or 2 correct
8(a)(ii) Correct curve 4 B3FT for 8 or 9 points correctly plotted
B2FT for 6 or 7 points correctly plotted
B1FT for 4 or 5 points correctly plotted
8(a)(iii) x = −1 oe 1
8(a)(iv) −3.3 to −3.1 1.1 to 1.3 2 FT their graph
B1FT for each
8(b) y = 5x – 2 final answer 2 B1 for y = 5x + k oe
or y = kx − 2 oe
or y = 5x + – 2 oe
or y = kx + – 2 oe
or 5x − 2 oe
or 5x + − 2 oe
(a) Write down the reciprocal of �
3
(b) Write down the value of 30�
3 4
(c) Find a fraction between and �
25 25
(d) Find the difference in temperature between −5 °C and 9 °C.
(e) Write in standard form�
(i) 5 600 000
(ii) 0�000 072
(f) Calculate (5.2 # 10 6) # (3.8 # 10 -2) �
Give your answer in standard form�
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.
Check your answers against it
Done this paper? Upload your script and CIE Buddy's AI marker marks it question by question against this exact scheme, puts the ticks on your own working and says what each lost mark needed.
Where can I find the 0580/32 October/November 2022 mark scheme?+
On this page, free: the mark scheme for IGCSE Mathematics 0580/32, October/November 2022 (0580_w22_ms_32), and the question paper (0580_w22_qp_32), to read or download, with each question's marking points written out underneath.
How many marks is 0580/32 out of?+
Mathematics 0580/32 for October/November 2022 is out of 104 marks, with 2 hours to answer it.
Can I get my 0580/32 answers marked?+
Yes. Upload your answers to 0580/32/O/N/22 as a PDF or photos, and CIE Buddy marks every question against this paper's official mark scheme, using Cambridge's marking rules. You get your score, each lost mark explained on your own script, and the topics to revise. It's a guide, not an official Cambridge grade.