Mathematics 0580/31 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.
Helga buys some items to do some knitting.
(a) Complete Helga’s bill from one shop.
Item Cost ($)
2 pairs of knitting needles at $4.95 a pair
6 buttons at $0.65 each
1 knitting pattern at $3.60 3.60
Total
[3]
(b) Helga also buys 8 balls of wool from another shop.
Each ball costs $3.12 .
Helga pays with a $50 note.
Work out the amount of change she receives.
$ …… [2]
(c) Helga knits some squares.
Each square is either white, pink or blue.
The number of squares are in the ratio white : pink : blue = 5 : 3 : 2.
30 squares are blue.
Show that Helga knits 150 squares.
[2]
(d) Helga uses some of the squares to make a rectangular blanket.
The blanket is 6 squares long and 4 squares wide.
(i) Calculate the percentage of the 150 squares she uses to make this blanket.
…… % [2]
(ii) Each square has side length 15 cm.
Work out the perimeter of this blanket.
Give your answer in metres.
…… m [3]
Mark scheme
1(a) 9.9[0] 2 B1 for each
3.9[0]
17.4[0] 1 FT their table
1(b) 25.04 2 M1 for 50 – (8 × 3.12)
or B1 for 24.96
1(c) 30 2 30 5+3+ 2
× (5 + 3 + 2) M1 for or
2 2 2
1(d)(i) 16 2 M1 for 6 × 4 soi by 24
1(d)(ii) 3 3 M2 for 2(6 × 15 + 4 × 15) oe
or 2(6 × 0.15 + 4 × 0.15) oe
or M1 for 6 × 15 or 4 × 15 oe
or 6 × 0.15 or 4 × 0.15 oe
or 2 × (6 + 4) oe
Triangles A, B and C are shown on the grid.
y
6
5
4
3
A
2
C
1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x
-1
-2
B
-3
-4
-5
-6
(a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
…… [3]
(ii) triangle A onto triangle C.
…… [3]
(b) On the grid,
(i) reflect triangle A in the line y = 0 , [2]
-7
(ii) translate triangle A by the vector e o. [2]
1
Mark scheme
2(a)(i) Rotation 3 B1 for each
180°
(0, 0)
2(a)(ii) Enlargement 3 B1 for each
0.5 oe
(–1, 1)
2(b)(i) Shape drawn at (3, –1), (5, –1), (3, –5) 2 B1 for reflection in x = 0 or y = k
2(b)(ii) Shape drawn at (–4, 2), (–2, 2), (–4, 6) 2 −7 k
B1 for a translation by or
k 1
Miguel works in an office.
(a) It takes Miguel 40 minutes to drive to work.
(i) He leaves home at 07 45.
What time does he arrive at work?
…… [1]
(ii) Miguel drives to work at an average speed of 57 km/h.
Show that he drives 38 km.
[2]
(b) White paper costs w cents per sheet and pink paper costs p cents per sheet.
Miguel uses 56 sheets of white paper and 21 sheets of pink paper.
Write down an expression, in terms of w and p, for the total cost, in cents, of the paper he uses.
…… cents [2]
(c) Miguel has a closed box of pens.
The box is in the shape of a cuboid measuring 20 cm by 12 cm by 7 cm.
Calculate the surface area of the box.
…… cm 2 [3]
(d) Miguel records the length of time of each telephone call he receives, correct to the nearest minute.
7 15 6 28 8 21 17 19 20 12
11 19 12 3 20 23 14 9 4 18
(i) Complete the frequency table.
You may use the tally column to help you.
Time (minutes) Tally Frequency
0-5
6 - 10
11 - 15
16 - 20
21 - 25
26 - 30
[2]
(ii) Draw a bar chart to show this information.
Complete the scale on the frequency axis.
Frequency
0
0–5 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30
Time (minutes)
[3]
(iii) Use the bar chart to write down the modal group.
…… — …… [1]
Mark scheme
3(a)(i) 08 25 1
3(a)(ii) 40 2 40
57 × [= 38] M1 for or 57 × 40
60 60
3(b) 56w + 21p final answer 2 B1 for 56w or 21p in final answer
or for 56w + 21p seen then spoilt
3(c) 928 3 M2 for [2 ×](20 × 12 + 20 × 7 + 12 × 7)
oe
or M1 for (20 × 12) or (20 × 7) or (12 × 7)
3(d)(i) 2 4 5 6 2 1 2 B1 for 4 or 5 correct frequencies
If 0 scored SC1 for correct tallies if
frequency column blank or all frequencies
correct but not in the frequency column
3(d)(ii) Suitable scales on y-axis 1
Bars at correct height 1 FT their frequency
Bars equal width 1
3(d)(iii) 16 – 20 1 FT their bar chart
(a) Find
(i) a multiple of 3 between 70 and 80,
…… [1]
(ii) a factor of 63 between 5 and 10,
…… [1]
(iii) a cube number between 60 and 90,
…… [1]
(iv) the reciprocal of 7.
…… [1]
2
(b) Work out of 84.
7
…… [1]
(c) Find the value of
3
(i) 3375,
…… [1]
(ii) 12 0 .
…… [1]
(d) Rana hires a car.
The cost is $74 per day plus a delivery cost of $17.50 .
Rana pays a total of $461.50 .
Calculate the number of days that Rana hires the car.
…… days [2]
(e) A train to town A leaves a station every 25 minutes.
A train to town B leaves the same station every 45 minutes.
Both trains leave at 08 00.
Find the next time both trains leave together.
…… [3]
Mark scheme
4(a)(i) 72 or 75 or 78 1
4(a)(ii) 7 or 9 1
4(a)(iii) 64 1
4(a)(iv) 1 1
or 0.143 or 0.142[8..]
7
4(b) 24 1
4(c)(i) 15 1
4(c)(ii) 1 1
4(d) 6 nfww 2
M1 for
( 461.5 –17.5) oe
74
4(e) 11 45 3 B2 for 225 or 3 hr 45 mins
or M1 for 225k
or 3 × 3 × 5 × 5
or [25 =] 5 × 5 and [45 =] 3 × 3 × 5
or two correct factor trees/tables of both 25
and 45
OR
M2 for listing times/multiples of both 25
and 45 to at least 11 45 or 225
or M1 for listing at least 3 consecutive
times/multiples of each correctly
or one full list
(a) The table shows the number of items sold to each of 60 customers in a shop.
Number of items Frequency sold
0 3
1 6
2 12
3 8
4 14
5 10
6 3
7 4
(i) Find the range.
…… [1]
(ii) Calculate the mean.
…… [3]
(iii) Find the probability that a customer picked at random buys more than 4 items.
…… [2]
(b) Carlotta buys a bicycle.
(i) The length, l cm, of the bicycle is 96 cm, correct to the nearest centimetre.
Complete this statement about the value of l.
…… G l 1 …… [2]
(ii) The diameter of each bicycle wheel is 46 cm.
Carlotta rides the bicycle a distance of 1.4 km.
Calculate the number of complete revolutions that a wheel makes during this journey.
…… [5]
Mark scheme
5(a)(i) 7 nfww 1
5(a)(ii) 13 3 M1 for [0 × 3] + 1 × 6 + 2 × 12 + 3 × 8 +
3.43 or 3
30 4 × 14 + 5 × 10 + 6 × 3 + 7 × 4
M1 dep for their 206 ÷ 60
5(a)(iii) 17 2 10 + 3 + 4
M1 for
60 60
or B1 for 17
5(b)(i) 95.5 96.5 2 B1 for each
If 0 scored, SC1 for both correct but
reversed
5(b)(ii) 968 5 B4 for 969 or 968.6 to 968.8 as final
answer
OR
140000
M3 for oe
46π
figs 1400
or M2 for oe
figs 46π
or M1 for figs 46 × π oe
or 2 × figs 23 × π oe
B1 for correctly truncating answer to
integer
(a)
Write down the mathematical name of this solid.
…… [1]
(b)
A B C D
104°
NOT TO
SCALE
x°
E
The diagram shows triangle BCE and a straight line ABCD.
BE = CE and angle ABE = 104°.
Find the value of x.
x = …… [2]
(c) Work out the size of one interior angle of a regular polygon with 15 sides.
…… [2]
(d)
B y°
O
A NOT TO
38°
SCALE
C
A, B and C are points on a circle, centre O.
(i) Write down the mathematical name of the line BC.
…… [1]
(ii) Draw a tangent to the circle at point B. [1]
(iii) The area of the circle is 245.5 cm 2 .
Calculate AB.
AB = …… cm [3]
(iv) Find the value of y.
y = …… [2]
Mark scheme
6(a) Cylinder 1
6(b) 28 2 M1 for 180 – 104 oe
6(c) 156 2
M1 for 180 –
360
oe or
(15 − 2 )180 oe
15 15
6(d)(i) Chord 1
6(d)(ii) Tangent drawn at point B 1
6(d)(iii) 17.7 or 17.67 to 17.68 3 M2 for [2×] 245.5 ÷ π oe
or M1 for 245.5 ÷ π oe
6(d)(iv) 52 2 M1 for 180 – 90 – 38 oe
or B1 for [angle ACB =] 90 correctly
identified
(a) Simplify.
5g - 3h - 7g + 6h
…… [2]
(b) j = 4k + 7m
Find the value of j when k =- 5 and m = 6 .
j = …… [2]
(c) Factorise completely.
14x 3 + 49x
…… [2]
(d) Solve.
8 (3t - 9) = 108
t = …… [3]
(e) (i) 9 24 ' 9 w = 9 5
Find the value of w.
w = …… [1]
(ii) 4x 2 = 256
Find the value of x.
x = …… [1]
(f) Ranjit’s age is x years.
Suzi’s age is 3 times Ranjit’s age.
Juan’s age is 4 years more than Suzi’s age.
The total of their ages is 46 years.
Use this information to write down an equation and solve it to find the value of x.
x = …… [4]
-3 7
Mark scheme
7(a) –2g +3h final answer 2 B1 for –2g or 3h in final answer
or –2g+ 3h seen then spoilt
7(b) 22 2 M1 for 4 × –5 + 7 × 6
or B1 for –20 or [+]42
7(c) 7x(2x2 + 7) final answer 2 B1 for 7(2x3 +7x) or x(14x2 + 49)
or correct answer seen then spoilt
7(d) 7.5 3 M1 for a first correct step
24t – 72 = 108 or 3t –9 =13.5
M1FT for a second correct step
e.g. 24t =180 or 3t =22.5
7(e)(i) 19 1
7(e)(ii) 8 1
7(f) x + 3x + 3x + 4 = 46 4 M2 for a correct equation which would
or 7x + 4 = 46 lead to 7x + 4 = 46
leading to x = 6 or B1 for 3x or 3x + 4 seen
M1 for 7x = 42 or for rearranging their
equation to ax = b
B1 for [x =] 6
(a) a=e o b=e o
5 -4
Work out.
(i) 4a
f p [1]
(ii) 2a - b
f p [2]
(b) y
4
3
2
P
1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x
-1
-2
-3
-4
(i) Write down the coordinates of point P.
( …… , …… ) [1]
(ii) On the grid, plot point Q at (- 4, 2) . [1]
-2
(iii) PR = e o
1
On the grid, plot point R. [1]
(iv) On the grid, draw the line y = 3. [1]
(c) y
3 L
2
1
-1 0 1 2 3 x
-1
-2
-3
-4
-5
Line L is shown on the grid.
(i) Find the equation of line L in the form y = mx + c .
y = …… [2]
(ii) Write down the equation of a line parallel to line L.
y = …… [1]
Question 9 is printed on the next page.
Mark scheme
8(a)(i) –12 1
20
8(a)(ii) –13 2 –13 k
B1 for or
14 j 14
8(b)(i) (3, 1) 1
8(b)(ii) Q plotted at (–4, 2) 1
8(b)(iii) R plotted at (1, 2) 1
8(b)(iv) Line y = 3 drawn 1
8(c)(i) [y =] 2x – 3 2 B1 for 2x + c or mx – 3 (m ≠ 0 or 2)
8(c)(ii) y = 2x + k 1 FT their gradient (not zero) with different
intercept than in (c)(i)
(a) Sami buys a new car.
(i) She pays a deposit of $2250 and 36 equal monthly payments of $437.50 .
Show that she pays a total amount of $18 000.
[2]
(ii) Sami later sells the car for $13 680.
Calculate the percentage loss.
…… % [2]
(b) Sami invests $12 750 for 6 years at a rate of 1.8% per year compound interest.
Calculate the value of her investment at the end of the 6 years.
$ …… [2]
Mark scheme
9(a)(i) 2250 + 437.5 × 36 [= 18 000] 2 M1 for 437.5 × 36
9(a)(ii) 24 2 18000 –13680
M1 for [×100] oe
18000
13680
or 1 – [× 100] oe
18000
13680
or [100 −] × 100 oe
18000
9(b) 14 200 or 14 190 2 1.8 6
or 14 190.5 or 14 190.47… M1 for 12 750 1 + oe
100
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Mathematics 0580/31 for October/November 2022 is out of 104 marks, with 2 hours to answer it.
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