Mathematics 0580/33 October/November 2021: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), October/November 2021. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
Roberto and his family fly from London to Los Angeles on a holiday.
(a) The flight takes 11 hours 15 minutes.
(i) The flight leaves London at 15 40 local time.
The local time in Los Angeles is 8 hours behind the local time in London.
Work out the local time in Los Angeles that the plane arrives.
…… [2]
(ii) The plane flies a total of 8760 km.
Calculate the average speed of the plane.
…… km/h [3]
(b) Roberto hires a car.
(i) The cost of hiring a car is $56 per day, plus a fixed cost of $436.
Write down a formula for the cost, C dollars, of hiring a car for d days.
…… [2]
(ii) Roberto is given a car at random.
There are four colours of car.
Colour Red Silver Black White
Probability 0.17 0.24 0.3
Complete the table. [2]
(c) The family visit a national park which has an area of 4986 km2.
(i) Write 4986 correct to the nearest hundred.
…… [1]
(ii) Write 4986 in standard form.
…… [1]
(d) A ticket for the park costs $17.50 plus 8% tax.
Calculate the amount of tax paid.
$ …… [1]
(e) The scale drawing shows the positions of two viewing points, A and B, in the park.
The scale is 1 centimetre represents 5 kilometres.
North
B North
A
Scale : 1 cm to 5 km
(i) Work out the actual distance between point A and point B.
…… km [2]
(ii) Point C is 20 km from point A on a bearing of 072°.
On the scale drawing mark the position of point C. [2]
Mark scheme
1(a)(i) 18 55 2 B1 for 07 40 or 02 55 or 3[h] 15 [min]
or
M1 for departure time + 11h 15 min − 8h
evaluated as a time with one interval
correctly added
1(a)(ii) 779 or 778.6 to 778.7 3 8760
M2 for 8760 ÷ 11.25 oe × 60
675
or B1 for 11.25
or M1 for 8760 ÷ their time
1(b)((i) C = 56d + 436 cao 2 B1 for C = 56d + 436 seen and spoilt
or 56d + 436 as final answer
1(b)(ii) 0.29 2 M1 for 1 – (0.17 + 0.24 + 0.3) oe or
better
1(c)(i) 5000 1
1(c)(ii) 4.986 × 103 1
1(d) 1.4[0] 1
1(e)(i) 35 2 B1 for 7
1(e)(ii) Correct length and bearing 2 B1 for length 4 cm from A
B1 for bearing 072° from A
(a) The bar chart shows the number of cars sold by a garage in each of six months.
16
14
12
Number of 10 cars sold 8
6
4
2
0
Jan Feb Mar Apr May Jun Jul
Month
(i) In July, 11 cars were sold.
Complete the bar chart. [1]
(ii) How many more cars were sold in March than in May?
…… [1]
(b) These are the opening times of the garage.
Monday to Friday 8.30 am to 5.30 pm
Saturday 8.30 am to 1.00 pm
Sunday Closed
Work out how many hours the garage is open in one week.
…… h [2]
(c) Mohammed works at the garage.
He works for 36 hours from Monday to Friday and for 2 hours on Saturday.
He is paid $10.50 per hour from Monday to Friday.
On Saturday he is paid 1 12 times this rate.
Calculate how much Mohammed is paid for this week.
$ …… [3]
(d) Viktor is saving to buy a car.
He invests $8000 for 5 years at a rate of 2.4% per year compound interest.
Calculate the value of Viktor’s investment at the end of the 5 years.
Give your answer correct to the nearest dollar.
$ …… [3]
(e) At the garage, Pierre, Luigi and Freda sell cars.
They share a bonus of $12 000 in the ratio Pierre : Luigi : Freda = 8 : 4 : 3.
Calculate the amount they each receive.
Pierre $ ……
Luigi $ ……
Freda $ …… [3]
Mark scheme
2(a)(i) Bar at height 11 1
2(a)(ii) 9 1
2(b) 49.5 2 M1 for 5 × 9 + 4.5 oe
2(c) 409.5[0] cao 3 M2 for 36 × 10.5 + 10.5 × 1.5 × 2 oe
or M1 for 36 × 10.5 or 10.5 × 1.5 × 2
or 36 + 1.5 × 2 oe
2(d) 9007 cao nfww 3 B2 for 9007.[...]
2.4 5
or M1 for 8000 × (1 + ) oe
100
If M0 or M1 scored, SC1 for their decimal
answer correctly rounded to the nearest
dollar
2(e) 6400 3 B2 for one correct answer in the correct
3200 place
2400
or M1 for 12 000 ÷ (8+4+3) [× k] where k
is 8, 4, 3 or 1
(a) Write down the order of rotational symmetry of each shape.
[2]
(b) Triangles A, B and C are shown on the grid.
y
8
7
6
5
4 C
3
2
1
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 x
–1
–2
–3
B
A –4
–5
–6
(i) Describe fully the single transformation that maps
(a) triangle A onto triangle B,
…… [3]
(b) triangle A onto triangle C.
…… [3]
(ii) On the grid, reflect triangle C in the line x =- 1. [2]
5
(iii) On the grid, translate triangle C by the vector e o. [2]
-1
Mark scheme
3(a) 8 2 B1 for each
4
3(b)(i)(a) Enlargement 3 B1 for each
[centre] (–7, –5)
[sf] 2
3(b)(i)(b) Rotation 3 B1 for each
[centre] (0, 0) oe
180°
3(b)(ii) Triangle at (–3, 5), (–5, 5), (–5, 2) 2 B1 for correct reflection in x = k k ≠ –1
3(b)(iii) Triangle at (6, 4), (8, 4), (8, 1) 2 5 k
B1 for a translation by or
k –1
(a)
x
(i) Measure the size of angle x.
Angle x = …… [1]
(ii) Write down the mathematical name of this type of angle.
…… [1]
(b)
D
NOT TO
74° SCALE
y°
A B C
ABC is a straight line and ABD is an isosceles triangle.
Find the value of y.
y = …… [3]
(c)
G
F
NOT TO
O SCALE
E
E, F and G are points on the circle, centre O.
EG = 12 cm.
(i) Write down the mathematical name for the line FG.
…… [1]
(ii) Explain why angle EFG is 90°.
…… [1]
(iii) Calculate the area of the circle.
…… cm2 [2]
Mark scheme
4(a)(i) 42 1
4(a)(ii) Acute 1
4(b) 127 3 B2 for 53
or M2 for 180 − [(180 – 74) ÷ 2]
or M1 for (180 – 74) ÷ 2 or better
4(c)(i) Chord 1
4(c)(ii) Angle in a semicircle = 90 1
4(c)(iii) 113 or 113.0 to 113.1[...] 2 M1 for 62 × π oe
(a) A cuboid measures 4 cm by 2 cm by 2 cm.
(i) On the 1 cm2 grid, draw an accurate net of this cuboid.
One face has been drawn for you.
[3]
(ii) Calculate the surface area of the cuboid.
…… cm2 [2]
(iii) A factory makes 5000 of these cuboids.
25 of the cuboids are checked and 3 of these cuboids are faulty.
How many of the 5000 cuboids are expected to be faulty?
…… [2]
(b) The surface area of a cube is 294 cm2.
Calculate the volume of the cube.
…… cm3 [3]
(c) The length, l cm, of a line is measured as 24 cm, correct to the nearest centimetre.
Complete the statement about the value of l.
…… G l 1 …… [2]
Mark scheme
5(a)(i) Fully correct net 3 B2 for 4 more correct faces in correct
position
or B1 for 2 or 3 more correct faces in
correct position
5(a)(ii) 40 2 M1 for 4 (4 × 2) + 2(2 × 2) oe
5(a)(iii) 600 2 M1 for 3 ÷ 25 [× 5000] oe
5(b) 343 3 M2 for (294 ÷ 6) 3 oe
or M1 for 294 ÷ 6 or better
5(c) 23.5 2 B1 for each
24.5
If 0 scored, SC1 for both correct but
reversed
(a) Jean asks 600 people to choose their favourite sport.
The pie chart shows some of this information.
Football
105°
60°
27°
Tennis
Rugby
(i) Show that 100 people choose tennis.
[1]
(ii) Work out how many people choose rugby.
…… [2]
(iii) 125 people choose cricket and the rest choose swimming.
Complete the pie chart to show this information.
[2]
(iv) One of the 600 people is picked at random.
Find the probability that this person chooses tennis or cricket.
Give your answer as a fraction in its simplest form.
…… [2]
(b) There are 80 people in a group.
H = {people who play hockey}
N = {people who play netball}
36 people play hockey.
53 people play netball.
8 people do not play hockey or netball.
H N
Complete the Venn diagram. [3]
Mark scheme
6(a)(i) 60 1
× 600 oe
360
6(a)(ii) 45 2 27
M1 for × 600 oe
360
6(a)(iii) Correct straight line on the pie chart 2 B1 for 75
6(a)(iv) 3 2 100 + 125 75 + 60
cao M1 for oe or oe
8 600 360
6(b) 3 B1 for 8
H N
B1 for 17
19 17 36
B1 for total in H equals 36 and total in N
equals 53 provided H ∩ N ≠ Ø
8 If 0 scored, SC1 for
36 – x + x + 53 – x +8 = 80 or better
(a) Write the number six hundred and three thousand eight hundred and twenty-one in figures.
…… [1]
(b) Pens cost 47 cents each.
Aroha buys 8 pens.
How much change does she receive from $5?
$ …… [2]
(c) Find the value of
(i) 81,
…… [1]
(ii) 63,
…… [1]
(iii) 30.
…… [1]
(d) Write 130 as a product of its prime factors.
…… [2]
(e) A tower has two bells, A and B.
Bell A rings every 12 minutes.
Bell B rings every 14 minutes.
Both bells ring at 09 30.
Find the next time both bells ring together.
…… [3]
Mark scheme
7(a) 603 821 1
7(b) 1.24 2 M1 for 5 – (0.47 × 8) oe
7(c)(i) 9 1
7(c)(ii) 216 1
7(c)(iii) 1 1
7(d) 2 × 5 × 13 2 B1 for 2, 5, 13
or M1 for correct factor tree/diagram/list/
table
7(e) 1054 3 B2 for 84 or 1 hr 24 mins
or M1 for 84k
or 2 × 2 × 3 × 7
or [12 =] 2 × 2 × 3 and [14 =] 2 × 7
or 2 correct factor trees / tables of both 12
and 14
OR
M2 for listing times/multiples of both 12
and 14 to at least 1054 or 84
or M1 for listing at least 3 of each or one
full list
(a) Line L is shown on the grid.
y
25
20
15 L
10
5
–6 –5 –4 –3 –2 –1 0 1 2 3 x
–5
– 10
Find the equation of line L in the form y = mx + c .
y = …… [3]
(b) (i) Complete the table of values for y = x 2 + 4x .
x -6 -5 -4 -3 -2 -1 0 1 2 3 y 12 5 0 -3 -3 0 5 12
[2]
(ii) On the grid, draw the graph of y = x 2 + 4x for - 6 G x G 3.
y
25
20
15
10
5
–6 –5 –4 –3 –2 –1 0 1 2 3 x
–5
– 10
[4]
(iii) Use your graph to solve the equation x 2 + 4x = 10 .
x = …… or x = …… [2]
Mark scheme
8(a) 2.5x + 10 final answer 3 B2 for 2.5x + c
OR
M1 for a correct rise over run
or for a right-angled triangle marked on
grid with rise =10 and run = 4 oe
B1 for [y =] kx +10 (k ≠ 0)
8(b)(i) –4 21 2 B1 for each
8(b)(ii) Correct curve 4 B3FT for 9 or 10 points correctly plotted
or B2FT for 7 or 8 points correctly plotted
or B1FT for 5 or 6 points correctly plotted
8(b)(iii) –5.8 to –5.6 and 1.6 to 1.8 2 FT their curve
B1 for each
(a) Simplify.
3g + 7g - 4g
…… [1]
(b) Solve.
4x + 5 = 27
x = …… [2]
(c) 6 p # 6 3 = 6 17
Work out the value of p.
p = …… [1]
(d) Mia buys 4 calculators and 2 pens for $20.60 .
Heidi buys 5 calculators and 3 pens for $26.90 .
Write down a pair of simultaneous equations and solve them to find the cost of a calculator and the cost of a pen.
Calculator $ ……
Pen $ …… [6]
Mark scheme
9(a) 6g 1
9(b) 5.5 2 4 x 5 27
M1 for 4x = 27– 5 or + =
4 4 4
or better
9(c) 14 1
9(d) 4c + 2p = 20.60 B1
5c + 3p = 26.90 B1
correctly equating one set of coefficients M1
correct method to eliminating one variable M1 Dependent on the coefficients being the
same for one of the variables
Correct consistent use of addition or
subtraction using their equations
[c =] 4 A1
[p =] 2.30 A1 If M0 scored, SC1 for two values that
satisfy one of the original or FT equations
SC1 if no working shown, but 2 correct
answers given
If A0A0 working in cents SC1 for final
answers of 400 and 230
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On this page, free: the mark scheme for IGCSE Mathematics 0580/33, October/November 2021 (0580_w21_ms_33), and the question paper (0580_w21_qp_33), to read or download, with each question's marking points written out underneath.
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Mathematics 0580/33 for October/November 2021 is out of 104 marks, with 2 hours to answer it.
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