Mathematics 0580/32 October/November 2020: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), October/November 2020. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
George, Louis and Beatriz have a café.
(a) George records the number of each type of meal sold.
He draws a pictogram to show his results.
All rows are complete except for Salad.
Type of meal Number of meals
Meat curry
Pasta
Vegetarian
Salad
Fish
Sandwich
Key: = 8 meals
(i) Six salads were sold.
Complete the pictogram. [1]
(ii) Write down which type of meal was sold most.
…… [1]
(iii) Find the number of meals sold altogether.
…… [1]
(b) The café also sells drinks.
Drinks
Cup of tea $2.20
Cup of coffee $2.80
Bottle of juice $1.50
Bottle of water $1.35
Johan buys 2 cups of tea, 1 bottle of juice and 1 bottle of water.
Calculate the change he receives from a $10 note.
$ …… [2]
(c) These are the opening times of the café.
Monday to Friday 8 am to 6 pm
Saturday 9.30 am to 3 pm
Sunday Closed
Work out the total number of hours the café is open in one week.
…… hours [2]
(d) One week the café makes a profit of $1027.
George, Louis and Beatriz share this profit in the ratio George : Louis : Beatriz = 7 : 4 : 2.
Calculate the amount of money they each receive.
George $ ……
Louis $ ……
Beatriz $ …… [3]
(e) In 2019 the rent for the café was $7275.
In 2020 the rent is $7566.
Calculate the percentage increase in the rent.
…… % [2]
(f) George drives 315 km from the café to the airport.
The journey takes 3 hours 30 minutes.
Calculate his average speed.
…… km/h [1]
Mark scheme
1(a)(i) 3 1
of rectangle marked on diagram
4
1(a)(ii) Pasta 1
1(a)(iii) 68 1
1(b) 2.75 2 M1 for [10 –] (2.20 + 2.20 + 1.50 + 1.35)
oe
1(c) 55.5 oe 2 M1 for (10 × 5 + 5.5) oe
1(d) 553 3 M2 for 1027 ÷ (7 + 4 + 2) × k or better
316 where k is 7, 4 or 2
158
M1 for 1027 ÷ (7 + 4 + 2) oe
1(e) 4 nfww 2 7566 − 7275
M1 for [× 100]
7275
7566
or −1 [× 100]
7275
7566
or × 100 [ − 100]
7275
1(f) 90 1
(a)
Measure the length of this line in millimetres.
…… mm [1]
(b)
x
(i) Measure the size of angle x.
…… [1]
(ii) Write down the mathematical name of this type of angle.
…… [1]
(c)
A B C x°
NOT TO
SCALE
26°
D
ABC is a straight line and BCD is an isosceles triangle.
Find the value of x.
x = …… [2]
(d) Work out the size of one interior angle of a regular 16-sided polygon.
…… [2]
(e)
X
NOT TO
O SCALE
Y
Z
(i) Complete this statement.
X, Y and Z are points on the …… of the circle, centre O. [1]
(ii) Give a reason why angle XYZ is 90°.
…… [1]
(f) A circle has diameter 6 cm.
Calculate the area of the circle.
Give the units of your answer.
…… …… [3]
Mark scheme
2(a) 46 to 50 1
2(b)(i) 221 to 225 1
2(b)(ii) Reflex 1
2(c) 103 2 M1 for (180 – 26) ÷ 2 oe
2(d) 157.5 2 M1 for 180 – 360 ÷ 16 oe
or (16 – 2) × 180 ÷ 16 oe
2(e)(i) Circumference 1
2(e)(ii) Angle [in a] semicircle [is] 90° 1
2(f) 28.3 or 28.27 to 28.28 2 M1 for 32 × π oe
cm2 1 indep
(a) Write down the mathematical name for this
(i) quadrilateral,
…… [1]
(ii) solid.
…… [1]
(b) The area of a square is 64 cm 2 .
Work out the length of one side of the square.
…… cm [1]
(c) The length, l, of a rectangle is 3 cm longer than the width, w.
The perimeter of the rectangle is 26 cm.
Calculate the length, l, and the width, w.
l = …… cm
w = …… cm [3]
(d) A cuboid measures 6 cm by 3 cm by 1 cm.
(i) On the 1 cm 2 grid, draw an accurate net of this cuboid.
One face has been drawn for you.
[3]
(ii) Calculate the surface area of the cuboid.
…… cm 2 [2]
Mark scheme
3(a)(i) Trapezium 1
3(a)(ii) Cylinder 1
3(b) 8 1
3(c) 8 3 M2 for 4w = 20 oe
5
or M1 for w + w + 3 + w + w + 3 = 26 oe
If 0 scored,
SC2 for correct answers reversed
or SC1 for 2 answers where l + w = 13
3(d)(i) Correct net 3 B2 for 4 more correct faces in correct
position
or B1 for 2 or 3 more correct faces in
correct position
3(d)(ii) 54 2 M1 for [2 ×] (6 × 3 + 6 × 1 + 3 × 1) oe
(a) Sami travels to work by bus.
The bus leaves the bus station at 07 35.
(i) It takes Sami 23 minutes to walk from his house to the bus station.
Work out the latest time Sami can leave his house.
…… [1]
(ii) The bus journey takes 41 minutes.
Work out the arrival time of the bus.
…… [1]
(b) The scale drawing shows the positions of two towns, A and B.
The scale is 1 centimetre represents 10 kilometres.
North
A
North
B
Scale : 1 cm to 10 km
(i) Work out the actual distance between town A and town B.
…… km [2]
(ii) Town C is 85 km from town A on a bearing of 100°.
On the scale drawing, mark the position of town C. [2]
Mark scheme
4(a)(i) [0]7 12 1
4(a)(ii) [0]8 16 1
4(b)(i) 93 to 97 2 B1 for 9.3 to 9.7
4(b)(ii) C in correct position 2 B1 for correct distance of 8.5 cm or correct
bearing of 100°
(a) Here are the weekly wages, in dollars, of the ten workers in an office.
280 200 175 1180 95 182 238 256 194 250
(i) Find the median.
$ …… [2]
(ii) Calculate the mean.
$ …… [2]
(iii) For this office, explain why the mean is not a suitable average.
…… [1]
(b) The stem-and-leaf diagram shows the ages of the workers in a factory.
1 6 7 7 9
2 2 3 4 6 8
3 0 2 3 6 9
4 1 4 4 8
5 0 1 6 6 6 9
6 1 5 8
Key : 2 3 represents 23
(i) Write down the mode.
…… [1]
(ii) Work out the range.
…… [1]
Mark scheme
5(a)(i) 219 2 B1 for a list of at least first or last 6
correctly ordered
or 200 and 238 identified
5(a)(ii) 305 2 M1 for (280 + 200 + 175 + 1180 + 95 + 182
+ 238 + 256 + 194 + 250) ÷ 10
5(a)(iii) One extreme value makes it higher oe 1
5(b)(i) 56 1
5(b)(ii) 52 1
(a) Write 60 025 in words.
…… [1]
(b) Write 849.481 correct to 1 decimal place.
…… [1]
(c) Write down
(i) all the factors of 21,
…… [2]
(ii) a prime number between 40 and 50.
…… [1]
2
(d) Write as a decimal.
5
…… [1]
(e) Find the value of
3
(i) 2744 ,
…… [1]
(ii) 70 .
…… [1]
(f) Gino invests $6000 for 5 years at a rate of 1.2% per year compound interest.
Calculate the value of his investment at the end of the 5 years.
Give your answer correct to the nearest dollar.
$ …… [3]
Mark scheme
6(a) Sixty thousand [and] twenty five 1
6(b) 849.5 cao 1
6(c)(i) 1, 3, 7, 21 2 B1 for 3 factors and no extras
or 4 correct and 1 extra
6(c)(ii) 41, 43 or 47 1
6(d) 0.4 cao 1
6(e)(i) 14 1
6(e)(ii) 1 1
6(f) 6369 cao 3 1.2 5
M1 for 6000 × 1 + or better
100
A1 for 6368.7...., or 6368 or 6370
If A0 scored, SC1 for correctly rounding
their decimal answer
y
8
7
6
5
4
D B
3
2
1
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 x
–1
–2
–3
A C
–4
–5
(a) Describe fully the single transformation that maps
(i) triangle A onto triangle B,
…… [3]
(ii) triangle A onto triangle C,
…… [2]
(iii) triangle A onto triangle D.
…… [2]
(b) On the grid, enlarge triangle A by scale factor 0.5, centre (4, 0). [2]
Mark scheme
7(a)(i) Rotation 3 B1 for each
180°
[centre] (0, 0)
7(a)(ii) Reflection 2 B1 for each
x = 0 or y axis
7(a)(iii) Translation 2 B1 for each
−1
7
7(b) Triangle at (–1, –2) (1, –2) (1, –1) 2 B1 for correct scale factor in wrong position
(a)
COMMONWEALTH
Lindon picks a letter at random from this word.
1
Explain why the probability that he picks a letter M is not .
10
…… [1]
(b) Tickets for athletics or swimming or hockey or diving are placed in a box.
A ticket is picked at random from the box.
Sport Athletics Swimming Hockey Diving
Probability 0.12 0.09 0.4
Complete the table. [2]
(c) In a group of 40 students,
• 24 students like football
• 19 students like cricket
• 10 students like football but not cricket.
Football Cricket
Complete the Venn diagram. [3]
(d) = {x : x is a positive integer less than 20}
A = {x : x is an even number}
B = {x : x is a multiple of 3}
A B
2 4 3
6
8 10 9
12
14 15
18
16
1 5 7 11 13 17 19
(i) Write down n (A) .
…… [1]
(ii) List the elements of set B.
B = { …… } [2]
(iii) One of these 19 numbers is picked at random.
Work out the probability that this number is
(a) not in set A and not in set B,
…… [1]
(b) in A , B .
…… [1]
(iv) Complete the statement.
A + B = {x : x is …… } [1]
Mark scheme
8(a) There are 2 M’s or 12 letters 1
8(b) 0.39 oe 2 M1 for 1– (0.12 + 0.09 + 0.4) oe
8(c) Football Cricket 3 B1 for 10
B1FT for 14 and 5
10 14 5 or their 10 + their 14 = 24 and
their 14 + their 5 = 19
11 B1FT for 11
or 40 – (their 10 + their 14 + their 5)
8(d)(i) 9 cao 1
8(d)(ii) 3 6 9 12 15 18 2 B1 for 4 or 5 correct and no extras
8(d)(iii)(a) 7 1
oe
19
8(d)(iii)(b) 12 1
oe
19
8(d)(iv) Even and a multiple of 3 1
or a multiple of 6 oe
(a) Simplify.
4x + 3y + 2x - 8y
…… [2]
(b) A pen costs 60 cents and a ruler costs 29 cents.
Write down an expression for the total cost, in cents, of x pens and y rulers.
…… cents [2]
(c) Solve.
5 (2x + 4) = 85
x = …… [3]
(d) (i) 28 # 2m = 26
Work out the value of m.
m = …… [1]
(ii) 5n ' 54 = 56
Work out the value of n.
n = …… [1]
(e) A plant costs p dollars and a bush costs b dollars.
Ana buys 2 plants and 4 bushes for $42.
Paola buys 7 plants and 9 bushes for $107.
Write down a pair of simultaneous equations and solve them to find the value of p and the value of b.
You must show all your working.
p = ……
b = …… [6]
Question 10 is printed on the next page.
Mark scheme
9(a) 6x – 5y final answer 2 B1 for 6x or – 5y in final answer
or for 6x – 5y seen then spoilt
9(b) 60x + 29y final answer 2 B1 for 60x or 29y in final answer
or for 60x + 29y seen then spoilt
or for 60p + 29r or [$] 0.60x + 0.29y
9(c) 6.5 oe 3 M1 for a first correct step e.g.
10x + 20 = 85 or 2x + 4 = 17
M1FT for a second correct step e.g.
10x = 65 or 2x = 13
9(d)(i) –2 cao 1
9(d)(ii) 10 cao 1
9(e) 2p + 4b = 42 and 7p + 9b = 107 B2 B1 for each
Correctly equating one set of M1 FT
coefficients
Correct method to eliminate one M1 FT
variable Dependent on the coefficients being the
same for one of the variables.
Correct consistent use of addition or
subtraction using their equations
[p =] 5 A1
[b =] 8 A1 If M0 scored, SC1 for 2 values satisfying
one of the/their original equations
or SC1 if no working, but 2 correct answers
(a) Complete the table of values for y = x 2 - 4x - 3 .
x -2 -1 0 1 2 3 4 5 y 2 -3 -6 -6 -3 2
[2]
(b) On the grid, draw the graph of y = x 2 - 4x - 3 for - 2 G x G 5.
y
10
8
6
4
2
–2 –1 0 1 2 3 4 5 x
–2
–4
–6
–8
[4]
(c) Use your graph to solve the equation x 2 - 4x - 3 = 0 .
x = …… or x = …… [2]
Mark scheme
10(a) 9 –7 2 B1 for each
10(b) Correct curve 4 B3FT for 7 or 8 points correctly plotted
B2FT for 5 or 6 points correctly plotted
B1FT for 3 or 4 points correctly plotted
10(c) – 0.8 to –0.5 and 4.5 to 4.8 2 B1 for each
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Mathematics 0580/32 for October/November 2020 is out of 104 marks, with 2 hours to answer it.
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