Mathematics 0580/31 May/June 2019: question paper and mark scheme
Cambridge IGCSE Mathematics (0580), Paper 3 (Core), May/June 2019. Read both free below, or download them. Done the paper? Get it marked by AI against this mark scheme.
Here is part of the menu for Jamie’s café.
Menu
Price ($)
Tea 2.35
Coffee 3.40
Lemonade 1.80
Cake 4.45
Biscuit 0.85
(a) Sue has one tea and one cake.
Calculate how much she pays.
$ …… [1]
(b) Derrick has one coffee and two biscuits.
How much change does he receive from a $10 note?
$ …… [2]
(c) Harriet works at the café for 34 hours each week.
She is paid $8.25 for each hour.
(i) Work out the amount she is paid each week.
$ …… [1]
(ii) One week she works 8 hours extra.
The extra hours are paid at 1.5 times her usual rate of $8.25 for each hour.
Work out the total amount she is paid for that week.
$ …… [2]
(d) Peter works these hours each week at the café.
Day Time
Monday 08 30 to 16 00
Tuesday 10 00 to 17 00
Thursday 08 30 to 16 30
Saturday 08 00 to 18 30
Work out the number of hours he works in one week.
…… hours [2]
(e) Jamie buys a clock for the café from Japan for 9395 yen.
The exchange rate is $1 = 110.27 yen.
Work out the cost of the clock in dollars, correct to the nearest cent.
$ …… [3]
(f) Jamie invests $12 000 at a rate of 5% per year compound interest.
Calculate the value of his investment at the end of 3 years.
$ …… [3]
Mark scheme
1(a) 6.8[0] 1
1(b) 4.9[0] 2 M1 for 3.4[0] + 2 × [0].85 soi
1(c)(i) 280.5[0] 1
1(c)(ii) 379.5[0] 2 FT their (c)(i) + 99
M1 for 8 × 1.5 × 8.25 soi
or (8 × 1.5 + 34) × 8.25 soi
1(d) 33 2 M1 for 7.5, 7, 8, 10.5
1(e) 85.20 cao 3 B2 for 85.1999…
OR
M1 for 9395 ÷ 110.27
B1 for their answer to at least 3 dp correctly
rounded to 2 dp
1(f) 13 891.5[0] 3 M2 for 12 000 × (1 + 100
5
)3 oe
5
or M1 for 12 000 × (1 + 100 )2 oe
(a) Work out 48 ' 3 - 5 # 2 .
…… [1]
(b) Insert one pair of brackets to make this statement correct.
3 + 2 # 12 - 4 = 19 [1]
(c) Write the following in order, starting with the smallest.
3 11
0.749 76%
4 15
…… 1 …… 1 …… 1 …… [2]
smallest
(d) Find the value of
(i) 265.69,
…… [1]
(ii) 83.
…… [1]
(e) Write down the smallest prime number.
…… [1]
(f) Write down all the factors of 18.
…… [2]
(g) Write down a common factor of 16 and 72 that is greater than 2.
…… [1]
28
(h) Write as a fraction in its simplest form.
140
…… [1]
(i) Jeff and his friends win a prize.
5
Jeff’s share is $160 which is of the prize.
11
Work out the value of the prize.
$ …… [2]
Mark scheme
2(a) 6 1
2(b) 3 + 2 × (12 – 4) = 19 1
2(c) 11
15
[0].749 34 76[%] 2 B1 for 3 in the correct order
or 0.75, (0.749) , 0.76, 0.73…
or 75%, 74.9%, (76%), 73….%
2(d)(i) 16.3 1
2(d)(ii) 512 1
2(e) 2 1
2(f) 1 2 3 6 9 18 2 B1 for 4 or 5 correct factors only
or 6 correct factors with one extra
or 1 × 18, 2 × 9, 3 × 6
2(g) 4 or 8 1
2(h) 1
5
cao 1
2(i) 352 2 M1 for 160 ÷ 5 [ × 11]
(a) On Monday, Main Street station sells 40 tickets.
There are four types of ticket; infant, child, adult and senior.
The bar chart shows the number of infant, child and adult tickets sold.
20
18
16
14
12
Frequency
10
8
6
4
2
0
Infant Child Adult Senior
Type of ticket
(i) Complete the bar chart. [3]
(ii) Find how many more adult tickets were sold than child tickets.
…… [1]
(iii) Write down the modal type of ticket.
…… [1]
(iv) One of these 40 people is chosen at random.
Find the probability that this person is a child.
…… [1]
(b) At Donville station the number of tickets sold each day is recorded for seven days.
104 18 72 31 27 45 60
Find
(i) the range,
…… [1]
(ii) the median,
…… [2]
(iii) the mean.
…… [2]
Mark scheme
3(a)(i) Correct bar 3 M1 for 5, 12, 17 or 34
M1 for 40 – their34
3(a)(ii) 5 1
3(a)(iii) Adult 1 FT
3(a)(iv) 12
40
oe 1
3(b)(i) 86 1
3(b)(ii) 45 2 M1 for 18, 27, 31, 45, or 45, 60, 72, 104
3(b)(iii) 51 2 M1 for
(104 + 18 + 72 + 31 + 27 + 45 + 60) ÷ 7
soi 357
7
(a)
A
NOT TO a°
SCALE
118°
B C D
ABC is an isosceles triangle.
BCD is a straight line.
Find the value of a.
a = …… [2]
(b) Find the size of one interior angle of a regular 10-sided polygon.
…… [3]
(c)
E
NOT TO y°
SCALE
F
O
x°
58°
J G H
The points E, F and G lie on the circumference of a circle, centre O.
JGH is a tangent to the circle.
Find the value of x and the value of y.
x = ……
y = …… [2]
(d)
G
E
C 28°
A NOT TO
B 67°
D SCALE
F
In the diagram AG and AF are straight lines.
Lines BC and DE are parallel.
Find angle CED and give a reason for your answer.
Angle CED = …… because …… [2]
(e)
R
NOT TO
SCALE
28 cm
P Q
21 cm
Calculate PR.
PR = …… cm [2]
Mark scheme
4(a) 56 2 M1 for 180 – 118 soi by 62
4(b) 144 3 M2 for 180 – (360 ÷ 10) oe
M1 for 360 ÷ 10 soi by 36
4(c) 32 2 B1 for each
58 or for their x + their y = 90
or angle F marked as 90
4(d) 28 alternate 2 B1 for each
4(e) 35 2 M1 for 212 + 282 or better
(a) The diagram shows a rectangle with length 7a and width 2a.
7a NOT TO
SCALE
2a
Write an expression, in its simplest form, for
(i) the perimeter,
…… [2]
(ii) the area.
…… [2]
(b) The nth term of a sequence is n2 + 5.
Find the first three terms of this sequence.
…… , …… , …… [2]
12
(c) (i) Complete the table of values for y = , x ! 0. x
x -6 -4 -3 -2 -1 1 2 3 4 6
y -2 -3 12 2
[3]
12
(ii) On the grid, draw the graph of y = for -6 G x G -1 and 1 G x G 6. x y
12
10
8
6
4
2
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–2
–4
–6
–8
– 10
–12
[4]
(iii) On the grid, draw the line y = 8. [1]
12
(iv) Use your graph to solve = 8. x
x = …… [1]
Mark scheme
5(a)(i) 18a final answer 2 M1 for 2 × (7a + 2a) oe
5(a)(ii) 14a2 final answer 2 M1 for 7a × 2a
5(b) 6 9 14 2 B1 for 2 correct or 5 6 9
5(c)(i) −4 −6 −12 6 4 3 3 B2 for 4 or 5 correct
or B1 for 2 or 3 correct
5(c)(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
5(c)(iii) Correct ruled line drawn 1
5(c)(iv) 1.3 to 1.7 1 FT their curve and their line
Fourteen students each take two tests in French, a speaking test and a written test.
The table shows the scores.
Speaking test 10 13 48 30 35 18 41 40 22 28 20 44 37 46
Written test 24 44 51 39 45 29 56 20 39 49 33 52 44 52
(a) Complete the scatter diagram.
The first ten points have been plotted for you.
60
55
50
45
40
35
Written test
30
25
20
15
10
5
0
0 5 10 15 20 25 30 35 40 45 50
Speaking test
[2]
(b) What type of correlation is shown in this scatter diagram?
…… [1]
(c) One student has a high score in the speaking test and a low score in the written test.
On the scatter diagram, put a ring around this point. [1]
(d) On the scatter diagram, draw a line of best fit. [1]
(e) Use your line of best fit to estimate a score in the written test for a student who scored 25 in the speaking test.
…… [1]
Mark scheme
6(a) 4 points correctly plotted 2 B1 for 2 or 3 points correctly plotted
6(b) Positive 1
6(c) (40, 20) indicated 1
6(d) Ruled line of best fit 1
6(e) 33 to 42 1 FT their positive line
y
9
8
7
6
C
5
4
3
2
1
–9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 x
–1
–2
–3 A
B –4
–5
–6
–7
–8
–9
(a) Describe fully the single transformation that maps shape A onto shape B.
…… [3]
(b) Describe fully the single transformation that maps shape A onto shape C.
…… [3]
3
(c) On the grid, draw the image of shape A after a translation by the vector e o . [2]
1
(d) On the grid, draw the image of shape B after a reflection in the line y = 1. [2]
Mark scheme
7(a) Rotation 3 B1 for each
[centre] (0, 0) oe
90[°] clockwise oe
7(b) Enlargement 3 B1 for each
[centre] (5, −7)
[sf=] 3
7(c) Correct shape plotted with points 2 3 k
(6, −1) (8, −1) (6, −3) (8, −3) B1 for a correct translation of or
(6, −5) k 1
7(d) Correct shape plotted with points 2 B1 for reflection in y = k or x = 1
(−2, 5) (−6, 5) (−2, 7) (−4, 5)
(−4, 7)
(a) A cylinder has a radius of 6 cm and a height of 17 cm.
Show that the volume of this cylinder is 1923 cm3, correct to 4 significant figures.
[2]
(b)
Q NOT TO
SCALE
P R
O
Points P, Q and R are on the circumference of a semicircle, centre O and radius 8 cm.
Angle POQ = 90°.
Calculate the shaded area.
……cm2 [5]
Mark scheme
8(a) π × 62 × 17 M1
1922.6 to 1922.91 A1
8(b) 36.5 or 36.53 to 36.54… 5 B2 for 100.53 to 100.54… or 32π
or M1 for [0.5 ×] π × 82 oe
and
B2 for 64
or M1 for [0.5 ×] 16 × 8 oe
(a) Simplify 8a + 3b - 2a + b.
…… [2]
(b) Calculate the value of 4x2 + xy when x = 3 and y = -2.
…… [2]
(c) Solve these equations. x
(i) = 20
4
x = …… [1]
(ii) 3x - 5 = 16
x = …… [2]
(iii) 5(2x + 1) = 27
x = …… [3]
(d) Make r the subject of this formula. p = 3r - 5
r = …… [2]
Question 10 is printed on the next page.
Mark scheme
9(a) 6a + 4b final answer 2 B1 for 6a + kb or ka + 4b
9(b) 30 2 M1 for 4 × 32 + 3 × −2 or better
9(c)(i) 80 1
9(c)(ii) 7 2 M1 for 3x = 16 + 5 or x – 53 = 163 or better
9(c)(iii) 2.2 oe 3 M1 for 10x + 5 [= 27] or 2 x + 1 = 275
M1 for second correct step
9(d) p+5 p 5 2 p
or + final answer M1 for p + 5 = 3r oe or = r − 53
3 3 3 3
The scale drawing shows a rectangle ABCD.
The scale is 1 centimetre represents 20 metres.
A B
D C
Scale: 1 cm to 20 m
(a) Using a straight edge and compasses only, construct the bisector of angle ADC.
Show all your construction arcs. [2]
(b) Shade the region inside the rectangle that is
• nearer to DA than to DC and
• less than 210 m from C.
[3]
Mark scheme
10(a) Correct angle bisector with two 2 B1 for correct angle bisector with
pairs of correct arcs no/incorrect arcs
or two pairs of correct arcs with no line
10(b) Correct arc with radius 10.5 cm 3 B2 for correct arc
centre C or B1 for any arc centre C or 10.5 seen
and correct region shaded
B1dep for shading correct region dep on at
least (a) B1(b) B1
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Mathematics 0580/31 for May/June 2019 is out of 104 marks, with 2 hours to answer it.
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