IGCSE Mathematics 0580 Paper 21, May/June 2023

Question paper and mark scheme70 marks21 questions

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Question paper

0580/21 · May/June 2023

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CDE is a straight line. Find angle ADE.

[2]

A train journey starts at 21 43. It takes 8 hours and 32 minutes. Find the time the journey finishes.

[1]

The diagram shows a straight line intersecting two parallel lines. Find the value of $a$ and the value of $b$ , giving a geometrical reason for each answer. $a = ...................$ because $....................................................................................................$ $b = ...................$ because $....................................................................................................$

[4]

By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of $\frac{6.7 \times 2.1}{18 - 5.9} .$ You must show all your working.

[2]

Eric has four colours of paint. The table shows the probability that he uses each colour.

Colour	Red	Blue	Green	Yellow
Probability	0.3	0.35	0.13	$x$

Find the value of $x$ .

[2]

Calculate the volume of a sphere with diameter $4.8 cm$ . [The volume, $V$ , of a sphere with radius $r$ is $V = \frac{4}{3} π r^{3}$ .]

[2]

The scale of a map is $1 : 125 000$ . On a map, the length of an island is $9.4 cm$ . Calculate the actual length of the island, giving your answer in kilometres.

[2]

The $n$ th term of a sequence is $10 - n^{2}$ . Write down the first three terms of this sequence.

[2]

These are the first four terms of another sequence. $7 10 13 16$ Find an expression for the $n$ th term of this sequence.

[2]

Triangle $A B C$ is similar to triangle $D E F$ . Calculate the value of $h$ .

[2]

Without using a calculator, work out $2 \frac{1}{7} \div \frac{5}{9}$ . You must show all your working and give your answer as a mixed number in its simplest form.

[3]

Describe the single transformation that maps

triangle $A$ onto triangle $B$

[3]

triangle $A$ onto triangle $C$ .

[3]

$A O$ , $O B$ and $O C$ are all radii of the circle. $A B = B C$ . Therefore triangle $A O B$ is congruent to triangle $C O B$ . Draw a ring around the correct criterion for this statement. $SAS RHS SSS ASA$

[1]

b(i)

$P$ , $Q$ , $R$ and $S$ are points on the circle and $T Q U$ is a tangent to the circle at $Q$ . $P R$ and $S Q$ intersect at the centre of the circle, $O$ , and $P Q$ is parallel to $S R$ . Angle $R Q U = 42^{\circ}$ . Calculate angle $Q S R$

[1]

b(ii)

angle $P Q S$

[1]

b(iii)

angle $P O S$ .

[1]

Anya invests $$ 6000$ in an account that pays compound interest at a rate of $r$ per year. At the end of 8 years, the account has earned $$ 621.70$ in interest. Calculate the value of $r$ .

[3]

$y$ is directly proportional to the square of $(x + 3)$ . When $x = 2$ , $y = 5$ . Find $y$ when $x = 1$ .

[3]

A bag contains 5 green buttons, 2 blue buttons and 6 white buttons. Maya takes two buttons at random from the bag, without replacement. Calculate the probability that one button is green and the other button is not green.

[3]

Find the magnitude of the vector $(\begin{array}{c} - 4 \\ 5 \end{array})$ .

[2]

The diagram shows a triangle $O A C$ . $A$ is the midpoint of the straight line $O B$ . $\vec{O A} = x$ and $\vec{O C} = y$ . Find $\vec{C B}$ in terms of $x$ and $y$ .

[1]

Simplify $(81 x^{12})^{\frac{3}{4}}$ .

[2]

The diagram shows the position of three towns, $U$ , $V$ and $W$ . $U$ is due west of $V$ and angle $U V W = 125^{\circ}$ . Calculate the bearing of $U$ from $W$ .

[4]

On the diagram, sketch the graph of $y = \cos x$ for $0^{\circ} ⩽ x ⩽ 360^{\circ}$ .

[2]

Solve the equation $5 \cos x + 3 = 0$ for $0^{\circ} ⩽ x ⩽ 360^{\circ}$ .

[3]

The table shows some values for $y = 3 x^{2} - 2 x - 1$ .

Complete the table.

[1]

On the grid, draw the graph of $y = 3 x^{2} - 2 x - 1$ for $- 1 ⩽ x ⩽ 1.5$ .

[3]

By drawing a suitable straight line, solve the equation $3 x^{2} - 4 x - 2 = 0$ for $- 1 ⩽ x ⩽ 1.5$ .

[3]

A curve has equation $y = x^{3} - 12 x$ .

Find the gradient of the curve at the point $(1, - 11)$ .

[3]

Find the coordinates of the turning points of the curve.

[3]

Mark scheme

0580/21 · May/June 2023

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1 · 2 marks

2 marks
51

2 · 1 mark

1 mark
06 15 or 6:15 am

3 · 4 marks

2 marks
58, vertically opposite
2 marks
122, interior

4 · 2 marks

M1
$\frac{7 \times 2}{20 - 6}$
A1
1 nfww

5 · 2 marks

2 marks
0.22 oe

6 · 2 marks

2 marks
57.9 or 57.90 to 57.91...

7 · 2 marks

2 marks
11.75

8a · 2 marks

2 marks
9 6 1

8b · 2 marks

2 marks
3n + 4 oe final answer

9 · 2 marks

2 marks
6.3

10 · 3 marks

M2
$\frac{15}{7} \times \frac{9}{5}$ oe or $\frac{135}{63} \div \frac{35}{63}$ oe with common denominator
A1
$3 \frac{6}{7}$ cao

11a · 3 marks

1 mark
Enlargement
1 mark
[sf] 2
1 mark
(0, 7)

11b · 3 marks

1 mark
Rotation
1 mark
(3, 1)
1 mark
90° clockwise oe

12a · 1 mark

1 mark
SSS

12b(i) · 1 mark

1 mark
42

12b(ii) · 1 mark

1 mark
42

12b(iii) · 1 mark

1 mark
84

13 · 3 marks

3 marks
1.24[0…]

14 · 3 marks

3 marks
3.2 oe

15 · 3 marks

3 marks
$\frac{20}{39}$ oe

16a · 2 marks

2 marks
6.4[0] or 6.403...

16b · 1 mark

1 mark
2x − y

17 · 2 marks

2 marks
$27 x^{9}$ final answer

18 · 4 marks

4 marks
236[.0…]

19a · 2 marks

2 marks
Correct sketch to go through (0, 1), (360, 1) and (180, –1)

19b · 3 marks

3 marks
126.9 or 126.86 to 126.87 233.1 or 233.13 to 233.14

20a · 1 mark

1 mark
0.75 and –1.25

20b · 3 marks

3 marks
Correct curve

20c · 3 marks

B2
ruled line $y = 2 x + 1$
B1
−0.35 to −0.45

21a · 3 marks

3 marks
− 9

21b · 3 marks

3 marks
(− 2, 16) (2, − 16)

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