IGCSE Mathematics 0580 Paper 42, Oct/Nov 2025

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0580/42 · Oct/Nov 2025

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Write the ratio 60 grams : 3 kilograms in the form $1 : n$ .

[2]

Solve. $8 x - 17 = 27$

[2]

Write down the order of rotational symmetry of a regular decagon.

[1]

Pedro makes cards.

He makes cards at a rate of 9 cards every 20 minutes. Work out the number of cards he makes in 8 hours.

[2]

Each card costs 12 cents to make. Pedro sells each card for 50 cents. Work out his percentage profit on each card.

[2]

Nuwa is buying a phone. One website sells the phone for 953 Yuan. A different website sells the same phone for $141. The exchange rate is 1 Yuan = $0.152 . Calculate the difference between these phone prices. Give your answer in dollars, correct to the nearest cent.

[2]

One morning, a dentist has appointments for 10 patients. The stem-and-leaf diagram shows the waiting time for 8 of these patients.

$0$	$1$	$4$
$1$	$0$	$2$	$9$
$2$	$1$	$5$	$5$

Key: $1 ∣ 0$ represents 10 minutes The times for the two other patients, $P$ and $Q$ , are not shown in the stem-and-leaf diagram. The mean waiting time of all 10 patients that morning is 16 minutes. The range of waiting times is 26 minutes. Patient $P$ waits longer than patient $Q$ . Find the waiting time for each of patient $P$ and patient $Q$ .

[4]

The diagram shows a parallelogram. The parallelogram has the same perimeter as a circle with radius 4 m.

Show that $x = 6.06 m$ , correct to 2 decimal places.

[4]

The floor of a room is in the shape of this parallelogram. It costs $18 per square metre to tile the floor. Calculate the total cost of tiling the floor.

[4]

a(i)

On the diagram, draw the image of shape $A$ after a translation by the vector $(\begin{array}{c} 1 \\ - 7 \end{array})$ .

[2]

a(ii)

On the diagram, draw the image of shape $A$ after a reflection in the line $y = x + 1$ .

[3]

Describe fully the single transformation that maps shape $A$ onto shape $B$ .

[3]

The diagram shows the speed–time graph for part of a car journey. Find the total distance travelled in the 25 minutes.

[3]

Find the $n th$ term of each sequence.

17, 9, 1, -7, -15, ...

[2]

3, 12, 27, 48, 75, ...

[2]

The table shows some values for $y = x^{3} - 2 x + 3$ . Where appropriate, values of $y$ are given correct to 2 decimal places.

Complete the table.

[2]

Draw the graph of $y = x^{3} - 2 x + 3$ for $- 2 ⩽ x ⩽ 2$ .

[4]

By drawing a suitable straight line on the grid, solve the equation $x^{3} - 2.5 x + 1 = 0$ .

[4]

$A$ , $B$ and $C$ lie on a circle centre $O$ . $D E$ is a tangent to the circle at $C$ . Angle $A B C = 52^{\circ}$ and angle $B C E = 65^{\circ}$ .

Find the value of $x$ . Give a geometrical reason for your answer.

[2]

Find the value of $y$ .

[2]

Simplify. $\frac{7}{2 m} + \frac{3}{8 m}$

[2]

Carlos invests $24\,000 at a rate of 3.2% per year compound interest. Calculate the value of his investment at the end of 4 years.

[2]

Carlos buys a painting for $x. He sells the painting for $40\,870. He makes a profit of 34%. Calculate the value of his profit.

[3]

Carlos also buys a car with a value of $32\,500. The value of the car decreases exponentially by 23% each year. Find a formula for the value, $V, of the car at the end of $n$ years.

[3]

The diagram shows a field, $A B C D$ , in the shape of a quadrilateral. $B D$ is a straight path across the field.

Calculate $B C$ .

[3]

Calculate angle $D B C$ .

[3]

The total area of the field, $A B C D$ , is $35 900 m^{2}$ . Work out the length of the shortest distance from $D$ to $A B$ .

[4]

The histogram shows information about the masses of some coconuts. The masses are classified into four categories $A$ , $B$ , $C$ and $D$ .

Show that there are 10 coconuts in category $D$ .

[1]

Two of the coconuts from those in category $C$ and category $D$ are chosen at random. Find the probability that both are from category $D$ .

[3]

Calculate an estimate of the mean mass of the coconuts.

[4]

Expand and simplify. $(x - 2) (2 x + 3) (x + 4)$

[3]

In the diagram, $O A$ is parallel to $C B$ . $O A : C B = 4 : 3$ $\vec{O A} = a$ and $\vec{O B} = b$ .

Find $\vec{A B}$ in terms of $a$ and $b$ .

[1]

M is the midpoint of $O C$ . Find $\vec{A M}$ in terms of $a$ and $b$ . Give your answer in its simplest form.

[3]

Solve the simultaneous equations. You must show all your working and give your answers correct to 2 decimal places. $y = 5 - 2 x$ $y = 3 x^{2} - 7 x - 6$

[6]

A solid metal prism has a mass of $4810 g$ , correct to the nearest $10 g$ . The density of the metal is $7.7 {g/cm}^{3}$ , correct to 1 decimal place. Calculate the lower bound for the volume of the prism. [ $Density = mass \div volume$ ]

[3]

$y$ is inversely proportional to $(x + 2)^{2}$ . $w$ is proportional to $x$ . When $y = 8$ , $x = 3.5$ . When $w = 15$ , $x = 90$ . Find $y$ in terms of $w$ .

[4]

Mark scheme

0580/42 · Oct/Nov 2025

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1 · 2 marks

2 marks
50

2 · 2 marks

2 marks
5.5 or $5 \frac{1}{2}$ or $\frac{11}{2}$

3 · 1 mark

1 mark
10

4a · 2 marks

2 marks
216

4b · 2 marks

2 marks
317 or 316.6 to 316.7

5 · 2 marks

2 marks
3.86 cao

6 · 4 marks

4 marks
[Patient P =] 27 [Patient Q =] 16

7a · 4 marks

M3
2 × π × 4 = 6.51 × 2 + 2x or better
A1
6.055 to 6.058 [= 6.06]

7b · 4 marks

4 marks
574 or 575 or 574.1 to 574.5…

8a(i) · 2 marks

2 marks
Image drawn at (–2, –3), (–3, –2), (–4, –2) and (–3, –4)

8a(ii) · 3 marks

3 marks
Image drawn at (2, –3), (3, –2), (4, –3) and (4, –4)

8b · 3 marks

3 marks
Rotation 90° anticlockwise oe (–2, 6)

9 · 3 marks

3 marks
24.2 or 24.16 to 24.17

10a · 2 marks

2 marks
25 – 8n oe final answer

10b · 2 marks

2 marks
3n^2 oe final answer

11a · 2 marks

2 marks
2.63 and 3.38

11b · 4 marks

4 marks
Correct graph

11c · 4 marks

M2
y = 2 + 0.5x ruled
A2
–1.85 to –1.7 , 0.4 to 0.5, 1.25 to 1.4

12a · 2 marks

2 marks
104 and angle at the centre is twice the angle at the circumference

12b · 2 marks

2 marks
27

13 · 2 marks

2 marks
$\frac{31}{8 m}$ final answer

14a · 2 marks

2 marks
27 223

14b · 3 marks

3 marks
10 370

14c · 3 marks

3 marks
V = 32 500 × 0.77^n final answer

15a · 3 marks

3 marks
392 or 392.4 to 392.5

15b · 3 marks

3 marks
10.6 or 10.7 or 10.55 to 10.69

15c · 4 marks

4 marks
279 or 278.9…

16a · 1 mark

1 mark
(1.6 – 1.35) oe × 40 [= 10]

16b · 3 marks

3 marks
$\frac{5}{39}$ oe

16c · 4 marks

4 marks
1.26 or 1.259… nfww

17 · 3 marks

3 marks
2x^3 + 7x^2 – 10x – 24 final answer

18a · 1 mark

1 mark
b – a

18b · 3 marks

3 marks
$- \frac{11}{8} a + \frac{1}{2} b$ oe simplified final answer

19 · 6 marks

M2
3x^2 – 5x – 11 [= 0] or 3y^2 – 20y – 19 [= 0]
M2
$\frac{[- (-)] 5 \pm \sqrt{([-] 5)^{2} - 4 \times 3 \times - 11}}{2 \times 3}$ OR ${(x - \frac{5}{6})}^{2} = \pm (\frac{11}{3} + {(\frac{5}{6})}^{2})$ oe
B2
x = 2.92, y = –0.84 and x = –1.25, y = 7.51

20 · 3 marks

3 marks
620 nfww

21 · 4 marks

4 marks
$y = \frac{242}{(6 w + 2)^{2}}$ oe final answer

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