IGCSE Mathematics 0580 Paper 13, Oct/Nov 2023

Question paper and mark scheme56 marks23 questions

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Question paper

0580/13 · Oct/Nov 2023

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Write down the letter of the shape that is congruent to the shaded shape.

[1]

Write down

all the factors of 32

[2]

the reciprocal of $\frac{1}{8}$

[1]

the value of the 7 in the number 473285.

[1]

Draw the lines of symmetry on this rhombus.

[2]

61 63 64 66 68 69 From this list, write down

a cube number

[1]

a prime number.

[1]

Tara goes on a journey by train. The train leaves at 0648. The journey takes 12 hours and 35 minutes. Find the time when Tara arrives.

[1]

Jamie records the masses of two samples of oranges, type A and type B. The stem-and-leaf diagram shows the mass, in grams, of each of 30 oranges of type A. Key: 17 | 6 represents 176 grams

Complete the table to show the range for type A oranges.

[1]

Use the information in the table to write down two comments comparing the masses of type A oranges with the masses of type B oranges.

[2]

In triangle $L M N$ , $L N = 7.5 cm$ and $M N = 8 cm$ .

Using a ruler and compasses only, construct triangle $L M N$ . Leave in your construction arcs. The line $L M$ has been drawn for you.

[2]

Write down the mathematical name for this type of triangle.

[1]

The surface area of a cube is $73.5 {cm}^{2}$ . Find the length of one side of the cube.

[2]

The diagram shows an equilateral triangle. Find the value of $x$ .

[2]

$a = (\begin{array}{c} 4 \\ 9 \end{array}) b = (\begin{array}{c} - 6 \\ 1 \end{array}) c = (\begin{array}{c} 13 \\ - 2 \end{array})$ Work out.

$a + b$

[1]

$3 c$

[1]

Factorise completely. $15 v^{2} - 3 v$

[2]

Rama asks a group of students how they travel to school. The table shows the probability of how a student, chosen at random, travels to school.

Complete the table.

[2]

There are 1800 students at the school. Find the expected number of students that walk to school.

[1]

Without using a calculator, work out $1 \frac{5}{6} \div \frac{11}{15}$ . You must show all your working and give your answer as a mixed number in its simplest form.

[3]

The diagram shows triangle $A B C$ . $M$ is the midpoint of $A C$ . Triangle $A B C$ is rotated $180^{\circ}$ about centre $M$ . The image and the original triangle together form a quadrilateral $A B C D$ .

Write down the mathematical name of the quadrilateral $A B C D$ .

[1]

Find angle $B A D$ .

[2]

Shubhu invests $$ 750$ in a savings account for 5 years. The account pays simple interest at a rate of 1.8% per year. Calculate the total interest she earns during the 5 years.

[2]

Solve the equation. $5 x + 7 = 9 x - 3$

[2]

Find the equation of line $L$ in the form $y = m x + c$ .

[2]

On the grid, draw a line that is perpendicular to line $L$ .

[1]

A bar of chocolate costs $$ 3$ and a bag of sweets costs $$ 5$ . Write down an expression for the total cost, in dollars, of $x$ bars of chocolate and $y$ bags of sweets.

[2]

A bag contains these cards. $1 7 3 9 4 5 2$ One of these cards is picked at random. Find the probability that the number on the card is greater than 3.

[1]

b(i)

A box contains 3 blue cards and 7 red cards. Kim picks one card at random, notes its colour and then replaces it in the box. She then picks another card at random. Complete the tree diagram.

[1]

b(ii)

Work out the probability that both of the cards Kim picks are blue.

[2]

The diagram shows a sector of a circle with radius $r cm$ and sector angle $72^{\circ}$ . The arc length is $9.35 cm$ . Calculate the value of $r$ .

[2]

$E = {2, 4, 8, 9, 10, 12}$ $Q = {square numbers}$ $R = {multiples of 4}$

Use this information to complete the Venn diagram.

[2]

Write down $n (Q \cap R)$ .

[1]

Find the highest common factor (HCF) of 48 and 80.

[2]

Solve the simultaneous equations. You must show all your working. $3 x + 5 y = 23$ $6 x - 4 y = 11$

[3]

Mark scheme

0580/13 · Oct/Nov 2023

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1 · 1 mark

1 mark
D

2a · 2 marks

2 marks
1, 2, 4, 8, 16, 32

2b · 1 mark

1 mark
8

2c · 1 mark

1 mark
70 000

3 · 2 marks

2 marks
2 correct lines of symmetry

4a · 1 mark

1 mark
64

4b · 1 mark

1 mark
61

5 · 1 mark

1 mark
19 23 or 7 23 pm

6a · 1 mark

1 mark
42

6b · 2 marks

B1
Type A [masses] lighter on average oe
B1
Type A [masses] more varied/less consistent oe

7a · 2 marks

2 marks
Correct construction

7b · 1 mark

1 mark
Scalene

8 · 2 marks

2 marks
3.5

9 · 2 marks

2 marks
150

10a · 1 mark

1 mark
$(\begin{array}{c} - 2 \\ 10 \end{array})$

10b · 1 mark

1 mark
$(\begin{array}{c} 39 \\ - 6 \end{array})$

11 · 2 marks

2 marks
3v(5v – 1) final answer

12a · 2 marks

2 marks
0.11 oe

12b · 1 mark

1 mark
576

13 · 3 marks

M2
$\frac{11}{6} \times \frac{15}{11}$ or $\frac{55 k}{30 k} \div \frac{22 k}{30 k}$ oe with common denominator
A1
$2 \frac{1}{2}$ cao

14a · 1 mark

1 mark
Parallelogram

14b · 2 marks

2 marks
68

15 · 2 marks

2 marks
67.5[0]

16 · 2 marks

2 marks
2.5

17a · 2 marks

2 marks
[y =] $\frac{1}{3} x + 1$

17b · 1 mark

1 mark
Any ruled perpendicular line

18 · 2 marks

2 marks
3x + 5y final answer

19a · 1 mark

1 mark
$\frac{4}{7}$ oe

19b(i) · 1 mark

1 mark
$\frac{7}{10}$ in each space on tree diagram

19b(ii) · 2 marks

2 marks
$\frac{9}{100}$ oe

20 · 2 marks

2 marks
7.44 or 7.439 to 7.440…

21a · 2 marks

2 marks
Venn diagram with elements placed: Q only: 9; Intersection: 4; R only: 8, 12; Outside: 2, 10

21b · 1 mark

1 mark
1

22 · 2 marks

2 marks
16

23 · 3 marks

M1
Correctly eliminates one variable
A1
[x =] 3.5
A1
[y =] 2.5

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