Cambridge IGCSE. 2025. Mathematics (0580). May/June - Paper 4 (43) · Calculator (Extended)

Find the median of these numbers.

5 11 11 13 17 21

In triangle *ABC*, *AC* = 21 m and *BC* = 15.9 m.

**Using a ruler and compasses only**, complete the scale drawing of the triangle.

Use a scale of 1 cm to represent 3 m.

The side *AB* is drawn for you.



(The picture on screen is not at true size: in the printed paper *AB* = 8 cm. Do the drawing on paper with *AB* = 8 cm.)

$\dfrac{2}{5}$ $\sqrt{15}$ 23 $\sqrt{144}$ $-2$ 0.8

From this list, write down

**(a)** a natural number

$\dfrac{2}{5}$ $\sqrt{15}$ 23 $\sqrt{144}$ $-2$ 0.8

From this list, write down

**(b)** an irrational number.

The diagram shows a pentagon made from two congruent trapeziums.



The area of the pentagon is 130.2 cm$^2$.

Calculate the value of *x*.

**(a)** Convert 780 cm$^2$ into m$^2$.

(answer in m$^2$)

**(b)** Convert 0.037 m$^3$ into cm$^3$.

(answer in cm$^3$)

One titanium atom has a mass of $7.95 \times 10^{-23}$ grams.

Calculate the number of titanium atoms in 1 kg of titanium.

Give your answer in standard form.

(Type the answer like 1.23 × 10^25)

ℰ = {*x*: *x* is an integer and $1 \le x \le 12$}

*E* = {even numbers}

*M* = {multiples of 3}

**(a)** Find n(*M*).

ℰ = {*x*: *x* is an integer and $1 \le x \le 12$}

*E* = {even numbers}

*M* = {multiples of 3}

**(b)** Write down the set $E \cap M$.

ℰ = {*x*: *x* is an integer and $1 \le x \le 12$}

*E* = {even numbers}

*M* = {multiples of 3}

**(c)** $y \in (E \cup M)'$

Write down a possible value of *y*.

Factorise.

**(a)** $28xy - 12x$

Factorise.

**(b)** $y - 6x + 2xy - 3$

**(a)** Simplify.

$5x^5y \times 7x^3y^2$

(Type powers with ^, e.g. 2x^4y^3)

**(b)** $7^n = \sqrt[5]{7}$

Find the value of *n*.

Expand and simplify.

**(a)** $2x - x(5 - x^2)$

(Type powers with ^, e.g. x^2)

Expand and simplify.

**(b)** $(x + 4)(x - 5)(x + 3)$

(Type powers with ^, e.g. x^3 + …)

The table shows three sequences.

| | 1st term | 2nd term | 3rd term | 4th term | 5th term | 6th term | *n*th term |
|---|---|---|---|---|---|---|---|
| Sequence *A* | 28 | 22 | 16 | 10 | 4 | | |
| Sequence *B* | $\frac{1}{6}$ | $\frac{2}{7}$ | $\frac{3}{8}$ | $\frac{4}{9}$ | $\frac{1}{2}$ | | |
| Sequence *C* | $\frac{1}{4}$ | $\frac{1}{2}$ | 1 | 2 | 4 | | |

Complete the table.

$\sqrt{\dfrac{10^{400}}{10^{220} \times 10^{80}}} = 10^k$

Find the value of *k*.

Line *L* has the equation $y = 2(x - 5)$.

**(a)** Find the coordinates of the point where line *L* intersects the *y*-axis.

(Type as (x, y))