IGCSE Mathematics 0580 Paper 41, May/June 2025

Solve. $$4c-9=13$$

Work out. $$\frac{16.71+46.13}{\sqrt{{8.6}^2-{3.5}^2}}$$ Give your answer correct to 2 significant figures.

In the USA, one gallon of fuel costs $4.83 . In the UK, one litre of fuel costs £1.62 . The exchange rate is £1 = $1.215 . 1 gallon = 3.785 litres In which country does 1 litre of fuel cost more and by how much? Give your answer in dollars.

Expand. $$5x^2(3x-2)$$

Write down the inequality in $y$ shown by the number line.

Hadi buys a dishwasher. He can either pay a single payment of $980 or he can pay using a monthly plan. The monthly plan is 20% of $980 plus 12 payments of $75.25 .

In a sale, the original price of a sewing machine is reduced by $38. This is an 8% reduction in the original price. Work out the original price of the sewing machine.

A warehouse has a floor area of $800{\text{ m}}^2$. The plan of the warehouse is drawn to a scale of $1:50$. Calculate the floor area on the plan. Give your answer in square centimetres.

The diagram shows triangle $PQR$. Calculate the shortest distance from $Q$ to $PR$.

Make $x$ the subject of this formula. $$A=w^2+5x^2$$

The table shows some values for $y=5x^2-x^3-4$.

The height of each of 140 basketball players is recorded. The table shows the results.

Mateo invests $1250 at a rate of $r$ per year compound interest. At the end of 6 years the total value of his investment is $1484. Calculate the value of $r$.

The diagram shows a quadrilateral $ABCD$.

$2x^2+12x-2$ can be written in the form $a(x+b{)}^2-c$. Find the values of $a$, $b$ and $c$.

The diagram shows a major sector of a circle with radius $7.5\text{ cm}$. Calculate the perimeter of the major sector.

The diagram shows a pyramid $OABCD$. The pyramid has a square base, $ABCD$, with sides $10.5\text{ cm}$. The vertex $O$ is vertically above the centre of the base, $M$. The height of the pyramid is $24\text{ cm}$.

$$\frac{{16}^{5m}}{4}={64}^{2n}$$ Find $m$ in terms of $n$.

$$I=\frac{V}{R}$$ $V$ is 50, correct to the nearest 10. $R$ is 13, correct to the nearest integer. Calculate the upper bound of $I$.