Question bank Cambridge IGCSE 2025

Solve.

$4c - 9 = 13$

$c = $ ?

Work out.

$\dfrac{16.71 + 46.13}{\sqrt{8.6^2 - 3.5^2}}$

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.

(Answer format: ...... by \$ ......)

**(a)** Describe fully the **single** transformation that maps

**(i)** shape *A* onto shape *B*.

**(a)** Describe fully the **single** transformation that maps

**(ii)** shape *A* onto shape *C*.

**(b)** On the grid, draw the image of shape *A* after a reflection in the line $x = -2$.

**(a)** These are the first 5 terms of a sequence.

1   8   27   64   125

Find the 10th term of this sequence.

**(b)** These are the first 5 terms of a different sequence.

5   8   13   20   29

Find the $n$th term of this sequence.

**(c)** The **sum of the first *n* terms** of another sequence is $\dfrac{n}{2}(5n - 1)$.

**(i)** Use $n = 2$ to find the sum of the first two terms in this sequence.

**(c)** The **sum of the first *n* terms** of another sequence is $\dfrac{n}{2}(5n - 1)$.

**(ii)** Find the 3rd term of this sequence.

(In part (c)(i) you found that the sum of the first two terms is 9.)

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 .

**(a)** Hadi uses the monthly plan.

Calculate the total amount Hadi pays. (Answer in dollars.)

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 .

**(b)** Find the percentage increase in the cost using the monthly plan compared to a single payment.

(In part (a) you found that the monthly plan costs \$1099 in total.)

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. (Answer in dollars.)

**(a)** Write down **all** the factors of 18.

**(b)** Factorise.

$3y - xy + 15 - 5x$

**(c)** $3y - xy + 15 - 5x = 18$

where $x$ and $y$ are positive integers.

Using your answers to **part (a)** and **part (b)**, find one possible value of $x$ and the corresponding value of $y$.

(In part (a) you found that the factors of 18 are 1, 2, 3, 6, 9, 18. In part (b) you found $3y - xy + 15 - 5x = (y + 5)(3 - x)$.)

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*. (Answer in cm.)