IGCSE Mathematics 0580 Paper 23, May/June 2023

A film lasts for 2 hours 50 minutes. The film ends at 23 05. Find the time the film starts.

Find the total surface area of the cuboid.

$v=u-9.8t$ Find the value of $v$ when $u=4$ and $t=-7$.

Simplify $d^8÷d^2$.

At the end of the day, a shopkeeper has 12 tins of cat food left. This is $\frac{3}{13}$ of the number he had at the beginning of the day. Calculate the number of tins he had at the beginning of the day.

A spinner has five sides. Each side is painted red, blue, green, yellow or orange. The table shows some of the probabilities of the spinner landing on each colour.

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

The distance–time graph shows information about Kai’s journey from home to the office.

Without using a calculator, work out $5\frac{11}{12}+2\frac{1}{4}$. You must show all your working and give your answer as a mixed number in its simplest form.

The position vector of $A$ is $\left(\begin{array}{c}5\\ 3\end{array}\right)$ and $\overrightarrow{BA}=\left(\begin{array}{c}4\\ 8\end{array}\right)$. Show that $\mathrm{\mid }\overrightarrow{OB}\mathrm{\mid }=5.1$, correct to 1 decimal place.

Calculate $\sqrt{42}+3^{0.4}$.

Write $0.5\dot{8}\dot{1}$ as a fraction. You must show all your working and give your answer in its simplest form.

The number of trees in a forest is decreasing exponentially at a rate of 1.75% per year. Eleven years ago there were 980 trees. Calculate the number of trees in the forest now. Give your answer correct to the nearest integer.

The volume of a cylinder is $1970{\text{ cm}}^3$. The height of the cylinder is $12.8\text{ cm}$. Calculate the radius of the cylinder.

Rearrange the formula to make $m$ the subject. $$R=\frac{2(m-k)}{m}$$

$y$ is inversely proportional to the cube root of $(x+5)$. When $x=3$, $y=12$. Find $y$ when $x=22$.

Solve the equation $x^2+5x-7=0$. You must show all your working and give your answers correct to 2 decimal places.

$\mathrm{f}(x)=6x-7\mathrm{g}(x)=x^{-3}$

Simplify. $$\frac{2x^2+5x-12}{4x^2-9}$$

These are the first four terms of a sequence. $$\begin{array}{cccc}2.75& 6& 11.25& 20\end{array}$$ The $n$th term of this sequence is $\frac{1}{4}{n}^3+a{n}^2+bn$. Calculate the value of $a$ and the value of $b$.

A train travels between two stations. The distance between the stations is $220\text{ km}$, correct to the nearest kilometre. The speed of the train is $125\text{ km/h}$, correct to the nearest $5\text{ km/h}$. Calculate the upper bound for the time the journey takes. Give your answer in hours and minutes.