IGCSE Mathematics 0580 Paper 41, Oct/Nov 2025

A quadrilateral has • rotational symmetry of order 2 • two diagonals that are the only lines of symmetry. Write down the geometrical name of this quadrilateral.

Solve. $$11-2x=4$$

The diagram shows two parallel lines and a straight line. Find the value of $x$.

A train journey starts at 22 16. The journey takes 5 hours 52 minutes. Find the time the train journey finishes.

Expand. $$g(3-2g)$$

Calculate. $$({3.5}^2-{2.2}^3{)}^{\frac{1}{4}}$$

An athlete runs at a speed of $9.5\text{ m/s}$. Convert this speed into $\text{km/h}$.

$A$ is the point $(2,1)$. $$\overrightarrow{AB}=\left(\begin{array}{c}2\\ 4\end{array}\right)$$ Find the coordinates of $B$.

In a sale, the prices of coats are reduced by 15%.

Some students are asked if they like football ($F$) or rugby ($R$). The Venn diagram shows the results.

The diagram shows two vertical poles, $AE$ and $PT$, standing on horizontal ground, $AP$. Calculate the angle of elevation of the point $T$ from the point $E$.

A cube contains a solid metal sphere. The sphere touches all the faces of the cube. The side length of the cube is $8\text{ cm}$.

$A$, $B$ and $C$ lie on a circle, centre $O$. $TA$ and $TB$ are tangents to the circle at $A$ and $B$. Calculate angle $ATB$.

The table shows some information about the heights of 50 plants. Calculate an estimate of the mean height.

Find the equation of the straight line that passes through the points $(2,0)$ and $(0,4)$. Give your answer in the form $y=mx+c$.

The diagram shows part of the speed–time graph for an athlete in a race.

The mass of a radioactive substance decays exponentially at a rate of 10% per day. The initial mass of the substance is $20\text{ g}$. Find the number of whole days it takes for the mass of the substance to first be less than $1\text{ g}$.

These are the first five terms of a sequence. $$48241263$$

In triangle $STU$, $ST=8\text{ cm}$, $SU=9\text{ cm}$ and angle $TSU={50}^{\circ }$. Calculate the area of triangle $STU$.

Alex invests $200 at a rate of $r$ per year compound interest. At the end of 25 years the value of this investment is $301.10 . Find the value of $r$.

$$y\propto \frac{1}{\sqrt{x+1}}$$ When $x=8$, $y=3$. Find $y$ in terms of $x$.

Martha walks a distance of $10\text{ km}$ at a speed of $x\text{ km/h}$. She then runs a distance of $5\text{ km}$ at a speed of $(x+4)\text{ km/h}$. The total time taken for the whole journey is 3.5 hours.

Kai sorts parcels into two types, light and heavy. The histogram shows some information about the number of parcels Kai sorts in one day.

Solve the simultaneous equations. You must show all your working. $$y=2x^2-3x-7$$ $$y=2x-7$$

The diagram shows a prism of length $15\text{ cm}$. The cross-section of the prism is a trapezium. Angle $DAB={90}^{\circ }$ and angle $ADC={90}^{\circ }$. $AB=10\text{ cm}$, $AD=5\text{ cm}$ and $DC=7\text{ cm}$. Calculate the angle the diagonal $AG$ makes with the base $ABFE$.

$$\mathrm{f}(x)=7^{x-4}$$ Find the value of $x$ when