IGCSE Mathematics 0580 Paper 21, Oct/Nov 2025

Describe fully the single transformation that maps triangle $T$ onto triangle $P$.

Draw the image of triangle $T$ after an enlargement of scale factor 2, centre $(3,3)$.

$5^{-5}\times 5^5$

${125}^{\frac{2}{3}}$.

$\frac{p}{t}÷\frac{2}{t}$

$\frac{3x}{4}-\frac{x-1}{2}$

$A\cap B$

$\mathrm{n}(A^{\mathrm{\prime }}\cup B)$.

Complete the statements, giving a geometrical reason in each part. Angle $CDB=\text{.........................}$ because $\text{......................................................................................}$ $\text{.....................................................................................................................................................}$ Angle $ABD=\text{.........................}$ because $\text{......................................................................................}$ $\text{.....................................................................................................................................................}$ Angle $AED=\text{.........................}$ because $\text{......................................................................................}$ $\text{.....................................................................................................................................................}$

Triangle $CXD$ is mathematically similar to triangle $BXA$. $DX=8.0\text{ cm},BX=2.7\text{ cm}$ and $AX=4.0\text{ cm}$. Work out the length of $CX$.

Complete the statement. Area of triangle $CXD$ : area of triangle $BXA=\text{.......................}:\text{.......................}$

Write 66000 in standard form.

Work out $(3.7\times {10}^8)+(3.7\times {10}^7)$. Give your answer in standard form.

Find the value of $I$ when $M=7,k=3$ and $c=2$.

Rearrange the formula to write $k$ in terms of $I,M$ and $c$.

Two balls are picked at random from bag B without replacement. Find the probability that both balls are black.

The balls are replaced into bag B. Kyle picks a ball at random from each bag. Complete the tree diagram.

Find the probability that the two balls are the same colour.

The balls are replaced into their bags. Jo picks a ball at random from bag A and places it into bag B. She then picks a ball at random from bag B. Find the probability that she picks a black ball from bag B.

$(3-\sqrt{5})(2+3\sqrt{5})=a+b\sqrt{5}$ Find the value of $a$ and the value of $b$.

Rationalise the denominator. Write your answer in its simplest form. $$\frac{6}{\sqrt{2}}$$