IGCSE Mathematics 0580 Paper 21, Oct/Nov 2024

A concert starts at 1950 and finishes 2 hours 42 minutes later. Work out the time the concert finishes.

Find the reciprocal of $1\frac{1}{4}$.

Use one of the symbols $<$, $>$ or $=$ to make each statement true. $$\frac{2}{7}\text{ ....................... }0.2861$$ $$\frac{99}{900}\text{ ....................... }11\mathrm{\%}$$ $$1^3\text{ ....................... }{4}^0$$

Safia has a piece of fabric of length $5.6\text{ m}$. She cuts the fabric into two parts, with lengths in the ratio $3:4$. Calculate the length of the longer part.

Work out.

The diagram shows a right-angled triangle $ABC$ and a quadrilateral $AEDC$. Find the value of

Factorise. $$28x-35$$

Edith invests $3000 in a savings account. The account pays simple interest at a rate of 2.6% per year. Calculate the total interest earned at the end of 3 years.

The diagram shows part of a regular polygon. The interior angle of the polygon is ${132}^{\circ }$ larger than the exterior angle. Calculate the number of sides of this polygon.

Jacinda plays a game with her friend. She can win, lose or draw the game. The probability that she wins the game is 0.28.

Without using a calculator, work out $5\frac{1}{3}-3\frac{4}{7}$. You must show all your working and give your answer as a mixed number in its simplest form.

Solve the simultaneous equations. You must show all your working. $$5x+6y=9$$ $$3x-2y=-17$$

Two solid steel statues are mathematically similar. The smaller statue has height $12\text{ cm}$ and the larger statue has height $15\text{ cm}$. The larger statue has a mass $2.5\text{ kg}$. The density of steel is $8{\text{ g/cm}}^3$. Calculate the volume of the smaller statue. [$\text{Density}=\text{mass}÷\text{volume}$.]

Students in class $P$ take a test. These statistics show information about their marks. • lower quartile = 38 • median = 53 • interquartile range = 28 • range = 81 • highest mark = 96

The diagram shows a sphere of radius $6\text{ cm}$ and a cylinder of height $18\text{ cm}$ and radius $R\text{ cm}$. The volume of the sphere is equal to the volume of the cylinder. Calculate the curved surface area of the cylinder. Give your answer in terms of $\pi$. [The volume, $V$, of a sphere with radius $r$ is $V=\frac{4}{3}\pi r^3$]

Solve. $$3x^2-7x-16=0$$ You must show all your working and give your answers correct to 2 decimal places.

$$\mathrm{g}(x)=4^{x+3}$$

$$\mathcal{E}=\{1,2,3,4,5,6,7,8,9,10\}$$ $$P=\{\text{odd numbers}\}$$ $$Q=\{\text{multiples of }3\}$$ $$R=\{\text{square numbers}\}$$

The diagram shows two right-angled triangles $PQS$ and $RQT$. $PQR$ and $QTS$ are straight lines. Calculate angle $QTR$.

Solve the equation $3\tan x+5=1$ for $0^{\circ }⩽x⩽{360}^{\circ }$.

The graph of $y=(x+2)(x-1{)}^2$ is shown on the grid.

$$(x-5{)}^2+k=x^2-px-21$$ Find the value of $p$ and the value of $k$.