IGCSE Mathematics 0580 Paper 22, Oct/Nov 2023

Write 24.07839

Write down the number that is 9 greater than $-23$.

$v=u+at$ Find the value of $v$ when $u=30$, $a=-2$ and $t=7$.

Change 62 000 millimetres into kilometres.

The diagram shows two intersecting straight lines crossing two parallel lines. Find the value of $x$.

Find the bearing of $Q$ from $P$.

Without using a calculator, work out $3\frac{1}{8}-1\frac{3}{4}$. You must show all your working and give your answer as a mixed number in its simplest form.

Write 90 as a product of its prime factors.

Expand and simplify. $$2(t+w)+3(w-t)$$

The two shapes are mathematically similar.

The diagram shows a speed–time graph for 16 seconds of a car journey.

$y=2w^2-x$ Rearrange the formula to make $w$ the subject.

Find the lowest common multiple (LCM) of $12x^8$ and $8x^{12}$.

A solid cylinder has radius $5\text{ cm}$ and height $8\text{ cm}$. Calculate the total surface area of the cylinder.

Find the $n$th term of each sequence.

The area of a rectangle is $55.2{\text{ cm}}^2$, correct to 1 decimal place. The length of the rectangle is $9\text{ cm}$, correct to the nearest cm. Calculate the upper bound of the width of the rectangle.

The line $y=x+1$ intersects the curve $y=x^2+x-3$ at two points. Find the coordinates of the two points.

$x$ is inversely proportional to the square root of $w$. When $w=16$, $x=3$. Find $x$ in terms of $w$.

Some students record their reaction times. The table shows the results.

On a histogram, the height of the block for the $0<t⩽6$ interval is $7.5\text{ cm}$. Calculate the height of the block for the $6<t⩽10$ interval.

Simplify. $$\frac{ax-2a-x+2}{a^2-1}$$

The derivative of $2a{x}^7+3x^k$ is $42x^6+15x^{k-1}$. Find the value of $a$ and the value of $k$.

The diagram shows a parallelogram $OPQT$. The position vector of $P$ is $\mathbf{a}$ and the position vector of $T$ is $\mathbf{b}$. $K$ is on $PQ$ so that $PK:KQ=3:1$. The lines $OK$ and $TQ$ are extended to meet at $X$. Find the position vector of $X$ in terms of $\mathbf{a}$ and $\mathbf{b}$. Give your answer in its simplest form.