O Level Mathematics 4024 Paper 22, Oct/Nov 2023

Idris repairs computers. This is how he calculates the charge for a repair. $56 for the first hour Then $12.25 for each additional 15 minutes Work out the amount Idris charges for a repair that takes him 2 hours.

Idris charges $166.25 for another repair. He starts work on the repair at 2.30 pm. Find the time when he completes the repair.

Idris invests $6200 in an account paying compound interest at a rate of 1.7% per year. Calculate the total amount of interest earned at the end of 4 years.

The exchange rate between dollars ($) and euros (€) is $1 = €0.84 . Idris buys some equipment from a website that charges in euros. The equipment costs €760. Idris must pay 2.5% tax on this cost. Work out the amount Idris pays for the equipment including tax. Give your answer in dollars.

Find the size of one interior angle of a regular 15-sided polygon.

The diagram shows part of a regular 15-sided polygon. Find the value of $x$.

$A$, $B$, $C$ and $D$ are points on the circle, centre $O$. $AB$ is a diameter of the circle. Angle $BAC={24}^{\circ }$. Find angle $ADC$. Give a reason for each step of your working.

Laila asks a group of people what type of exercise they prefer. The results are shown in the pie chart. 90 people prefer running. Calculate the total number of people Laila asks.

Work out the fraction of the group who prefer yoga. Write your answer in its simplest form.

Laila records the number of steps she walks each day for 60 days. The table shows the results.

Complete the histogram to represent the data.

Laila has a target of 11 000 steps every day. Find an estimate for the percentage of these 60 days that Laila met her target.

Solve. $$5x+6=3x$$

The mass of a plum is $n$ grams. The mass of an apple is twice the mass of the plum. The mass of a banana is 50 grams more than the mass of the apple. The total mass of the plum, the apple and the banana is 450 grams. Form an equation in $n$ and solve it to find the mass of the plum.

Solve by factorisation. $$x^2-4x-21=0$$

A bag contains 40 balls. 28 of the balls are red and the rest are green. Aisha takes a ball from the bag at random, notes its colour and replaces it. Find the probability that this ball is green.

Aisha repeats this 200 times. Work out the number of times she expects to take a green ball.

A bag contains 9 blue balls and 7 yellow balls. Sergio takes two balls from the bag at random without replacement. Complete the tree diagram.

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

Complete the table for $y=\frac{4^x}{10}$.

Draw the graph of $y=\frac{4^x}{10}$ for $0⩽x⩽3$.

Use your graph to solve the equation $\frac{4^x}{10}=5$.

By drawing a tangent, estimate the gradient of $y=\frac{4^x}{10}$ when $x=2$.

This is a sketch of the graph of $y=x^2+ax+b$. Find the value of $a$ and the value of $b$.

Point $A$ and point $B$ are shown on a centimetre square grid. $ABC$ is a triangle. Here are five possible coordinates for point $C$. $$(-2,4)(-2,-1)(-1,-2)(6,1)(-4,6)$$ Tick (✓) the two coordinates from the list that make $ABC$ an isosceles triangle.

Find the column vector $\overrightarrow{AB}$.

$A$ is the midpoint of the line $DB$. Find $\mathrm{\mid }\overrightarrow{DB}\mathrm{\mid }$.

The equation of line $P$ is $y=4x-3$. Line $L$ is perpendicular to line $P$. Line $L$ passes through the point $(6,4)$. Find the coordinates of the point where line $L$ crosses the $x$-axis.

Form an equation in $x$ and show that it simplifies to $2x^2-15x-22=0$.

Solve the equation $2x^2-15x-22=0$. Show your working and give your answers correct to 2 decimal places.

Calculate the shaded area.

$ABCD$ is a rectangular field. $C$ is due south of $A$. $AB=450\text{ m}$ and $BC=210\text{ m}$. Martha walks at an average speed of $5.2\text{ km/h}$. Calculate the time Martha takes to walk once around the perimeter of the field. Give your answer correct to the nearest minute.

Show that the bearing of $D$ from $A$ is ${245}^{\circ }$, correct to 3 significant figures.

$PQR$ is a triangle and $S$ is a point on $PR$. $PS=10.3\text{ cm}$, $QR=12.6\text{ cm}$, $Q\widehat{P}S={42}^{\circ }$ and $Q\widehat{R}S={35}^{\circ }$. Calculate $QS$.

[Volume of a cone $=\frac{1}{3}\pi r^{2}h$] [Curved surface area of a cone $=\pi rl$] A solid is formed from a large cone with a small cone removed from the centre. The small cone is mathematically similar to the large cone. The vertex of the large cone is vertically below the vertex of the small cone. The height of the large cone is $21\text{ cm}$ and the diameter of the top is $18\text{ cm}$. The height of the small cone is $14\text{ cm}$. Show that the volume of the solid is $399\pi {\text{ cm}}^3$.

Calculate the total surface area of the solid.

The height of a cylinder is $13\text{ cm}$, correct to the nearest centimetre. The radius of the base of the cylinder is $4.5\text{ cm}$, correct to the nearest 0.1 centimetre. Calculate the upper bound of the volume, in ${\text{cm}}^3$, of the cylinder.

Find $\mathrm{f}(-3)$.

Find ${\mathrm{g}}^{-1}(x)$.

Simplify $\frac{2}{\mathrm{f}(x)}+\frac{1}{\mathrm{g}(x)}$. Give your answer as a single fraction, in terms of $x$, in its simplest form.