O Level Mathematics 4024 Paper 21, Oct/Nov 2024

The sign shows the opening hours for the shop. Saturday to Wednesday 1030 to 1800 Thursday and Friday 1000 to 1930 Work out the length of time the shop is open in one week.

Basma employs 5 sales assistants and 2 supervisors. On one particular week, the 5 sales assistants each work for 30 hours and the 2 supervisors each work for 38 hours. For that week, the total amount Basma pays these 7 employees is $3324.70 . Basma pays each sales assistant $13.45 per hour. Calculate the amount Basma pays each supervisor per hour.

The exchange rate between dollars ($) and pounds (£) is $1 = £0.77 . Basma buys 50 identical games for a total of £245. She makes a profit of 39% when she sells each game. Calculate the selling price of one game in dollars. Give your answer correct to the nearest cent.

Basma invests $12000 in an account paying compound interest at a rate of 1.5% per year. At the end of year 1, she invests another $12000 in the same account. At the end of year 4, she takes $20000 out of the account. Calculate the amount of money remaining in the account at the end of year 4. Give your answer correct to the nearest cent.

160 vehicles pass the checkpoint in the morning. The table shows the number of people in each of these vehicles.

Complete the table.

Complete the pie chart to show the results.

The histogram shows the speeds of vehicles passing the checkpoint in the afternoon. Sanjay says the histogram shows that the range of the speeds is $50\text{ km/h}$. Explain why he may not be correct.

Complete the frequency table.

Complete the table for $y=4+2x-\frac{x^2}{2}$.

Draw the graph of $y=4+2x-\frac{x^2}{2}$ for $-2⩽x⩽6$.

Find the equation of the line of symmetry of the graph of $y=4+2x-\frac{x^2}{2}$.

On the grid, draw the line $3y=x+6$ for $-2⩽x⩽6$.

Write down the $x$-coordinates of the points of intersection of the graphs of $y=4+2x-\frac{x^2}{2}$ and $3y=x+6$.

Write down the elements of $A$.

Complete the Venn diagram.

$x\in (A\cup B{)}^{\mathrm{\prime }}$ Find the smallest value of $x$.

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

Solve. $\frac{y}{4}=8$

Solve. $3-4x=2x+12$

$w=5x-6y$ Find the value of $w$ when $x=6.2$ and $y=-1.8$.

Rearrange the formula to make $x$ the subject.

Factorise. $15y-x^2-3xy+5x$

Write as a single fraction in its simplest form. $\frac{2}{x-3}-\frac{4}{x+3}+1$

[Volume of sphere $=\frac{4}{3}\pi r^3$] The diagram shows a sphere inside a cube. The sphere touches all 6 faces of the cube. The volume of the cube is $343{\text{ cm}}^3$. Calculate the volume of the sphere.

Solid $A$ is mathematically similar to solid $B$. The volume of solid $A$ is $540{\text{ cm}}^3$ and its height is $15\text{ cm}$. The volume of solid $B$ is $1280{\text{ cm}}^3$. Calculate the height of solid $B$.

[Curved surface area of a cone $=\pi rl$] The diagram shows a solid formed by joining a cone to a cylinder. The cone and the cylinder each have radius $6.3\text{ cm}$. The slant height of the cone is $8.7\text{ cm}$. The ratio $\text{height of cone}:\text{height of cylinder}=2:3$. Calculate the total surface area of the solid.

Find the coordinates of point $D$.

Find $\mathrm{\mid }\overrightarrow{AD}\mathrm{\mid }$.

Find $\overrightarrow{AC}$.

Line $L$ is the line perpendicular to $AB$ that passes through point $D$. Find the equation of line $L$.

Ray walks from $A$ to $B$ at an average speed of $1.6\text{ m/s}$. He then runs from $B$ to $C$ at an average speed of $2.8\text{ m/s}$. Calculate Ray’s average speed from $A$ to $B$ to $C$.

The bearing of $D$ from $A$ is ${243}^{\circ }$. Calculate the bearing of $B$ from $A$.

$ABD$ is a triangle. $C$ is a point on $BD$ and $E$ is a point on $AD$. $AB$ is parallel to $EC$ and $CD=DE$. Find the value of $x$ and the value of $y$.

$PQR$ is a triangle. $P$ and $R$ are points on a circle, centre $O$. $O$ is a point on $PQ$. $QR$ is a tangent to the circle at $R$. $QR=12\text{ cm}$ and angle $RPQ={35}^{\circ }$. Calculate the area of triangle $PQR$.

Show that the fraction of the balls in bag A that are red is $\frac{x-6}{2x}$.

Bag B also contains red balls and green balls. The number of red balls in bag B is $x$. The number of green balls in bag B is 4 times the number of green balls in bag A. Show that the fraction of the balls in bag B that are red is $\frac{x}{3x+12}$.

$\frac{x-6}{2x}=\frac{x}{3x+12}$ Show that $x^2-6x-72=0$.

Solve by factorisation $x^2-6x-72=0$.

$x$ is the total number of balls in bag A. Use your answer to part (d) to find the number of green balls in bag A.

Mia takes one of the triangles at random, notes its properties and replaces it. Find the probability that it has line symmetry.

Mia takes one of the 25 shapes at random, notes its properties and replaces it. She then takes a second shape at random, notes its properties and replaces it. Find the probability that both shapes are quadrilaterals.

Mia takes three of the 25 shapes at random without replacement. Find the probability that only one of the shapes is a triangle with line symmetry.