O Level Mathematics 4024 Paper 22, Oct/Nov 2024

These are the contents of a bag of mixed fruit.

Calculate the mass of mango as a percentage of the total mass of the mixed fruit.

Tom makes a drink by mixing juice and water in the ratio $3:7$. He makes $1.4\text{ litres}$ of this drink. Calculate the amount of juice Tom uses. Give your answer in millilitres.

The cost of a fruit drink is directly proportional to the amount of juice it contains. A fruit drink containing $125\text{ ml}$ of juice costs $\mathrm{\$}1.50$. Calculate the cost of a fruit drink containing $175\text{ ml}$ of juice.

Kofi has a bag containing nuts and raisins. There are $285\text{ g}$ of raisins in the bag. The remaining $62\mathrm{\%}$ of the mass in the bag is nuts. Calculate the mass of nuts in the bag.

The mass of mixed nuts and seeds in a bag is $500\text{ g}$, correct to the nearest $10\text{ g}$. The mass of nuts in the bag is $350\text{ g}$, correct to the nearest $5\text{ g}$. Calculate the upper bound and the lower bound of the mass of seeds in the bag.

The table shows the age and value of 10 cars of the same model.

Complete the scatter diagram. The first 6 points have been plotted for you.

Draw a line of best fit.

Use your line of best fit to find an estimate for the value of a car of this model that is 7 years old.

Jay has a car of this model that is 12 years old and he wants to find its value. Explain why Jay should not use this scatter diagram to find an estimate for the value of this car.

Jay records the distances travelled by 50 cars. The frequency table shows the results.

Work out the fraction of the cars that have travelled more than $50000\text{ km}$. Give your answer in its simplest form.

Find the interval that contains the median.

Calculate an estimate of the mean distance travelled.

The diagram shows a tank. The tank is a cuboid with length $1.2\text{ m}$, width $0.6\text{ m}$ and height $h\text{ m}$. The volume of the tank is $1.8{\text{ m}}^3$. Calculate the value of $h$.

Fuel is pumped into the empty tank at a rate of $0.2{\text{ m}}^3$ per minute. Calculate the time taken to fill the tank to $90\mathrm{\%}$ of its volume. Give your answer in minutes and seconds.

The diagram shows a tank with an open top. The tank is a prism with trapezium $ABCD$ as its cross-section. $AD=BC=70\text{ cm}$, $CD=80\text{ cm}$ and $AB=110\text{ cm}$. The base of the tank is a square. Calculate the total surface area of the outside of the tank.

Anya buys 4 shirts and 3 hats. She pays $\mathrm{\$}100$ and receives $\mathrm{\$}21.50$ in change. Each shirt costs the same amount. Each hat costs $\mathrm{\$}13.50$. Work out the cost of one shirt.

The exchange rate between dollars ($\$) and euros (€) is $\mathrm{\$}1=\text{€}0.91$. Anya buys a new camera for $\mathrm{\$}150$. She sees the same camera for sale online for €140. Calculate the difference between the price in dollars and the price in euros. Give your answer in dollars, correct to the nearest cent.

Anya invests $\mathrm{\$}600$ in a savings account. The account pays compound interest at a rate of $r\mathrm{\%}$ per year. At the end of 3 years the total interest is $\mathrm{\$}21.86$. Calculate the value of $r$.

She takes one of the 9 cards at random, notes the number and replaces it. Find the probability that the card shows an odd number.

Mandeep takes one of the 9 cards at random, notes the number and replaces it. She then takes a second card at random. Find the probability that both cards show the number 1.

Mandeep takes two of the 9 cards at random without replacement. She calculates the product of the two numbers shown. Find the probability that the product is less than 5.

Complete the table for $y=\frac{x}{4}(2x^2-x-10)$.

Draw the graph of $y=\frac{x}{4}(2x^2-x-10)$ for $-3⩽x⩽3$.

The equation $\frac{x}{4}(2x^2-x-10)=k$ has exactly two solutions. Use your graph to find the possible values of $k$.

By drawing a suitable line on the grid, find the solutions of $2x^3-x^2-10x=2x-4$.

Solve. $$4x+7=16$$

Solve. $$5(4-y)=30$$

Write down all the integers that satisfy this inequality. $$-\frac{3}{2}⩽x<3$$

Rearrange the formula $y=\frac{4y-x}{3x}$ to make $x$ the subject.

Simplify $\frac{12x^2-3y^2}{2x^2+8x-xy-4y}$.

Complete the missing angles and reasons to show that triangle $ABC$ is similar to triangle $ADE$. In triangle $ABC$ and triangle $ADE$, angle $BAC$ = angle ............. because common angle angle $ABC$ = angle ............. because ................................................................................ angle $ACB$ = angle ............. because ................................................................................ As the three pairs of angles are equal, triangle $ABC$ is similar to triangle $ADE$.

Show that $AD=3.6\text{ cm}$ and $AE=5.2\text{ cm}$.

Calculate angle $DAE$.

Calculate the area of triangle $ABC$.

$A$, $B$, $C$ and $D$ are points on a circle, centre $O$. $AOD$ and $OCE$ are straight lines. $DE$ is a tangent to the circle at $D$. Angle $ABC={126}^{\circ }$ and $DE=10.5\text{ cm}$. Calculate the radius of the circle.

$P$ and $Q$ are points on a different circle, centre $O$. The angle of the minor sector $POQ$ is ${82}^{\circ }$. The length of the minor arc $PQ$ is $7.3\text{ cm}$. Calculate the area of the major sector.

Write down an expression for the mass, in kilograms, of apples Mina receives.

The cost of pears is 40 cents per kilogram more than the cost of apples. Mina spends $\mathrm{\$}9$ on pears. The mass of pears Mina receives is $0.75\text{ kg}$ less than the mass of apples. Form an equation in $x$ and show that it simplifies to $x^2+40x-48000=0$.

Solve the equation $x^2+40x-48000=0$. Show your working.

Narinder buys $1.5\text{ kg}$ of apples and $0.8\text{ kg}$ of pears. Work out the total amount he pays in dollars.