IGCSE Mathematics 0580 Paper 43, Oct/Nov 2024

One day the mass of fruit and vegetables he sells is in the ratio $\text{fruit}:\text{vegetables}=9:8$. He sells $48\text{ kg}$ of vegetables. Find the mass of the fruit he sells.

On another day he receives $\mathrm{\$}280$ for the fruit and vegetables he sells. The $\mathrm{\$}280$ is in the ratio $fruit:vegetables=(c+3):(c-1)$. Find the amount he receives from selling the fruit.

In one week Dinari buys fruit and vegetables for $\mathrm{\$}1620$. He sells the fruit and vegetables for $\mathrm{\$}1750$. Calculate his percentage profit.

In another week Dinari sells fruit and vegetables for $\mathrm{\$}1738$. He makes a profit of $10\mathrm{\%}$. Calculate the amount he paid for the fruit and vegetables in that week.

$A$ is the point $(3,7)$ and $B$ is the point $(-1,5)$. Find the coordinates of the midpoint of the line $AB$.

Write $\overrightarrow{AB}$ as a column vector.

$\overrightarrow{AC}=3\overrightarrow{BA}$ Find the coordinates of $C$.

Rotate shape $P$ through ${180}^{\circ }$ about the point $(4,1)$.

Reflect shape $P$ in the line $y=x+2$.

Describe fully the single transformation that maps shape $P$ onto shape $Q$.

Ed invests $\mathrm{\$}500$ in an account paying $r$ per year simple interest. At the end of 14 years the total amount in Ed's account is $\mathrm{\$}675$. Find the value of $r$.

Eva invests $\mathrm{\$}400$ at a rate of $2.2$ per year compound interest. Calculate the total interest earned at the end of 11 years.

Erin invests $\mathrm{\$}700$ at a rate of $p$ per month compound interest. At the end of 21 years the value of Erin's investment is $\mathrm{\$}1074$, correct to the nearest dollar. Calculate the value of $p$.

A box contains 50 cuboids. Each cuboid has a mass of $135\text{ g}$. The total mass of the cuboids and the box is $7\text{ kg}$. Calculate the mass of the box. Give your answer in grams.

A solid cube of side $4\text{ cm}$ is fixed to the base inside an empty cube of side $6\text{ cm}$. Water is poured into the larger cube until it reaches the top of the smaller cube. Calculate the amount of water poured into the larger cube.

The diagram shows a solid triangular prism of length $20\text{ cm}$. The cross-section is an equilateral triangle with side length $4\text{ cm}$. The prism is made of wood with a density of $0.85{\text{ g/cm}}^3$. Calculate the mass of the prism. $[\text{Density}=\text{mass}÷\text{volume}]$

The diagram shows a solid cone with base radius $10\text{ cm}$ and height $24\text{ cm}$. Show that the total surface area of the cone is $1131{\text{ cm}}^2$, correct to the nearest ${\text{cm}}^2$. [The curved surface area of a cone with base radius $r$ and slant height $l$ is $A=\pi rl$.]

The total surface area of the cone is painted. The cost to paint the cone is $\mathrm{\$}1.71$. Calculate the cost to paint $1{\text{ cm}}^2$ of the cone. Give your answer in cents.

One tin of paint has enough paint to cover $2.5{\text{ m}}^2$. Calculate the number of these cones that can be painted completely using one tin of paint.

Naomi runs $100\text{ m}$ in 15 seconds. Calculate Naomi's average speed in kilometres per hour.

Olav runs for 45 minutes at a speed of $9.5\text{ km/h}$. He then runs $8.1\text{ km}$ at a speed of $7.5\text{ km/h}$. Calculate Olav's average speed for the whole run.

A train has length $p$ metres. The train passes through a station of length $q$ metres. The speed of the train is $v$ kilometres per hour. Find an expression for the time the train takes to completely pass through the station. Give your answer in seconds, in terms of $p$, $q$ and $v$.

Simplify ${\displaystyle \frac{24u}{5y}}\times {\displaystyle \frac{10}{3u}}$.

Expand and simplify $(x-1)(x+2)(x+3)$.

Solve the equation $2x^2+x-5=0$. You must show all your working and give your answers correct to 2 decimal places.

Calculate the area of the trapezium.

The area of this trapezium is $264{\text{ cm}}^2$. Show that $2y^2+9y-518=0$.

Solve $2y^2+9y-518=0$ by factorisation to find the value of $y$.

The diagram shows a sector of a circle with radius $8\text{ cm}$ and angle ${75}^{\circ }$. Find the perimeter of the sector.

The diagram shows a shape $ABQP$ made from three straight lines and an arc of a sector of a circle. The sector has centre $O$ and angle ${90}^{\circ }$. $POQ$ is a straight line and $AP=PO=OQ=QB=5\text{ cm}$. Find the area of $ABQP$. Give your answer in the form $a+k\pi$.

Guillaume draws a pie chart for this data. Calculate the angle for the interval $45<v⩽50$.

Calculate an estimate of the mean speed.

Complete the histogram to show the data in the table.

Marwan picks a ball from the bag at random and then replaces it. Find the probability that the ball is white.

Naomi picks a ball from the bag at random and then replaces it. She repeats this 120 times. Find the number of times the ball is expected to be white.

Oscar picks a ball from the bag at random. He replaces it and then picks a second ball from the bag at random. Find the probability that the balls are the same colour.

Find the probability that the balls are not the same colour.

Priya picks 3 of the 8 balls from the bag at random without replacement. Find the probability that she picks two white balls and one black ball.

Find the derivative of $3+2x-x^2$.

Show that the equation of the tangent at $A$ is $y=4x+4$.

The line $L$ is perpendicular to the line $y=4x+4$. The line $L$ passes through the point $B$. Find the equation of the line $L$. Give your answer in the form $y=mx+c$.

Find the coordinates of the maximum point on the graph of $y=3+2x-x^2$.

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

Find $\mathrm{f}(x)\mathrm{g}(x)+\mathrm{f}\mathrm{g}(x)+1$. Give your answer in its simplest form.

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

Find $\mathrm{h}\mathrm{h}(1)$.

Simplify ${\displaystyle \frac{1}{\mathrm{f}(x)}}-\mathrm{h}(x)$. Give your answer as a single fraction in its simplest form.

Find $x$ when $\mathrm{j}(x)={\displaystyle \frac{1}{32}}$.

Find $x$ when ${\mathrm{j}}^{-1}(x)=0$.

Show that $AC=17.37\text{ cm}$, correct to 2 decimal places.

Angle $AEC$ is obtuse. Calculate angle $ACE$.

Calculate the perimeter of quadrilateral $ABCD$.