IGCSE Mathematics 0580 Paper 43, Oct/Nov 2023

Brad changes $250 to Indian rupees. Calculate the amount he receives correct to the nearest rupee.

Wang changes 5400 Chinese yuan into dollars. Calculate how much he receives in dollars, correct to the nearest cent.

Gretal lives in Spain and goes on holiday to Wales. She spends 3500 euros in total on travel and hotels in the ratio $$\text{travel}:\text{hotels}=4:3.$$ Work out how much Gretal spends, in euros, on travel.

Work out how much she spends, in pounds, on hotels.

Gretal flies home to Spain. The plane flies a distance of $2200\text{ km}$, correct to the nearest $100\text{ km}$. The average speed of the plane is $740\text{ km/h}$, correct to the nearest $20\text{ km/h}$. Calculate the lower bound of the time taken, in hours and minutes, for this flight.

Find the percentage of the birds that are Starlings.

In the table, complete the column for the pie chart sector angle.

Complete the pie chart to show the information in the table.

On Tuesday, the number of Goldfinches seen in the garden increased by $262.5\mathrm{\%}$. Calculate the number of Goldfinches seen on Tuesday.

One of the most common birds in the world is the Red-Billed Quelea which lives in Sub-Saharan Africa. There are approximately 1500 million of these birds in this area. Write 1500 million in standard form.

The land area of Sub-Saharan Africa is approximately 21.2 million square kilometres. Work out the average number of these birds per square kilometre.

Describe fully the single transformation that maps triangle $A$ onto triangle $B$.

Draw the image of triangle $A$ after a reflection in the line $y=1$

Draw the image of triangle $A$ after a translation by the vector $\left(\begin{array}{c}5\\ -7\end{array}\right)$

Draw the image of triangle $A$ after an enlargement, scale factor 2, centre $(-4,5)$.

Find the size of one interior angle of a regular 10-sided polygon.

The points $A$, $B$, $C$, $D$ and $E$ lie on a circle. $FG$ is a tangent to the circle at $D$. $EB$ is parallel to $DC$. Find the value of each of $w$, $x$, $y$ and $z$.

Complete the table and the histogram.

Calculate an estimate of the mean time.

Rashid says: ‘The longest time that any of these workers take to travel to work is 80 minutes.’ Give a reason why Rashid may be wrong.

Indira picks three workers at random from those who take longer than 25 minutes to travel to work. Calculate the probability that one worker takes 60 minutes or less and the other two each take more than 60 minutes.

Find the value of $\mathrm{f}(2)$

Find the value of $\mathrm{g}\mathrm{f}(0.5)$.

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

Find $x$ when $\mathrm{g}(x)=\frac{1}{2^5}$.

Write as a single fraction in its simplest form $\frac{1}{\mathrm{f}(x)}-\mathrm{h}(x)$.

Complete the table of values for $y=3\cos 2x^{\circ }$. Values are given correct to 1 decimal place.

Draw the graph of $y=3\cos 2x^{\circ }$ for $0⩽x⩽90$.

Use your graph to solve the equation $3\cos 2x^{\circ }=-2$ for $0⩽x⩽90$.

By drawing a suitable straight line, solve the equation $120\cos 2x^{\circ }=80-x$ for $0⩽x⩽90$.

The diagram shows a shape made from a major sector $AOB$ and triangles $OBC$ and $AOD$. $OB=6\text{ cm}$, $BC=2\text{ cm}$, obtuse angle $AOC={135}^{\circ }$ and angle $BCO={90}^{\circ }$. Show that angle $BOC={19.5}^{\circ }$, correct to 1 decimal place.

Calculate the area of the major sector $AOB$.

$C$ is the midpoint of $OD$. Calculate $AD$.

Calculate the total area of the shape.

A sector of a circle has radius $8\text{ cm}$ and area $160{\text{ cm}}^2$. A mathematically similar sector has radius $20\text{ cm}$. Calculate the area of the larger sector.

Determine if triangle $ABC$ is scalene, isosceles or equilateral. You must show all your working.

Find the equation of the line $AC$. Give your answer in the form $y=mx+c$.

Find the equation of the perpendicular bisector of $AC$. Give your answer in the form $y=mx+c$.

$ABCD$ is a kite. The point $D$ has coordinates $(w,4w+1)$. Find the coordinates of $D$.

Expand and simplify. $$4(2x-1)-6(3-x)$$

Factorise completely. $$6x^{2}y+9xy$$

Factorise completely. $$4x^2-y^2+8x+4y$$

Antonio travels $100\text{ km}$ at an average speed of $x\text{ km/h}$. He then travels a further $150\text{ km}$ at an average speed of $(x+10)\text{ km/h}$. The time taken for the whole journey is 4 hours 20 minutes. Show that $13x^2-620x-3000=0$.

Solve $13x^2-620x-3000=0$ to find the speed Antonio travels for the first $100\text{ km}$ of the journey. You must show all your working and give your answer correct to 1 decimal place.

Find the coordinates of the points $A$, $B$ and $C$.

Differentiate $18+5x-2x^2$.

Find the coordinates of the point on $y=18+5x-2x^2$ where the gradient is 17.