IGCSE Mathematics 0580 Paper 41, Oct/Nov 2024

Write 70 as a product of its prime factors.

Find the highest common factor (HCF) of 70 and 112.

Find the lowest common multiple (LCM) of $70x^4{y}^2$ and $112x^3{y}^5$.

Simplify. $a^{12}÷a^4$

Simplify. $\frac{5}{2b}\times \frac{bc}{20}$

Solve. $4+2x=15$

Solve. $\frac{34+2x}{5}=4-x$

$P=d+\sqrt[3]{m^2}$ Find $P$ when $d=7$ and $m=-8$.

Rearrange the formula to make $m$ the subject.

On the grid, draw the image of triangle $A$ after a reflection in the line $x=1$

On the grid, draw the image of triangle $A$ after an enlargement by scale factor $\frac{1}{2}$ with centre $(5,1)$.

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

The point $(a,b)$ is reflected in the line $y=k$ where $k$ is an integer and $b<k$. Write the coordinates of the image of point $(a,b)$ in terms of $a$, $b$ and $k$.

The table shows the waiting times for 120 patients at a medical centre.

Calculate an estimate of the mean waiting time.

The histogram shows some information about the waiting times at a different medical centre. The total number of patients is 90 and no patient waits for more than 80 minutes. Complete the histogram for the patients that have a waiting time between 10 and 30 minutes.

Enzo, Rashid and Blessy each swim as many lengths of a swimming pool as they can in 15 minutes. The results are shown in the table.

Find the number of lengths Enzo swims as a percentage of the total number of lengths all three people swim.

Write the ratio of the number of lengths each person swims in the form $$\text{Enzo}:\text{Rashid}:\text{Blessy}\mathrm{.}$$ Give your answer in its simplest form.

Each length of the pool is $25\text{ m}$. Work out Blessy’s average swimming speed for the 15 minutes. Give your answer in metres per second.

Rashid continues to swim at the same rate. Calculate the time it takes Rashid to swim a total distance of $5\text{ km}$. Give your answer in hours and minutes.

Blessy swims for one hour. The number of lengths she swims decreases by 5% every 15 minutes. Calculate the number of lengths she swims in the final 15 minutes.

Another swimmer, Adam, swims $450\text{ m}$, correct to the nearest 25 metres. This takes 10 minutes, correct to the nearest minute. Calculate the minimum distance Adam swims in one hour at this rate.

Mia picks a pen from the box at random. Find the probability that she picks a red pen.

Mia puts the pen back into the box. She then picks a pen at random and replaces it. She then picks a second pen at random. Complete the tree diagram.

Find the probability that Mia picks two pens that have the same colour.

Mia now picks 3 of the 8 pens in the box at random without replacement. Find the probability that she picks 2 blue pens and 1 red pen.

Show that $AC=1028\text{ m}$, correct to the nearest metre.

Angle $ACB$ is obtuse. Calculate angle $ACB$.

Part of the field, triangle $ACD$, is sold for $\mathrm{\$}41500$. Calculate the cost of 1 hectare of this part of the field. Give your answer correct to the nearest dollar. [$1\text{ hectare}=10000{\text{ m}}^2$]

Complete these two statements. The company makes fewer than ...................... scientific calculators each day. The company can make a maximum of ...................... calculators each day.

Scientific calculators cost $\mathrm{\$}12$ to make. Graphic calculators cost $\mathrm{\$}18$ to make. Each day the company spends at least $\mathrm{\$}2700$ making calculators. Show that $2x+3y⩾450$.

The region $R$ satisfies these four inequalities. $$x<180y⩽90x+y⩽2402x+3y⩾450$$ By drawing four suitable lines and shading unwanted regions, find and label the region $R$.

Scientific calculators are sold for a profit of $\mathrm{\$}10$. Graphic calculators are sold for a profit of $\mathrm{\$}30$. Calculate the maximum profit made by the company in one day.

$\mathrm{f}(x)=7-3x\mathrm{g}(x)=x^2-16$ Find the values of $x$ when $\mathrm{g}(x)=20$.

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

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

On the axes, sketch the graph of $y=\mathrm{g}(x)$. On your sketch, indicate the values where the graph crosses the axes.

Find the equation of the tangent to the graph of $y=\mathrm{g}(x)$ when $x=-3$. Give your answer in the form $y=mx+c$.

$\mathrm{h}(x)=3^x$ On the axes, sketch the graph of $y=\mathrm{h}(x)$.

Write down the equation of the asymptote to the graph of $y=\mathrm{h}(x)$.

Work out the volume of the cuboid.

Work out the total surface area of the cuboid.

Calculate the angle between $GA$ and the base $ABCD$.

A straight rod $PQ$ is placed inside the cuboid. One end of the rod, $P$, is placed at the midpoint of $AB$. The other end of the rod, $Q$, rests on $GH$. $HQ:QG=4:1$. Calculate the length of the rod $PQ$.

This rectangle has area $190{\text{ cm}}^2$. By forming and solving an equation, show that $x=8.5$.

Work out the perimeter of the rectangle.

The diagram shows a sector $OAB$ of a circle, with centre $O$, and a chord $AB$. The shaded segment has area $30{\text{ cm}}^2$. Show that $r=23.7\text{ cm}$, correct to 1 decimal place.

Calculate the perimeter of the shaded segment.