IGCSE Mathematics 0580 Paper 31, May/June 2023

Write the number forty thousand and thirty-three in figures.

Find the value of $\sqrt[3]{729}$.

Find the reciprocal of $\frac{7}{9}$. Give your answer as a decimal, correct to 3 decimal places.

Find the value of $6^5÷3^4$.

Work out $(-9)\times (-7)÷(-3)$.

Work out. $11+9\times 5-4$

Work out. $(11+9)\times 5-4$

$$-0.67\sqrt{123}\sqrt{49}\frac{5}{9}3.142$$ From this list, write down an irrational number.

Find the lowest common multiple (LCM) of 24 and 104.

Find the highest common factor (HCF) of 24 and 104.

Complete this statement. The mathematical name of any polygon with 4 sides is a ...........................................................

Three of these shapes are shown on the grid. Describe fully the single transformation that maps the shaded shape onto shape $A$

Three of these shapes are shown on the grid. Describe fully the single transformation that maps the shaded shape onto shape $B$.

On the grid, draw the image of the shaded shape after a translation by the vector $\left(\begin{array}{c}9\\ -6\end{array}\right)$

On the grid, draw the image of the shaded shape after a reflection in the line $y=-1$.

Complete the stem-and-leaf diagram. Key: $1\mid 5$ represents 15

Find the mode.

Find the median.

Find the range.

Complete the bar chart for the test scores of the 16 students.

Work out the percentage of students with a test score of 40 or more.

The diagram shows the net of a solid on a $1{\text{ cm}}^2$ grid. When the net is folded to make the solid, point $C$ will join with point $A$. Write down which other point will join with point $A$.

Calculate the total surface area of the solid.

Complete this statement. The solid is a .................... with the cross-section in the shape of a ....................................

Draw a sketch of the solid.

The diagram shows a cuboid. The volume of the cuboid is $540{\text{ cm}}^3$. Calculate the value of $x$.

Show that he has $\mathrm{\$}144000$ left after buying the restaurant.

Some of the $\mathrm{\$}144000$ is spent on expenses. Expenses are wages, equipment and supplies in the ratio $$\text{wages}:\text{equipment}:\text{supplies}=9:5:8.$$ The amount spent on wages is $\mathrm{\$}45000$. Find the amount spent on equipment

Some of the $\mathrm{\$}144000$ is spent on expenses. Expenses are wages, equipment and supplies in the ratio $$\text{wages}:\text{equipment}:\text{supplies}=9:5:8.$$ The amount spent on wages is $\mathrm{\$}45000$. Find the amount spent on supplies.

Work out the amount Antonio has left now.

Antonio borrows $\mathrm{\$}25400$ for 6 years at a rate of 5% per year simple interest. Calculate the total amount he repays at the end of the 6 years.

In one week, the number of customers in the restaurant was 560. In the next week, the number of customers in the restaurant was 656. Calculate the percentage increase.

Complete the table of values for $y=5+3x-x^2$.

On the grid, draw the graph of $y=5+3x-x^2$ for $-2⩽x⩽5$.

Write down the equation of the line of symmetry of the graph.

Complete the table of values for $y=2x+1$.

On the grid, draw the graph of $y=2x+1$ for $-2⩽x⩽5$.

Write down the coordinates of the two points where the two graphs intersect.

The diagram shows a circle, centre $O$, with points $B$, $D$ and $E$ on the circumference. $AOEF$ is a straight line. The straight line $AC$ touches the circle at $B$. Write down the mathematical name for line $BOD$

Write down the mathematical name for line $ABC$.

Write down the two geometrical reasons why angle $AOB$ is ${62}^{\circ }$.

Give the geometrical reason why angle $DOE$ is also ${62}^{\circ }$.

Find angle $DEB$.

Find angle $ODE$.

Find angle $BEF$.

Write down two geometrical properties that show that a polygon is regular.

Work out the interior angle of a regular 10-sided polygon.

Calculate Diego’s speed for his journey from his home to the swimming pool. Give your answer in kilometres per hour.

Diego stays at the swimming pool until 1220. On the grid, draw the line representing the time he stays at the swimming pool.

Work out how long, in hours and minutes, he is at the swimming pool.

Javier leaves his home 15 minutes later than Diego. He walks to the swimming pool at a constant speed of $6\text{ km/h}$. On the grid, show Javier’s journey from his home to the swimming pool.

They both leave the swimming pool at 1220 and return to their own homes, each at a constant speed. Diego arrives home at 1245. Javier arrives home 5 minutes later than Diego. Complete the travel graph.

Maria spins a fair 7-sided spinner numbered 1 to 7. Explain why the probability that the spinner lands on a prime number is $\frac{4}{7}$.

Maria spins the spinner a 2nd time. Complete the tree diagram.

Work out the probability that the spinner lands on a prime number both times.

Calculate the shaded area. Give the units of your answer.

Calculate $AB$.