IGCSE Mathematics 0580 Paper 21, May/June 2024

The diagram shows two sides of a parallelogram $ABCD$. Find the coordinates of point $D$.

Geetha has a box of toys. She picks a toy at random from the box. The probability that she picks a wooden toy is 0.6 .

The table shows some information about two sequences.

Find the greatest odd number that is a factor of 140 and a factor of 210.

Calculate.

The diagram shows 5 kites that are congruent to kite $ABCD$. Each kite is joined to the next kite along one edge. Angle $DAB={40}^{\circ }$ and $DCE$ is a straight line. Find the value of $x$.

The diagram shows a shape made from a triangle $JKL$ and a semicircle with diameter $JL$. $JKL$ is an isosceles right-angled triangle with $JK=JL=12.8\text{ cm}$.

These are the first five terms of a sequence. $$\begin{array}{ccccc}11& 18& 25& 32& 39\end{array}$$ Find an expression for the $n$th term of the sequence.

The value of a car is $\mathrm{\$}8000$. Each year the value of the car decreases exponentially by 25%. Calculate the value of this car after 3 years.

Amir invests $\mathrm{\$}1500$ in an account. The account pays compound interest at a rate of $r\mathrm{\%}$ per year. At the end of 8 years the value of his investment is $\mathrm{\$}1656.73$. Find the value of $r$.

Find the inequalities that define the unshaded region, R.

Solve the simultaneous equations. You must show all your working. $$\frac{3x}{2}+5y=5$$ $$4x-3y=46$$

The diagram shows a cyclic quadrilateral. Find the value of $p$.

The diagram shows a circle with radius $9\text{ cm}$. Calculate the area of the shaded major sector.

Write $0.1\dot{4}\dot{6}$ as a fraction in its simplest form. You must show all your working.

Calculate the area of triangle $ABC$.

The diagram shows the graph of $y=x^3+4x^2-2$ for $-3⩽x⩽1.5$. By drawing a suitable straight line, solve the equation $x^3+4x^2-2=2x$ for $-3⩽x⩽1.5$.

Factorise completely.

Solve the equation $8\sin x+6=1$ for $0^{\circ }⩽x⩽{360}^{\circ }$.

The diagram shows a cuboid. $HD=4\text{ cm}$, $EH=6.5\text{ cm}$ and $EF=9.1\text{ cm}$. Calculate the angle between $CE$ and the base $CDHG$.

Bag $A$ and bag $B$ each contain red counters and blue counters only. Stephan picks a counter at random from bag $A$ and Jen picks a counter at random from bag $B$. The probability that Stephan picks a red counter is 0.4 . The probability that Stephan and Jen both pick a red counter is 0.25 . Find the probability that Stephan and Jen both pick a blue counter.