Cambridge IGCSE. 2025. Mathematics (0580). May/June - Paper 4 (42) · Calculator (Extended)
A quadrilateral has these properties
- the diagonals are the only lines of symmetry
- it has rotational symmetry of order 2.
Write down the mathematical name of this quadrilateral.
The diagram shows the net of a solid.
Write down the mathematical name of this solid.
Mass of box *A* : Mass of box *B* = 4 : 7
The mass of box *B* is 2.4 kg more than the mass of box *A*.
Calculate the mass of box *A* and the mass of box *B*.
box *A* = ...... kg, box *B* = ...... kg
*ABCD* is a trapezium.
Work out the area of the trapezium.
(answer in cm²)
Scott changes \$300 into pounds (£).
The exchange rate is £1 = \$1.20 .
Calculate the amount Scott receives.
(answer in pounds)
A solid wooden cone has base radius 4 cm and height 12 cm.
The density of the wood is 0.74 g/cm³.
Calculate the mass of the cone.
[Density = Mass ÷ Volume]
(answer in g) (Give non-exact answers correct to 3 significant figures.)
$y = mx + c$
Rearrange the formula to make *m* the subject.
$m = \ldots$
Calculate.
$\dfrac{2.1^2 - 1.9}{0.5}$
Solve the simultaneous equations.
You must show all your working.
$2w - 3y = 11$
$3w + y = 11$
$w = \ldots$, $y = \ldots$
A group of 12 adults and 9 children travel on a bus.
The cost of an adult ticket is \$*n*.
The cost of a child ticket is \$(*n* − 10).
The total cost of the tickets is \$277.50 .
Find the cost of one adult ticket.
(answer in dollars)
In a sale, the original price of a shirt is reduced by 15%.
The sale price of the shirt is \$23.63 .
Find the original price of the shirt.
(answer in dollars)
The length of a rectangle is 16 cm, correct to the nearest centimetre.
The width of the rectangle is 14 cm, correct to the nearest centimetre.
Calculate the lower bound of the perimeter of the rectangle.
(answer in cm)
Triangle *ABC* and triangle *PQR* are mathematically similar.
**(a)** Calculate the length of *PR*.
(answer in cm)
Triangle *ABC* and triangle *PQR* are mathematically similar.
**(b)** Triangle *ABC* and triangle *PQR* are the cross-sections of two prisms.
These prisms are mathematically similar.
The volume of the smaller prism is 1120 cm³.
Calculate the volume of the larger prism.
(answer in cm³)
Factorise.
$5x - 10 - ax + 2a$
The interior angle of a regular polygon is 172°.
Find the number of sides of this polygon.
On any day, the probability that the weather will be sunny is 0.7 .
**(a)** Find the probability that on any day the weather will not be sunny.
On any day, the probability that the weather will be sunny is 0.7 .
**(b)** When the weather is sunny, the probability that Rohit goes for a walk is 0.9 .
When the weather is not sunny, the probability that Rohit goes for a walk is 0.2 .
Find the probability that on any day Rohit goes for a walk.
**(a)** Alex invests \$400 at a rate of 2.3% per year simple interest.
Find the total amount Alex has at the end of 5 years.
(answer in dollars)
**(b)** Virat has \$100 to spend.
In February he spends \$*x* .
In March he spends 10% more than he spends in February.
In April he spends 10% more than he spends in March.
At the end of April, Virat has \$33.80 remaining.
Find the value of *x*.
