Practice Paper 1 (Cambridge International IGCSE Maths)

Simplify.

$( y^{5} )^{3}$

Factorise.

$12y^{2}-9y$

Here is an inequality, in $x$, shown on a number line.

Write down the inequality.

Simplify $8a+3b-2a+b$

i) Navja weighs a parcel with mass $w$kg on her scales. She uses the masses shown to balance the scales.

Work out the value of $w$.

$w$ = ................................................. [3]

ii) Sometimes Navja uses an electronic weighing machine. The machine gives the mass, $p$ kg, of a parcel as 12.4kg, correct to the nearest 100g.

Complete this statement about the value of $p$.

.................. less-than or slanted equal to p less than ................... [2]

Make $y$ the subject of the formula $h^{2}=x^{2}+2y^{2}$.

$y=$ .................................................

Gabriela designs the seating layout for a new theatre. There are three sections of seats, A, B and C.

Section A has 152 seats.

In Section A:

• There are 12 seats in the front row.
• Each row has 2 more seats than the row in front of it.

Work out the number of rows for the 152 seats in Section A.

......................................... rows [2]

Simplify fully.

$\frac{a^{3}b}{ab^{2}}$

A shop sells pens and notebooks. The cost of a pen is $p$ cents and the cost of a notebook is $n$ cents.

On Monday, the shop sells 5 pens and 4 notebooks for 450 cents.

Complete the equation.

$5p+4n=$..................

On Tuesday, the shop sells 10 pens and 3 notebooks for 525 cents.

Write this information as an equation.

................................................ = .........................

Extract:

A shop sells pens and notebooks. The cost of a pen is p cents and the cost of a notebook is n cents. On Monday, the shop sells 5 pens and 4 notebooks for 450 cents. On Tuesday, the shop sells 10 pens and 3 notebooks for 525 cents.

Solve your two equations to find the cost of a pen and the cost of a notebook.

You must show all your working.

Cost of a pen = ...................................... cents Cost of a notebook = ...................................... cents

A is the point (2, 1) and B is the point (9, 4).

Find the length of AB.

On the diagram, sketch the graph of $y=x^{3}$ for $-2\leq x\leq2$

On the same diagram as part (a), sketch the graph of $y=2-x$ for $-2\leq x\leq2$

Find the coordinates of the point of intersection of $y=x^{3}$ and $y=2-x$.

Extract:

Find the coordinates of the point of intersection of y = x^3 and y = 2 - x.

Solve the equation

$x^{3}=2-x$

The diagram shows two parallel lines and a straight line crossing them.

Write down, using letters from $a$ to $g$,

the angle that is alternate to angle $X$,

Extract:

The diagram shows two parallel lines and a straight line crossing them. Write down, using letters from a to g, the angle that is alternate to angle X.

the angle that is corresponding to angle $X$.

The diagram shows an isosceles triangle.

Find the value of $x$.

$x$= .................................................

The diagram shows a map of Kingswood Park. There are two straight paths and one circular path. The scale is 1cm represents 200m.

Measure the bearing of South Gate from North Gate.

$P$ and $Q$ are points on the circle, centre $O$. $APB$ is a tangent to the circle at $P$.

i) Write down the mathematical name for the line $PQ$.

ii) Explain why angle $OPB$ is 90°.

iii) Find the value of $x$.

$x$ = ................................................. [3]

Three quadrilaterals are shown on a 1 cm² grid.

Write down the mathematical name of the shaded quadrilateral.

The hexagonal numbers are shown above.

The first six triangular numbers are shown below.

Show that the first three hexagonal numbers are all triangular numbers.

Explain whether or not the fourth hexagonal number is also a triangular number.

Extract:

The hexagonal numbers are shown above. The first six triangular numbers are shown below.

Is it true that all triangular numbers are hexagonal numbers?

Explain your answer.

Extract:

Is it true that all triangular numbers are hexagonal numbers?

Explain your answer.

Based on the results above, which triangular number out of $T_{150}$ or $T_{151}$ is more likely to be a hexagonal number?

Give a reason for your answer.

Calculate the area of the trapezium.

......................................... cm²

Points $P,Q$ and $R$ are on the circumference of a semicircle, centre $O$ and radius 8 cm. Angle $POQ$ = 90°.

Calculate the shaded area.

.........................................cm²

Pick the word that describes two polygons that are the same shape and size.

A plant pot is a cylinder with radius 15 cm and height 24 cm.

Calculate the volume of the pot.

.......................................... cm³