Practice Paper 2 (Cambridge International IGCSE Maths)

Simplify $x^{3}y^{4}\times x^{5}y^{3}$

Factorise completely.

$6d^{2}e-9e^{2}$

List all of the integers which satisfy all three of the following inequalities.

$x\leq7$

$2<x\leq8$

$4\leq x\leq8.5$

Simplify 5t+4t-2t

Make$x$the subject of this formula.

$2y=5x-7$

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

Here are the first four terms of a sequence.

32 27 22 17

i) Write down the next term.

ii) Write down the rule for continuing the sequence.

Simplify fully.

$\frac{2y^{2}}{6y}$

A cost to hire a minibus depends on the number of hours it is hired for, and the number of passengers. The cost is $h per hour plus $p per passenger.

i) When the minibus is hired for 3 hours with 10 passengers the cost is $61.

Complete the equation.

$3h+10p=$............................

ii) When the minibus is hired for 5 hours with 8 passengers the cost is $80.

Write this information as an equation.

iii) Solve your two simultaneous equations to find $h$ and $p$. You must show all your working.

$h=$................................................

$p=$................................................[4]

Find the co-ordinates of the point where the line $y=3x-8$ crosses the $y$-axis.

On the diagram, sketch the graph of $y=0.25x^{4}$ for $-2\leq x\leq2$.

i) Write down the mathematical name for an 8-sided polygon.

ii) Work out the size of an interior angle of a regular 24-sided polygon.

$ABC$is a straight line and $BCD$ is an isosceles triangle. Find the value of$x$.

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

The diagram shows the positions of two towns, $A$ and $B$. 1 centimetre on the diagram represents 10 kilometres.

i) Work out the actual distance between town $A$ and town $B$.

............................................ km [2]

ii) Town C is 85 km from town A on a bearing of 100°.

On the diagram, mark the position of town C.

$S$ and $T$ are points on the circumference of a circle, centre $O$. $PT$ is a tangent to the circle. $SOP$ is a straight line.

Angle $OPT=32^{\circ}$

Work out the size of the angle marked $x$.

i) Measure the size of angle $x$.

ii) Write down the mathematical name of this type of angle.

This investigation introduces and explores the properties and patterns of the sequence of hexagonal numbers.

Hexagonal numbers are numbers formed by summing equally spaced dots around hexagons that sit inside of each other, as shown below.

If $n$ is the position of the term in the sequence then $H_{n}$ is the $n$th hexagonal number.

The first hexagonal number is 1 and the second hexagonal number is 6.

Use information on the diagram to write down the third hexagonal number.

Extract:

Hexagonal numbers are numbers formed by summing equally spaced dots around hexagons that sit inside of each other, as shown below. If n is the position of the term in the sequence then H_n is the nth hexagonal number. The diagram shows hexagonal numbers from n=1 to n=6, showing black dots in hexagon patterns. The first hexagonal number is 1 and the second hexagonal number is 6.

By counting the total number of dots in the diagram for $n=4$, work out the value of the fourth hexagonal number, $H_{4}$.

Extract:

If n is the position of the term in the sequence then H_n is the nth hexagonal number.

The next hexagonal number after 66, not shown on the diagram, is 91.

Write down the value of $n$ for this term.

Find an estimate for the area of the shape drawn on this 1 cm² grid.

............................... cm²

The diagram shows a semicircle with diameter 9 cm.

Calculate the total perimeter of this semicircle.

......................................... cm

Explain why triangle $ABC$ is similar to triangle $PQR$.

A cylinder has a radius of 6 cm and a height of 17 cm.

Show that the volume of this cylinder is 1923 cm³, correct to 4 significant figures.

Kiran leaves home at 9.45 am. She drives 135 km to visit a friend. She arrives at her friend’s house at 11.15 am.

Work out her average speed in km/h.

........................................... km/h

i) Write 26% as a decimal.

ii) Write 0.48 as a fraction.

Write down

i) a fraction that is equivalent to $\frac{5}{9}$.

ii) the 7th odd positive number,

iii) a decimal number that is larger than $0.0467$ but smaller than $0.0468$.

Write down the fraction of the rectangle that is shaded. Give your answer in its simplest form.

Write down a fraction that is equivalent to $\frac{7}{12}.$

The cost of each visit to a car park is shown in the table.

i) Samarth arrives at 11 40 and leaves at 1530.

Find the cost of his visit.

$ ................................ [1]

ii) Radhika leaves the car park at 1750 and pays $8.50.

a) Work out the earliest time she could have arrived at the car park.

b) Work out the change she receives from a $20 note.

$ ............................... [1]

iii) Dhruv bought a weekly car park ticket for $26. That week, he visited the car park four times. These are the lengths of time he parked his car for.

$17\mathrm{minutes}6\frac{1}{2}\mathrm{hours}11\mathrm{hours}9\frac{1}{4}\mathrm{hours}$

Work out how much he saved by buying a weekly ticket.

$ .................................. [3]

Without using a calculator, work out $\frac{5}{6}\div1\frac{1}{3}$

You must show all your working and give your answer as a fraction in its simplest form.

Calculate $3 + 2 \times ( 8 - 6 )$

In 2019 the rent for a café was $7275. In 2020 the rent was $7566.

Calculate the percentage increase in the rent between 2019 and 2020.

Write 0.0000523 in standard form.

Find the lowest common multiple (LCM) of 8 and 14.

Asif and Ben share $2100 in the ratio Asif : Ben = 3 : 7.

Work out how much Asif receives.

$ .........................................

Write down the number that is 7 more than -38.

$T=\frac{49.2-9.59}{4.085\times2.35}$

By writing each number correct to 1 significant figure, work out an estimate for $T$. You must show all your working.

i) $E$= {2, 4, 8, 16, 32, 64}

$A$ = {square numbers}

$B$ = {cube numbers}

Use this information to complete the Venn diagram.

ii) On this Venn diagram, shade the region $P\cup Q$.

Trina invests $16000 at a rate of 5% per year compound interest.

Work out the value of her investment at the end of 4 years.

$.........................