Practice Paper 2 (Cambridge International IGCSE Mathematics)

$4^{w}=\frac{1}{16}$

Find the value of $w$.

$w=$ ...............................

Expand and simplify.

$( x - 5 ) ( x - 7 )$

Write down the inequality shown on the number line.

Simplify $3c-5d-c+2d$

Cara has $n$ pencils. Alice has twice as many pencils as Cara. Leon has three more pencils than Alice. The three children have a total of 58 pencils.

Use this information to write down an equation and solve it to find the value of $n$.

$n$ = ...................................................

Rearrange $T = 5 ( p + 2 )$ to make $p$ the subject.

$p$ = ...................................................

These are the first four terms of a sequence.

Write down the next term.

Extract:

These are the first four terms of a sequence.

| 5 | 8 | 11 | 14 |

Find an expression, in terms of $n$, for the $n$th term.

Complete the table of values for $y=\frac{8}{x}$.

Extract:

| x | -5 | -4 | -3 | -2 | -1 | | 1 | 2 | 3 | 4 | 5 | | y | | -2 | -2.7 | -4 | -8 | | 8 | 4 | 2.7 | | |

On the grid, draw the graph of $y=\frac{8}{x}$for negative 5 less-than or slanted equal to x less-than or slanted equal to negative 1 and 1 less-than or slanted equal to x less-than or slanted equal to 5.

Find the equation of line $L$ in the form $y=mx+c$

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

Extract:

Find the equation of line L in the form y = m x + c y = ..................................................

On the grid, draw a line that is perpendicular to line $L$.

Simon went for a cycle ride. He left home at 2 pm.

The travel graph represents part of Simon's cycle ride.

At 3 pm Simon stopped for a rest.

How many minutes did he rest?

How far was Simon from home at 5 pm?

A model of a hall in the shape of a trapezium is made by joining together three equilateral triangles.

The perimeter of one of the triangles is 72 cm.

Work out the perimeter of the trapezium.

The trapezium model from part (a) is duplicated, with the copy being rotated and attached along the bottom of the original trapezium, making a regular polygon.

Give the name of this regular polygon.

Calculate the exterior angle, $x$, of the polygon in part (b).

Work out the interior angle, $y$,of the polygon in part (b).

The diagram shows an isosceles triangle and a straight line. Work out the value of $w$.

$w=$...............................[2]

In triangle $ABC$, $BC$ = 7.6cm and $AC$ = 6.2 cm.

Using a ruler and compasses only, construct triangle $ABC$. Leave in your construction arcs. The side $AB$ has been drawn for you.

The diagram shows a circle, centre $O$, with points $B$ and $D$ on the circumference. The line $AC$ touches the circle at $B$. $OB$ is parallel to $DC$ and angle $OAB=49^{\circ}$.

i) Write down the mathematical name of the line $OB$.

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

ii) Write down the reason why angle $ABO$ is $90^{\circ}$.

......................................................................................................................................................

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

iii) Find angle$AOB$.

$\mathrm{Angle}AOB=$ ................................................ [1]

iv) Write down the reason why angle $ADC$ = angle $AOB$.

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

v) Complete the statement using a mathematical word.

Triangle $AOB$ is ................................................................. to triangle $ADC$. [1]

$AB=5.4\mathrm{cm}$.

Calculate

via) $OB$,

$OB=$ ......................................... cm [2]

vib) $OA$,

$OA=$ ......................................... cm [2]

via) the area of triangle $OAB$.

.........................................cm² [2]

On each shape, draw all the lines of symmetry.

i)

ii)

Write down the name of a quadrilateral that has

• rotational symmetry of order 2

and

• exactly two lines of symmetry.

The diagram shows a quadrilateral on a 1 cm² grid.

Work out the area of this quadrilateral.

Give the units of your answer.

Henry buys a circular mirror for the room. The diameter of the mirror is 80 cm.

Calculate the circumference of the mirror.

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

Soraya designs two mathematically similar flags.

Calculate the height, $h$, of the larger flag.

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

These two cuboids have the same volume.

Find the value of $h$.

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

The diagram shows the path of a plane from airport $A$ to airport $B$.

i) Show that the distance between $A$and $B$ is 375km.

ii) The plane flies at an average speed of 450km/h. It leaves $A$ at 1445 and flies directly to $B$.

Work out the time the plane arrives at $B$.

Write these in order of size, starting with the smallest.

.

$...............<................<................<................\,smallest$

Find $\frac{1}{5}$ of $200.

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

Henry decorates a room.

Complete Henry’s shopping bill.

Write down a fraction that completes this calculation.

$\frac{13}{11}\times\frac{..............}{..............}=1$

Put one pair of brackets in each statement to make it correct.

$16\div8+4\times2=1$

$16\div8+4\times2=12$

A geography examination lasts for 1 hour 40 minutes. Hari is allowed 25% extra time for his geography examination.

Work out the total time Hari has for this examination. Give your answer in hours and minutes.

.............. h .............. min

Write 2020 in standard form.

Find the lowest common multiple (LCM) of 48 and 60.

Raoul makes a profit when he sells his watch for $36. The ratio of the price Raoul paid for the watch and the profit he makes is price paid : profit = 7 : 2.

Work out the profit that Raoul makes.

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

Work out the difference in temperature between -6 °C and 5 °C.

............................................. °C

The width, $w$ metres, of a room is 4.2 metres, correct to the nearest 10 centimetres.

Complete this statement about the value of $w$.

.............. less-than or slanted equal to w less than ..............