Practice Paper 2 (Edexcel IGCSE Maths)

$n$ is a positive integer.

Prove algebraically that $2 n^{2} ( \frac{3}{n} + n ) + 6 n ( n^{2} - 1 )$ is a cube number.

Rana sells 192 cakes in the ratio small : medium : large = 7 : 6 : 11

The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake.

Her total profit is £532.48

Work out the profit for one small cake.

£.....................

Rearrange $y=\sqrt{w^{3}}$ to make $w$ the subject.

Circle your answer.

Here are the first five terms of an arithmetic sequence.

4 9 14 19 24

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

Here are the first five terms of a different sequence.

2 2 0 -4 -10

An expression for the $n$th term of this sequence is $3n---n^{2}$

Write down, in terms of $n$, an expression for the $n$th term of a sequence whose first five terms are

4 4 0 -8 -20

Prove algebraically that the straight line with equation $x-2y=10$ is a tangent to the circle with equation $x^{2}+y^{2}=20$

$m^{2}>9$

Circle the possible value of $m$.

A particle is moving along a straight line and passes a fixed point $O$.

The displacement of the particle, from point $O$, at time $t$ seconds is

$s=\frac{1}{3}t^{3}-\frac{5}{2}t^{2}+20t-15$

where $s$ is measured in metres. Initially how far is the particle from $O$?

Find, in terms of $t$, the velocity of the particle.

Find the time at which the particle’s velocity is at its minimum.

For how long is the particle decelerating?

The functions $f$ and $g$ are defined as

$\mathrm{f} ( x ) = 1 \frac{1}{2} x + 4 \mathrm{g} ( x ) = \frac{2 x}{x + 1}$

Work out $f(6)$

Work out $\mathrm{fg}(---3)$

$g(a)=-2$

Work out the value of $a$.

Express the inverse function $f^{-1}$ in the form $f^{-1}(x)$ = ...

The diagram shows two straight lines drawn on a grid.

Show, by shading on the grid, the region defined by all five of the inequalities

Label the region $R$.

For all values of $x$

$f(x)=\mathrm{sin}x\,g(x)=x+90$

On the grid, draw the graph of the composite function $y = \text{fg} ( x )$ for $0 ^{\circ} \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360 ^{\circ}$

$ABC$ and $EDC$ are straight lines. $AE$ and $BD$ are parallel. Angle $ABD=125^{\circ}$ Angle $BCD=30^{\circ}$

Work out the size of the angle marked $x$. Give reasons for your answer.

$ABCDE$ and $AFGHJ$ are regular pentagons.

$AEJ$ and $ABF$are straight lines.

$EJ=4AE$ The area of $ABCDE$ is $8\mathrm{cm}^{2}$

Calculate the area of the shaded region.

.............................$\mathrm{cm}^{2}$

The scale drawing shows the position of a hall and the position of a library.

A post box is $140\mathrm{metres}$ from the library on a bearing of $220^{\circ}$

Show the position of the post box on the scale drawing. Mark the position with a cross $(\times)$ and label it $P.$

Use your scale drawing to find

i) the real distance, in metres, of the hall from the post box,

ii) the bearing of the hall from the post box.

A, B, C and D are points on the circumference of a circle, centre O.

Angle CAD = 28° and CD = 6.4cm. BD is a diameter of the circle.

Calculate the area of the circle.

...................... cm²

The diagram shows two water towers in Kuwait.

The real height of tower $A$ is $187m$. The real height of tower $B$ is $147m$.

Ahmed makes a scale model of both towers.

The height of tower $A$ on the scale model is $90\mathrm{cm}$.

Work out the height of tower $B$ on the scale model. Give your answer correct to the nearest centimetre.

Here is a sector, $AOB$ , of a circle with centre $O$and angle $AOB$= $x^{\circ}$

The sector can form the curved surface of a cone by joining $OA$to $OB$ .

The height of the cone is $25\mathrm{cm}$. The volume of the cone is $1600\mathrm{cm}^{3}$

Work out the value of $x.$ Give your answer correct to the nearest whole number.

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

Toby invested £7500 for 2 years in a savings account. He was paid 4% per annum compound interest.

How much money did Toby have in his savings account at the end of 2 years?

$y$ is directly proportional to the square of $x$.

When $x=3,y=36$

Find the value of $y$ when $x=5$

Lily buys and sells microwaves.

She buys each one for £32 and sells it for £60. She also pays £7 for the delivery of each microwave she sells.

If she sells a microwave that is faulty then Lily must pay for its repair and redelivery.
This costs her another £25 for each faulty microwave.

Last month, 6 out of the 80 microwaves Lily sold were faulty.

This month she has orders for 133 microwaves.

Calculate her expected percentage profit on this month’s order. Showing your working in the boxes below may help you present your work.

............................%

Here are three lamps.

Lamp A flashes every 20 seconds. Lamp B flashes every 45 seconds. Lamp C flashes every 120 seconds.

The three lamps start flashing at the same time.

How many times in one hour will the three lamps flash at the same time?

Some people who work for a company are in the following age groups.

The ratio of the number in group A to the number in group B is 7 : 10. The ratio of the number in group B to the number in group C is 4 : 3.

i) Find the ratio of the number in group A to the number in group C. Give your answer in its simplest form.

....................... : ....................... [3]

ii) There are 45 people in group C.

Find the total number of people who work for the company.