Practice Paper 2 (Edexcel IGCSE Maths)

These graphs show four different proportionality relationships between $y$ and $x$.

Match each graph with a statement in the table below.

Toothpaste is sold in three different sizes of tube.

A 50 ml tube costs £ 1.09 A 75 ml tube costs £ 1.68 A 125 *ml *tube costs £ 2.69

Which tube of toothpaste is the best value for money? You must show all your working.

The people working for a company work in Team $A$ or in Team $B$.

number of people in Team $A$ : number of people in Team $B$ = 3 : 4

$\frac{4}{5}$ of Team $A$ work full time. 24% of Team $B$ work full time.

Work out what fraction of the people working for the company work full time. Give your fraction in its simplest form.

Without using a calculator, work out $1\frac{1}{7}\times2\frac{1}{10}$.

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

Renee buys 5 kg of sweets to sell. She pays £10 for the sweets.

Renee puts all the sweets into bags. She puts 250 g of sweets into each bag. She sells each bag of sweets for 65p.

Renee sells all the bags of sweets.

Work out her percentage profit.

A grain of salt weighs $6.48\times10^{-5}$kg on average.

A packet contains 0.35 kg of salt.

Use this information to calculate the number of grains of salt in the packet.

Explain why your answer to part (a) is unlikely to be the actual number of grains of salt in the packet.

Two numbers, $P$ and $Q$, are written as products of their prime factors

$P=2^{5}\times3^{2}\times5^{3}\times11$ $Q=2^{4}\times3\times5^{4}\times7$

i) Find the lowest common multiple (LCM) of $P$ and $Q$.

ii) The number $C$ is written as the product of its prime factors.

$C=2^{3}\times3\times5^{2}$

Work out $P\div C$ , leaving your answer as a product of powers of prime numbers.

i) Write 450 as a product of its prime factors.

ii) Find the highest common factor (HCF) of 270 and 450.

In a village

the number of houses and the number of flats are in the ratio 7 : 4 the number of flats and the number of bungalows are in the ratio 8 : 5

There are 50 bungalows in the village. How many houses are there in the village?

There are 1200 students at a school.

Kate is helping to organise a party. She is going to order pizza.

Kate takes a sample of 60 of the students at the school. She asks each student to tell her one type of pizza they want.

The table shows information about her results.

Work out how much ham pizza Kate should order. Write down any assumption you make and explain how this could affect your answer.

In a competition, a prize is won every 2014 seconds.

Work out an estimate for the number of prizes won in 24 hours. You must show your working.

ξ = {whole numbers}

A = {factors of 100}

B = {multiples of 5}

List the members of the set A ∩ B.

Calculate $\sqrt[3]{8.1^{2} - 1.3^{0.8} } .$

$y=p-2qx^{2}\,\,p=-10\,q=3\,x=-5$

Work out the value of $y$.

Show that $\frac{2x^{2}-3x-5}{x^{2}+6x+5}$ can be written in the form $\frac{ax+b}{cx+d}$ where $a,b,c$ and $d$ are integers.

Tick whether the following statement is true or false.

Give a reason for your answer.

When $n$ is a positive integer, the value of $2n$ is always a factor of the value of $20n$.

True $\text{square}$ False $\text{square}$

Simplify $a^{4}\times a^{5}$

Simplify $\frac{45e^{6}f^{8}}{5ef^{2}}$

Write down the value of $9^{\frac{1}{2}}$

Write $3x^{2}-12x+7$ in the form $a(x+b)^{2}+c$

The line $L$ is the line of symmetry of the curve with equation $y=3x^{2}-12x+7$

Using your answer to part (a) or otherwise, write down an equation of $L$.

Expand and simplify $( m + 9 ) ( m - 5 )$

Factorise fully $6y^{2}+15y$

Here is a right-angled triangle.

Four of these triangles are joined to enclose the square $ABCD$ as shown below.

Show that the area of the square $ABCD$is $x^{2}+y^{2}$

Solve $\frac{5x-3}{4}=2x+3$

Show clear algebraic working.

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

Make $t$ the subject of the formula $y=\frac{t}{3}-2a$

Solve the simultaneous equations

$3x+4y=5$

$2x-3y=9$

Solve.

$5x+1>x+13$

Alison is using the quadratic formula to solve a quadratic equation.

She substitutes values into the formula and correctly gets.

$x=\frac{-7\pm\sqrt{49-32}}{4}$

Work out the quadratic equation that Alison is solving.

Give your answer in the form $ax^{2}+bx+c=0$, where $a,b$ and $c$ are integers.

$A$ (0, 2) and $B$ (6, 5) are points on the straight line $ABCD$.

$AB=BC=CD$ Work out the coordinates of $D$.