Practice Paper 2 (Edexcel IGCSE Maths)

$ABCDEF$ is a triangular prism which represents part of a hill.

$ABCF$ is the horizontal rectangular base. $D$ is vertically above $C$.

Work out the height $CD$.

..........................m

Jamil walks in a straight line from $A$ to $D$.

Work out the size of angle $DAC$. You must show your working.

........................degrees

$s=ut+\frac{1}{2}at^{2}$

Find the value of $s$ when $u=5.2,t=7$ and $a=1.6.$

$s=$ ................................................

Write $\frac{5}{x-3}-\frac{4}{x+3}$ as a single fraction in its simplest form.

Simplify $e^{8}\div e^{2}$

Given that $x^{2 } - 6 x + 1 = ( x - a )^{2 } - b$ for all values of $x$.

(i) Find the value of $a$ and the value of $b$.

(ii) Hence write down the coordinates of the turning point of the graph of $y=x^{2}-6x+1$.

Multiply out and simplify $( x - 8 )^{2}$

Factorise $3e^{2}+5e$

Solve $\frac{5w-8}{3}=4w+2$

The lengths of the sides are in centimetres.

The area of triangle T₁ is equal to the area of triangle T₂.

Work out the value of $x$, giving your answer in the form $a+\sqrt{b}$ where $a$ and $b$ are integers.

$Q,R$ and $S$ are points on a grid.

$Q$ is the point with coordinates (106, 103) $R$ is the point with coordinates (106, 105) $S$ is the point with coordinates (104, 105.5)

$P$ and $A$ are two other points on the grid such that

$R$ is the midpoint of $PQ$
$S$ is the midpoint of $PA$

Work out the coordinates of the point $A$.

Complete the table of values for $y=x^{2}---2x---1$

On the grid, draw the graph of $y=x^{2}---2x---1$ for values of $x$ from $---2\mathrm{to}4$

Solve $x^{2}-2x-1=x+3$

The points $P$ and $Q$* *have coordinates $( - 1 , 6 )$ and $( 9 , 0 )$ respectively.

The line $l$ is perpendicular to $PQ$ and passes through the midpoint of $PQ.$

Find an equation for $l.$

At 9 am, Bradley began a journey on his bicycle.

From 9 am to 9.36 am, he cycled at an average speed of 15 km/h From 9.36 am to 10.45 am, he cycled a further 8 km.

Draw a travel graph to show Bradley's journey.

From 10.45 am to 11 am, Bradley cycled at an average speed of 18 km/h.

Work out the distance Bradley cycled from 10.45 am to 11 am.

In London, 1 litre of petrol costs 108.9p In New York, 1 US gallon of petrol costs $2.83

1 US gallon = 3.785 litres
£1 = $1.46

In which city is petrol better value for money, London or New York? You must show your working.

Use algebra to show that $4. \dot{5} \dot{7} = 4 \frac{19}{33}$

Show that $3\frac{1}{5}\times1\frac{5}{6}=5\frac{13}{15}$

Complete the list of factors of 36.

1, 2, ............................................. , 36

Circle the expression that has the largest value when $a<--1$

Sunil makes 7.5 litres of soup, correct to the nearest 0.5 litre. He serves the soup in 300 ml portions, correct to the nearest 10 ml. 24 people order this soup.

Does Sunil definitely have enough soup to serve the 24 people? Show how you decide.

The Venn diagram shows a universal set ξ and three sets A, B and C.

2, 4, 7, 3, 6 and 10 represent the number of elements in each set.

Find

n(A ∩ B)

n(B′)

n(A ∩ C′)

n(B′ ∩ C′)

Show that $\frac{12}{\sqrt{3}}$ can be rewritten as $4\sqrt{3}$

Show that $( \sqrt{2} + \sqrt{8} )^{2} = 18$

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

The diagram shows a wall.

The area of the wall is 39.2 m²

Work out the length of the wall.

..........................m

The diagram shows a shaded shape made from three identical semicircles, $X$, $Y$ and $Z$.

$ABCDE$ is a straight line.

$AC$is the diameter of semicircle $X$ and $B$ is the centre of semicircle $X$ $BD$ is the diameter of semicircle $Y$ and $C$ is the centre of semicircle $Y$ $CE$ is the diameter of semicircle $Z$ and $D$ is the centre of semicircle $Z$

$AC=BD=CE=20\mathrm{cm}$

Work out the perimeter of the shaded shape. Give your answer correct to the nearest whole number.

$A,B$ and $C$ are 3 service stations on a motorway.

$AB$ = 25 miles $BC$ = 25 miles

Aysha drives along the motorway from $A$ to $C$

Aysha drives at an average speed of 50 mph from $A$ to $B$. She drives at an average speed of 60 mph from $B$ to $C$.

Work out the difference in the time Aysha takes to drive from $A$ to $B$ and the time Aysha takes to drive from$B$ to $C$. Give your answer in minutes.

Students are asked to choose one subject from Option A and one subject from Option B.

If a student chooses their subjects at random, what is the probability that both subjects have the same first letter?