Practice Paper 1 (Cambridge International IGCSE Maths)

The diagram shows a solid prism $ABCDEFGH$.

The trapezium $ABCD$, in which $AD$ is parallel to $BC$, is a cross section of the prism.

The base $ADEH$ of the prism is a horizontal plane.

$ADEH$ and $BCFG$ are rectangles.

The midpoint of $BC$ is vertically above the midpoint of $AD$ so that $BA=CD$.

$AD=37\mathrm{cm}$ $GF=28\mathrm{cm}$ $DE=24\mathrm{cm}$

The perpendicular distance between edges $AD$ and $BC$ is 20 $\mathrm{cm}$.

Calculate the size of the angle between $AF$ and the plane $ADEH$. Give your answer correct to one decimal place.

Show that $\frac{1}{6x^{2}+7x-5}\div\frac{1}{4x^{2}-1}$ simplifies to $\frac{ax+b}{cx+d}$ where a, b, c and d are integers.

Simplify $a^{2}\div a^{6}$.

Expand and simplify.

$(y+3)(y-4)(2y-1)$

A small tree is initially 2 metres tall. Each year, the height of the tree increases by 20%.

The height, $H$ metres, of the tree at the end of $n$ years is given by the formula:

$H=A\times b^{n}$

(i) Write down the value of $A$and $b$.

(ii) Find the exact time it takes for the tree to reach a height of 5 metres.

Give your answer in the form $n=\mathrm{log}_{b}a$.

Ahmed sells different types of cake in his shop. The cost of each cake depends on its type and its size.

Every small cake costs $ x and every large cake costs \ ( 2 x + 1 )The total cost of 3 small lemon cakes and 2 large lemon cakes is \12.36.

Find the cost of a small lemon cake.

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

The cost of 18 small chocolate cakes is the same as the cost of 7 large chocolate cakes.

Find the cost of a small chocolate cake.

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

$g(x)=2x+3h(x)=2^{x}$

Find $x$ when $\mathrm{gg}(x)=7$.

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

Extract:

straight h left parenthesis x right parenthesis space equals space 2 to the power of x

Find $x$ when $h^{-1}(x)=5$.

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

Use the formula $s=ut+\frac{1}{2}at^{2}$.

Calculate $s$ when $u$ = 5, $t$ = 10 and $a$ = 3.

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

Solve the equation.

$3(x-4)+\frac{x+2}{5}=6$

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

$y$ is inversely proportional to $x^{3}$. When $x=2$, $y=0.5$.

Find $y$ in terms of $x$.

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

Use the quadratic formula to solve $9x^{2}-12x-23=0$. Give your answers correct to 2 decimal places.

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

Rearrange the formula to make $x$ the subject.

$k=\frac{2m-x}{x}$

Find the $n$th term of each sequence.

4, 8, 12, 16, 20, .........

11, 20, 35, 56, 83, ..........

Solve the simultaneous equations. You must show all your working.

$2x+3y=-12\,5x+2y=14$

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

A triangle has vertices $P,Q$ and $R$.

The coordinates of $P$ are (—3, —6) The coordinates of $Q$ are (1, 4) The coordinates of $R$ are (5, —2)

$M$ is the midpoint of $PQ$. $N$ is the midpoint of $QR$.

Prove that $MN$ is parallel to $PR$. You must show each stage of your working.

By shading the unwanted regions of the grid, find and label the region $R$ that satisfies the following inequalities

$y\leq52x+y\geq6y\geq x+1$

Line L is drawn on the grid below.

Find the equation for the straight line L.

Give your answer in the form $y=mx+c$

A curve with equation$y=f(x)$is translated so that the point at $(0,0)$ is mapped onto the point $(4,0)$.

(i) Find the translation vector.

(ii) Find the equation of the translated curve.

Sketch the graph of the function.

$y=\frac{1}{x}$

$2^{3x+1}=8^{2-x}$

Find the value of $x$

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