Practice Paper 2 (Cambridge International IGCSE Mathematics)

The diagram shows a solid pyramid $ABCDE$ with a horizontal base.

The base, $BCDE$ , of the pyramid is a square of side 10 $\mathrm{cm}$.

The vertex $A$ of the pyramid is vertically above the centre $O$ of the base so that $AB=AC=AD=AE$

The total surface area of the pyramid is 360 $\mathrm{cm}^{2}$

Work out the size of the angle between $AC$ and the base $BCDE$. Give your answer correct to 3 significant figures.

The body mass index, $B$ , for a person of mass $m$ kg and height $h$ metres is given by the formula

$B=\frac{m}{h^{2}}$

Usman has a mass of 50 kg.

He has a height of 1.57 m.

Work out Usman's body mass index.

Give your answer correct to one decimal place.

Extract:

The body mass index, B, for a person of mass m kg and height h metres is given by the formula B = m / h^2.

Tom's height is 1.80m. He wants his body mass index to be 21

Work out the mass that will give Tom a body mass index of 21.

Simplify $p^{2}\times p^{4}$.

Simplify $m^{15}\div m^{5}$.

Simplify $( k^{3} )^{5}$.

Factorise completely

$3x^{2}-12xy$

In this question, all measurements are in metres.

The diagram shows a right-angled triangle.

Show that $5x^{2}-12x-27=0.$

Extract:

5 x squared minus 12 x minus 27 equals 0.

Solve $5x^{2}-12x-27=0.$ Show all your working and give your answers correct to 2 decimal places.

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

Extract:

The diagram shows a right-angled triangle.

Show that 5 x squared minus 12 x minus 27 equals 0.

Solve 5 x squared minus 12 x minus 27 equals 0. Show all your working and give your answers correct to 2 decimal places. x equals......................... or x equals..........................

Calculate the perimeter of the triangle.

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

Extract:

The diagram shows a right-angled triangle. Show that 5 x squared minus 12 x minus 27 equals 0. Solve 5 x squared minus 12 x minus 27 equals 0. Show all your working and give your answers correct to 2 decimal places. x equals......................... or x equals..........................

Calculate the smallest angle of the triangle.

Solve $30+2x=3(3-4x)$.

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

$t$ is inversely proportional to the square of $(x+1)$. When $x=2$, $t=5$.

Write $t$ in terms of $x$.

$t$ = ...................................................

Extract:

t is inversely proportional to the square of (x + 1). When x = 2, t = 5.

When $t=1.8$, find the positive value of $x$.

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

The $n$th term of a sequence is $4n^{2}+n+3.$ Find the value of $n$ when the $n$th term is 498.

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

Rearrange the formula $5w--3y+7=0$ to make $w$ the subject.

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

$912172433$

Write down the next term in the sequence.

Find the $n^{\mathrm{th}}$ term of the sequence.

The graphs of $y = ( x - 1 )^{2}$ and $y=\frac{1}{2}x+1$ intersect at A and B. Find the length of AB.

AB = ................................................

$y=5x^{m}+px^{12}$ and $\frac{dy}{dx}=30x^{m-1}+6x^{11}$

Find the value of $m$ and the value of $p$.

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

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

The diagram shows the graph of a function.

By drawing a suitable tangent, find an estimate for the gradient of the function at the point P.

The coordinates of P are $(-3,8)$ and the coordinates of Q are $(9,-2)$.

Find the equation of the perpendicular bisector of PQ.

The coordinates of P are $(-3,8)$ and the coordinates of Q are $(9,-2)$.

Find the equation of the line parallel to PQ that passes through the point $(6,-1)$.

The curve $C$has equation $y=4(x-1)^{2}-a$ where $a>4$

Using the axes below, sketch the curve $C$. On your sketch show clearly, in terms of $a$,

i) the coordinates of any points of intersection of $C$ with the coordinate axes,

ii) the coordinates of the turning point.

The diagram shows the speed–time graph for the final 40 seconds of a car journey.

At the start of the 40 seconds the speed is $v$ m/s.

The total distance travelled during the 40 seconds is 1.24 kilometres.

Find the value of $v$.

$v=$................................................

Given that $x$ and $y$ are integers such that

$3<x<7\,4<y<9\,\mathrm{and}x+y=13$

find all the possible values of $x$.

On the grid below show, by shading, the region defined by the inequalities

$y \text{greater} - \text{than} or \text{slanted} \text{equal} to - 1 y \text{less} - \text{than} or \text{slanted} \text{equal} to 4 - x y \text{less} - \text{than} or \text{slanted} \text{equal} to 3 x - 1$

Mark this region with the letter R.

Calculate the size of one interior angle of a regular polygon with 40 sides.

In triangle ABC, BC = 7.6 cm 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.

K, L and M are points on the circle. KS is a tangent to the circle at K. KM is a diameter and triangle KLM is isosceles.

Find the value of $z$.

$z=$...............................................