Practice Paper 2 (Cambridge International IGCSE Maths)

The diagram shows a pyramid with a square base ABCD.

The diagonals AC and BD intersect at *M. *

The vertex V is vertically above *M. *

AB = 11 cm and AV = 18.6 cm.

Calculate the angle that AV makes with the base.

Simplify.

$\frac{2x^{2}-x-1}{2x^{2}+x}$

Find the value of log _ 3 ( fourth sqrt of 1 / 9 ) )

i) Factorise $y^{2}+5y-84$.

ii)

The area of the rectangle is 84 cm².

Find the perimeter.

.......................................... cm [3]

$f(x)=3--2xg(x)=2x+3$

i) Find $f(--3)$.

ii) Find $\mathrm{gf}(--3)$.

Extract:

f(x) = 3 - 2x

Find $\mathrm{f}^{- 1} ( x )$.

$\mathrm{f}^{- 1} ( x ) = ....................$

$\frac{a}{b}=3c$

$\frac{b}{c}=2$

Work out the value of $a$ when $c=8$

Solve the equation

$\frac{y-3}{7}=\frac{2y+1}{5}$

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

$y$ is inversely proportional to the square root of $(x+1)$. When $x=8,y=2$.

Find $y$ when $x=99$.

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

Solve the equation $3x^{2}-2x-2=0$. Show all your working and give your answers correct to 2 decimal places.

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

$y=\sqrt{u^{2}x}$

Rearrange the formula to write $x$ in terms of $u$ and $y$.

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

The $n$ th term of a number sequence is $n^{2}+1$

Write down the first three terms of the sequence.

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

$\begin{gathered} y = 4 - x \\ x^{2} + 2 y^{2} & = 67 \end{gathered}$

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

A straight line goes through the points ($p,q$) and ($r,s$), where

• $p+2=r$
• $q+4=s.$

Find the gradient of the line.

Klaus buys $x$ silver balloons and $y$ gold balloons for a party.

He buys

• more gold balloons than silver balloons
• at least 15 silver balloons
• less than 50 gold balloons
• a total of no more than 70 balloons.

Write down four inequalities, in terms of $x$ and/or $y$, to show this information.

.................................................

.................................................

.................................................

.................................................

Extract:

Klaus buys x silver balloons and y gold balloons for a party.

He buys

• more gold balloons than silver balloons
• at least 15 silver balloons
• less than 50 gold balloons
• a total of no more than 70 balloons.

Write down four inequalities, in terms of x and/or y, to show this information.

On the grid, show the information from part (a) by drawing four straight lines and shading the unwanted regions.

A is the point (7, 2) and B is the point (−5, 8).

Find the equation of the line that is perpendicular to AB and that passes through the point (−1, 3).

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

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

The point $P(3,2)$ lies on the curve with equation $y=f(x).$

On the graph of $y=f(x)+a$, where $a$is a constant, the point $P$ is mapped to the point $(3,-5)$.

Determine the value of $a$.

On the graph of $y=f(x+b)$, where $b$is a constant, the point $P$ is mapped to the point $(-1,2)$.

Determine the value of $b$.

A different function, $\mathrm{g} ( x )$, is a cubic function of the form $\mathrm{g} ( x ) = a x^{3} + b x^{2} + c x + d$.

The graph of $y = \mathrm{g} ( x )$ is translated by the vector $( \begin{gathered} 5 \\ 0 \end{gathered} )$.

Write down the equation of the transformed graph in terms of $a,b,c,d$, and $x$.

The curve $C$ has equation $y = ( x - 3 )^{2} - 5$

Using the axes below, sketch the curve $C$. On your sketch show clearly

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

(ii) the coordinates of the turning point.

$\mathrm{f} ( x ) = ( x - 2 )^{3} - 5 x + 12$ for $-1\leq x\leq4.7$

On the diagram, sketch the graph of $y = \mathrm{f} ( x )$.

Write down the coordinates of the local maximum.

Extract:

f(x) = (x - 2)^3 - 5x + 12

The equation $( x - 2 )^{3} - 5 x + 12 = k$ has exactly 2 solutions.

Find the values of $k$.

$\mathrm{g} ( x ) = - ( x - 1 )^{2}$ for $-1\leq x\leq4.7$

On the diagram, sketch the graph of $y = \mathrm{g} ( x )$.

Extract:

f(x) = (x - 2)^3 - 5x + 12 for -1 ≤ x ≤ 4.7 g(x) = -(x - 1)^2 for -1 ≤ x ≤ 4.7

Solve $\mathrm{f} ( x ) = \mathrm{g} ( x )$.

In the diagram, AC and BD are straight lines.

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

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

$q$ = ...................................................

The diagram shows the positions of three towns, Acton ($A$), Barston ($B$) and Chorlton ($C$).

Barston is 8 km from Acton on a bearing of $037^{\circ}$. Chorlton is 9km from Barston on a bearing of $150^{\circ}$.

Find the bearing of Chorlton from Acton. Give your answer correct to 1 decimal place. You must show all your working.