Practice Paper 1 (Cambridge International IGCSE Mathematics)

The diagram shows a pyramid.

$BCDE$is a square with sides of length 10 cm.

The other faces of the pyramid are equilateral triangles with sides of length 10 cm.

Calculate the volume of the pyramid.

Give your answer in the form $\frac{a}{b}\sqrt{2}\mathrm{cm}^{3}$ where $a$ and $b$ are integers to be found.

Extract:

The diagram shows a pyramid. [B C D E] is a square with sides of length 10 cm. The other faces of the pyramid are equilateral triangles with sides of length 10 cm.

Find the size of angle $DAB$.

$y=mx+c$*. *

Find the value of y when $m=-2$, $x=-7$ and* *$c=-3$.

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

Simplify $\frac{x^{2}-25}{x^{2}-17x+60}$.

Simplify completely $( (16 w ^ 8)/(y ^ 20) ) ^ - 3 / 4$

Factorise completely.

$2t^{2}-98m^{2}$

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

ii)

The area of the rectangle is 84 cm².

Find the perimeter.

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

$\mathrm{f} ( x ) = 2 x - 7$ The domain of $\mathrm{f} ( x )$ is $\{ - 2 , 0 , 5 \}$.

Find the range of $\mathrm{f} ( x )$.

$\{ ........................................... \}$

Solve.

$4 ( 5 - 3 x ) = 23$

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

A ball falls $d$ metres in $t$ seconds. $d$ is directly proportional to the square of $t$. The ball falls 44.1 m in 3 seconds.

Find a formula for $d$ in terms of $t$.

$d=$................................................

Extract:

A ball falls d metres in t seconds. d is directly proportional to the square of t. The ball falls 44.1 m in 3 seconds. Find a formula for d in terms of t.

Calculate the distance the ball falls in 2 seconds.

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

The diagram shows a trapezium.

All the measurements are in centimetres.

The area of the trapezium is 351 cm².

Show that $2x^{2}+x-351=0$

Extract:

2 x squared plus x minus 351 equals 0

Work out the value of $x$.

$m=\sqrt{\frac{k^{3}+1}{4}}$

Make *k *the subject of the formula.

0, 1, 1, 2, 3, 5, 8, 13, 21 , ...

This sequence is a Fibonacci sequence. After the first two terms, the rule to find the next term is “add the two previous terms”. For example, 5 + 8 = 13.

Use this rule to complete each of the following Fibonacci sequences.

$24........................\,\,1........................11\,\,........-1................1$

Solve the simultaneous equations

$\begin{gathered} 5 a + 2 c & = 10 \\ 2 a - 4 c & = 7 \end{gathered}$

Show clear algebraic working.

$a=$ .......................................................
$c=$ .......................................................

A rhombus $ABCD$ has a diagonal $AC$ where $A$ is the point $(-3,10)$ and C is the point $(4,-4).$

Calculate the length $AC.$

A curve has equation $y=x^{3}--6x^{2}+16$.

Find the coordinates of the two turning points.

(............ , ............) and (............ , ............)

Extract:

A curve has equation y = x cubed – 6 x squared + 16. Find the coordinates of the two turning points. (............ , ............) and (............ , ............)

Determine whether each of the turning points is a maximum or a minimum.

Give reasons for your answers.

Complete the table of values for $y=x^{2}-x-6$

On the grid, draw the graph of $y=x^{2}-x-6$ for values of $x$ from $-3$ to $3$

Use your graph to find estimates of the solutions to the equation $x^{2}-x-6=-2$