Practice Paper 1 (Edexcel IAL Maths)

A machine computes a calculation in time, $t$ seconds, that is proportional to the number of processes, $p$, involved. For a calculation involving 10 processes the machine takes 0.01 seconds.

Show that the constant of proportionality is 0.001.

Hence write down an equation linking the number of processes $( p )$ to the time taken $( t )$.

Find the time it takes for the machine to compute a calculation involving 200 processes.

How many processes are involved for a calculation taking 2.3 seconds?

Find the values of $x$ that satisfy the inequalities

$x^{2}+x<2$

$x^{2}<4$

A rectangle has an area of 14 m² and a length of $( 3 - \sqrt{2} )$ m. Find the width of the rectangle, showing clear algebraic working. Give your answer as an exact value.

Factorise

(i) $5x-20$

(ii) $2y^{2}-4y$

(iii) $8xy^{2}+6xy$

Sketch the graph of $y=12x^{2}-5x-72$, labelling any points where the graph crosses the coordinate axes. (You do not need to label the turning point.)

Solve the simultaneous equations

$2x+5y=3$ $6x-10y=34$

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

State the coordinates of the image of point $P$ on the curves with the following equations:

(i) $y-2=f(x)-6$

(ii) $y=f(x-3)$

(iii) $2y=f(x)$

(iv) $y=f(\frac{1}{2}x)$

An electrician charges a fixed fee of £45 plus £22 per hour.

Defining suitable variables, write down an equation to represent the charges made by the electrician.

A rival electrician charges a fixed fee of £36 and £25 per hour. Determine which electrician is cheapest for a job taking 4 hours?

Given that $y=2x^{3}-8\sqrt{x}$, find

$\frac{dy}{dx}$

$\frac{d^{2}y}{dx^{2}}$

Find the equation of the curve passing through the point (4, -8) and given by

$y = \int ( \frac{2}{ \sqrt{x} } - x - 3 ) d x$

A triangle ABC has side lengths AB = $2x$ cm, BC = $( x + 5 )$ cm and AC = 7 cm. The angle ABC = 60°

Find the value of $x$, giving your answer as a simplified surd.

The area of the triangle can be written in the form $a\sqrt{6}+b\sqrt{3}$, where $a$ and $b$ are integers. Find the values of a and $b$

The circle sector $OAB$ is shown in the diagram below.

The angle at the centre is $θ$ radians, and the radii $OA$and $OB$ are each equal to $r$cm.

Additionally,$CD$ is parallel to AB , so that $AD=BC$and $OD=OC$.

In the case when $AD=BC=1$cm, show that the area of the shaded shape $ABCD$ is given by $1 \frac{1}{2} \\theta r^{2} - 1 \frac{1}{2} ( r - 1 )^{2 } \sin \\theta$.

Show that for small values of $θ$, the area of $ABCD$ is approximately $1 \frac{1}{2} \\theta ( 2 r - 1 )$.