Practice Paper Pure 1 (Edexcel International A Level Maths: Pure 3)

A curve has the equation .

Find .

Find the coordinates of the point on the curve where the gradient is 2.

Solve the inequality .

Write down the inequalities that define the region R shown in the diagram below.

On the same set of axes, sketch the graphs of and  in the interval , giving the coordinates of all points of intersection with the coordinate axes.

Two perpendicular lines and intersect at point (2, 5).

 crosses the x-axis at point (-3, 0).

Find an equation for the line .

crosses the x-axis at the point .
Find the area of the triangle .

Sketch the graph of  labelling any points where the graph intersects the coordinate axes.

The curve C has equation .  The point P lies on C.

Find an expression for .

Show that an equation of the normal to C at point P  is .

This normal cuts the x-axis at the point Q.

Find the length of PQ, giving your answer as an exact value.

The diagram below shows the sector of a circle .

Given that the area of triangle cm², find the area of the shaded segment. Give your answer correct to 3 significant figures.

Find the perimeter of the sector , giving your answer correct to 3 significant figures.

Write the quadratic function  in the form  where a, b and c are constants to be found.

Write down the maximum point on the graph of .

Sketch the graph of , clearly labelling the maximum point and any point where the graph intersects the coordinate axes.

The line passes through the points (4, 2) and (8, 5).

Find the equation of the line , giving your answer in the form
where , and are integers to be found.

Given that 

Sketch the graph of  , showing clearly the coordinates of the points where the curve crosses or touches the coordinate axes.

The functions  and  are defined by the equations

The graph of  touches the -axis at the point .  Find the value of , giving your answer as an exact value.

A function,, has second derivative given by

Given that , and find

Given that , find the value of a.

Simplify