Coordinate Geometry (Edexcel IGCSE Further Pure Maths): Exam Questions

Figure 1 shows the curve with equation

The point , with coordinate −2, lies on and line is the tangent to at the point .

The point lies on and the line is the tangent to at the point .

Given that and are parallel,

The normal to at meets at the point .

Find the exact length of the line .

The tangent and normal at and the tangent and normal at form a rectangle.

Find the exact area of this rectangle.

The line passes through the point with coordinates and the point with coordinates

The point with coordinates lies on such that

Find the value of and the value of

The line is perpendicular to and passes through the point

Show that an equation of is

The line crosses the -axis at the point

Find the exact length of

The point with coordinates lies on such that

area of triangle = 80 units²

Given that

find the value of and the value of

On the grid below, draw the line with equation

(i)

(ii)

The curve with equation where and the line with equation where intersect at the points and , as shown in Figure 2.

(i) Show that the coordinates of point are (0, 2)

(ii) Find the coordinates of the point

On the grid opposite draw the line with equation

(i)

(ii)

(iii)

Expand in ascending powers of up to and including the term in

Where appropriate express each coefficient as an exact fraction in its lowest terms.

Write down the range of values of for which your expression is valid.

Express in the form where and are rational numbers whose values should be stated.

Obtain a series expansion for in ascending powers of up to and including the term in

Hence, using algebraic integration, obtain an estimate of

Give your answer to 5 significant figures.

The point with coordinates and the point with coordinates where is a constant, lie on the straight line with equation where is a constant.

Find the value of and the value of

The line is perpendicular to and passes through the point , which lies on such that

Find an equation for in the form where , and are integers to be found.

On the axes opposite, draw the line with equation

(i)

(ii)

(iii)

The point has coordinates (–5, 3), the point has coordinates (4, 0) and the point has coordinates (–1, 5).

The line passes through and is perpendicular to .

Find an equation of .
Give your answer in the form where , and are integers.

The line passes through and is perpendicular to .

The point has coordinates (–5, 3), the point has coordinates (4, 0) and the point has coordinates (–1, 5).

Show that is not the perpendicular bisector of .