Equations & Identities (Edexcel IGCSE Further Pure Maths): Exam Questions

where is a constant

Given that is a factor of

show that

Hence show algebraically that the curve has only one intersection with the -axis.

Given that can be expressed in the form where , and are positive constants

find the value of , the value of and the value of

Given that can be expressed in the form where , and are positive constants

Hence write down the maximum value of

The equation has roots and

Without solving the equation , form a quadratic equation, with integer coefficients, that has roots and

Show that

where and are constants

The equation has roots and where and are the roots of the equation

Using your answer to part (d), find in simplified exact form, the value of and the value of

Use the factor theorem to show that is a factor of

Use the factor theorem to show that is a factor of

Hence, or otherwise, find the exact roots of the equation

A geometric series has first term and common ratio
The third term of is 9 and the sum to infinity of is 192

Show that

A geometric series has first term and common ratio
The third term of is 9 and the sum to infinity of is 192

Given that is a rational number

write down the value of

A geometric series has first term and common ratio
The third term of is 9 and the sum to infinity of is 192

show that =144

The sum to terms of is

Using logarithms, find the least value of such that

Given that is a factor of

show that the curve with equation has only one intersection with the -axis.

where is an integer

The curve passes through the point with coordinates

Given that is a factor of

show that

where is an integer

The curve passes through the point with coordinates

Given that is a factor of

Hence, or otherwise, use algebra to solve the equation

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 intersects at the point .

Show that the coordinates of are (-2, 2).

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 .

Find the value of .
Give your answer in its simplest form.

where and are constants.

Given that is a factor of and that when is divided by the remainder is 8

(i) show that

(ii) find the value of

Hence, solve the equation

The region , shown shaded in Figure 2, is bounded by the curve with equation and the curve with equation

The two curves intersect at the point and at the point .

Find the coordinate of the point and the coordinate of the point .

The region is rotated through 360° about the ‑axis.

Use algebraic integration to find the volume, to 2 decimal places, of the solid generated.