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.

Show that

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

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 .

The line intersects at the point .

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

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 .