Graphs (Edexcel IGCSE Further Pure Maths): Exam Questions

The curve with equation

where and are integers, crosses the -axis at the point .

The asymptote to which is parallel to the -axis has equation

(i) Show that

(ii) Find the value of .

Find the coordinates of the point where crosses the -axis.

Find the equation of the asymptote to which is parallel to the -axis.

Using the axes below, sketch the curve showing clearly the asymptotes and the coordinates of the points where crosses the coordinate axes.

Figure 1 shows a sketch of part of the curve with equation

The point lies on and has coordinates

Show that

The curve has equation where and are integers and

One intersection of with the coordinate axes is at the point with coordinates

The asymptote parallel to the -axis has equation

Find the value of and the value of

Sketch , showing clearly the asymptotes with their equations and the coordinates of the points of intersection with the coordinate axes.

Figure 2 shows part of the curve with equation for

By drawing a suitable straight line on the grid, obtain estimates, to one decimal place, of the roots of the equation in the interval

Complete the table of values for giving your answers to 2 decimal places.

On the grid opposite, draw the graph of for

By drawing a suitable straight line on the grid, obtain an estimate, to one decimal place, of the root of the equation

in the interval

A curve has equation

Find the coordinates of the point where intersects the

(i) -axis

[1]

(ii) -axis

[1]

A curve has equation

Write down an equation of the asymptote to that is

(i) parallel to the -axis

[1]

(ii) parallel to the -axis

[1]

Sketch on the opposite page.
Show and label the asymptotes and the coordinates of the points where crosses the coordinate axes.

Figure 1 shows part of the curve with equation in the interval

By drawing a suitable straight line on the grid, obtain an estimate, to one decimal place, of the roots of the equation in the interval

The curve with equation where ≠ 4 , crosses the -axis at the point and the -axis at the point

Find the coordinates of

(i)

(ii)

The curve with equation where ≠ 4 , crosses the -axis at the point and the -axis at the point

Write down an equation of the asymptote to which is

(i) parallel to the -axis

(ii) parallel to the -axis

The curve with equation where ≠ 4 , crosses the -axis at the point and the -axis at the point

Sketch showing clearly the asymptotes and the coordinates of the points and

The line is the normal to at the point on where

Find an equation of

The line intersects again at the point

Find the coordinate of

Curve has equation where and is a constant.

The asymptote to that is parallel to the ‑axis has equation

Find the value of

Write down the equation of the asymptote to that is parallel to the ‑axis.

Find the coordinates of the point where crosses

(i) the ‑axis,

(ii)  the ‑axis.

Using the axes below, sketch , showing clearly the asymptotes and the coordinates of the points where crosses the coordinate axes.

On the grid opposite, draw the graph of for

By drawing a suitable straight line on the grid, obtain an estimate, to one decimal place, of the root of the equation

in the interval