Cubic, reciprocal and exponential graphs

Complete the table of values for y 2x³ 5x 3

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

By drawing a suitable straight line on your grid, find estimates to one decimal place, for the solutions of the equation 2x³ 5x 3 2 in the range 2 x 2

Part of the curve C with equation y x² x is drawn on the grid.

By drawing a suitable straight line on the grid, find estimates, to one decimal place, for the solutions of the equation

The equation of curve D is given by

Complete the table of values for y x³ x² 3x, giving your values to 2 decimal places where necessary.

x	2	1.5	1	0.5	0	0.5	1	1.5	2
y	2		3	1.63	0	1.13			6

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

Curve C and curve D intersect twice in the range 2 x 2

Write down the coordinates, to one decimal place, of these 2 points of intersection.

Work out the equation of the line that passes through these 2 points of intersection.

Give your answer in the form y = mx + c where the values of m and c are given to one decimal place.

Show your working clearly.

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Only use this grid if you need to redraw your curve.

The curve C has equation

Find, to one decimal place, the coordinates of the stationary point of C

Complete the table of values for y

Give your values of y to one decimal place where necessary.

On the grid opposite, plot the stationary point and plot the points from your completed table. Join these to form a smooth curve.

By drawing a suitable straight line on the grid, find estimates, to one decimal place, of the solutions to the equation

within the range 0 < x 5

Turn over for a spare grid if you need to redraw your curve.

Only use this grid if you need to redraw your curve.

Complete the table of values for y = x³ – 5x – 3

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

By drawing a suitable straight line on your grid, find estimates, to one decimal place, of the solutions to the equation

Turn over for a spare grid if you need to redraw your graph.

Only use this grid if you need to redraw your graph.

The equation of a curve C is y 1 where k is a constant. A minimum point on C occurs when x = –1.5

Show that the value of k is 12

Complete the table of values for y 1

Give your values of y to 2 decimal places.

On the grid opposite, plot the minimum point and the points from your completed table.

Join all the points to form a smooth curve.

By drawing a suitable straight line on the grid, find the range of values, to one decimal place, of x in 6 x 0 8., for which

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Only use this grid if you need to redraw your graph.

A particle P is moving along a straight line through the fixed point O

The speed, v m/s, of P at time t seconds is given by

Complete the table of values for v 2

Give your values of v to 2 decimal places.

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

Using your curve, find an estimate, to one decimal place, for the speed of P when t = 1.75

The acceleration of P at time t seconds where 1 t 5 is a m/s²

Find an expression for a in terms of t

Using your answer to part (d), find the value of t when P has its minimum speed in

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Only use this grid if you need to redraw your curve.

The equation of a curve is y = f (x) where f (x) = x³ − 10x² + 20

Complete the table of values for y = x³ − 10x² + 20

Give your values of y to one decimal place where necessary.

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

A curve C has equation y = g (x) where B = g (x) and = f (x)

The curve C has two turning points in −2 x 3

Using your graph, find the x coordinates of these two turning points on the curve C.

Referring to your graph, determine which of these two turning points is a maximum and which is a minimum.

You should explain your reasoning clearly.

Turn over for a spare grid if you need to redraw your curve.

Only use this grid if you need to redraw your curve.

f (x) = 4x³ – 13x – 6

Use the factor theorem to show that (2x + 1) is a factor of f (x).

Hence factorise f (x) fully.

The curve C has equation y = f (x)

Find the coordinates of the points of intersection of C with the x‑axis.

Find the coordinates, to 2 decimal places, of the turning points of C.

The table below gives the coordinates of three points on C.

On the grid opposite, draw the curve C for –2 x 2

Clearly label the coordinates of the turning points of C and the coordinates of the points of intersection with the x ‑axis and the y ‑axis.

Turn over for a spare grid if you need to redraw your curve.

Only use this grid if you need to redraw your curve.