Exponential & Logarithms (Edexcel A Level Maths: Pure): Exam Questions

Sketch the curve with equation

stating any points of intersection with the coordinate axes.

Solve

giving your answer to 2 decimal places.

On the same set of coordinate axes, sketch the curves

and

Label clearly

• any points where the curves meet the coordinate axes

• the equation(s) of any asymptotes

Sketch the curve

State whether the graph shows exponential growth or exponential decay.

Find the exact value of when .

Solve the equation

Use algebra to solve

On the same set of coordinate axes, sketch the curves

and

Label clearly

• any points where the curves meet the coordinate axes

• the equation(s) of any asymptotes

Write down the gradient of the curve

at the point .

Given that

write down an expression for

Given that

write down an expression for

A curve has equation

Find the gradient of the point on the curve where .

Give your answer in the form

where  and  are integers to be found.

(i) Write down the gradient function of the curve

(ii) Find the gradient of the curve  at the point where

(i) write down the exact gradient of the point on the curve where

(ii) Find the -coordinate of the point on the curve  which has a gradient of

The function  is defined by

(i) Write down the function .

(ii) On the same set of coordinate axes, sketch the curves of  and .

Label any points where the graphs intersect the coordinate axes.

A different function is given by

State the single graph transformation that maps the curve to the curve .

Solve

giving your answer(s) to 3 significant figures.

On the same set of coordinate axes, sketch the curves

and

Label clearly

• any points where the curves meet the coordinate axes

• the equation(s) of any asymptotes

Write down an equation of the curve that is a reflection of in the -axis.

(i) Sketch the curve with equation

(ii) State whether the curve represents exponential growth or exponential decay.

Find the value of  when .

Find the value of

Solve

Find the value of

Sketch the curve with equation

stating any points of intersection with the coordinate axes.

Write down the equations of any asymptotes.

Find the gradient of the point on the curve where .

Solve

Solve

On the same set of coordinate axes, sketch the curves

and

Label clearly

• any points where the curves meet the coordinate axes

• the equation(s) of any asymptotes

Write down an equation of the curve that is a reflection of in the -axis.

Sketch the curve

State

• the equation of the asymptote

• whether the graph shows exponential growth or exponential decay.

Find the value of when .

Sketch the curve with equation

stating any points of intersection with the coordinate axes.

Write down the equations of any asymptotes.

Find the gradient of the point on the curve where .

Give your answer correct to 3 significant figures.

The growth of population, , at time t years is modelled by the equation

Write down the initial population.

A curve has equation

where and and  are non-zero constants.

At the point , the gradient of the curve is 12.

Find an expression for in terms of .

Hence write down the equation of the curve in terms of and only.

The function is defined by

where is a constant.

Deduce the value of .

Find the range of values of for which

Solve

giving your answer(s) to 3 significant figures.

Solve

Show that the equation

has only one real solution, which you should find.

Show that the equation

has no real solutions.

Without using a calculator, find the value of

Show the steps in your solution clearly.

Solve

Find two values of  for which

is true.

A curve has equation

where and are non-zero constants.

State a condition on to ensure the curve represents exponential decay.

At the point on the curve, the gradient is 10.

Use this information to find an expression for  in terms of and only.

A particle is travelling with velocity  ms^-1 at time  seconds.

The velocity of the particle is modelled by

where  is a constant.

Write down the initial velocity of the particle.

Find an expression in terms of and for the acceleration of the particle.

After 12 seconds, the velocity of the particle is 0.9 ms^-1.

Find the value of , giving your answer to 3 significant figures.

State a problem with the model for large values of .

Solve the equation

giving your answer(s) to 3 significant figures.