Practice Paper Pure 2 (Edexcel International A Level Maths: Pure 2)

The trapezium rule is to be used to find an estimate for the integral

The table below shows values for x and f(x), rounded to three significant figures where appropriate.

Using the values in the table find 

(i)      an estimate for the integral using 2 strips,
(ii)     an estimate for the integral using 4 strips,
(iii)    an estimate for the integral using 8 strips.

Justify which of the estimates from part (a) will be the most accurate estimate for the integral.

The function   has  as a factor, and when  is divided by the remainder is 7. 

Show that and  must satisfy the simultaneous equations:  

Hence find and 

A curve has the equation .

Find expressions for and  .

Determine the coordinates of the local minimum of the curve.

A circle  has centre (-2, 3) and passes through the point (6, -3). 

Find an equation for the circle .

Find an equation for the tangent to the circle at P.

A training track for cyclists is in the shape of a circle made up of several lane

One lap of the inner lane is m, with each lane working outwards having a lap distance of m more than the lane immediately inside it.

During a training session, a cyclist is expected to complete one lap of each lane, starting with the inner lane, before moving onto the next one.

A cyclist trains until they have completed the first five lanes.
Find the total distance travelled by the cyclist.

There are 8 lanes in total on the training track.

Find the lap distance of the outside lane.

During a particular training session, a cyclist completes a lap of each lane but in addition, also completes a further 10 laps of the outside lane.
Find the total distance the cyclist travels during this training session.

The diagram below shows the graphs of  

Find the area of the shaded region, .

Show that

Solve the equation tan    for  .

A convergent geometric series has first term 64, and the sum to infinity of the series is 384.

Show that the common ratio, , of the series is .  

Find the difference between the ninth and tenth terms of the series, giving your answer correct to 3 significant figures.

Calculate the sum of the first eight terms in the series, giving your answer correct to 3 significant figures.

Given that the sum of the first  terms of the series is greater than 380, find the smallest possible value of .

Solve the equation

giving your answers correct to 3 significant figures.

Solve the equation

giving your answers in the form  , where and  are rational numbers to be found.