Practice Paper Pure 2 (Edexcel International AS Maths: Pure 1)

The first terms of a series are given by .

Show that this is an arithmetic series, and determine its first term and common difference.

Given that    ,

Show that 

Hence find the value of .

The trapezium rule is to be used to estimate the integral

By completing the table of values below, use the trapezium rule to estimate the integral given above. 

Show that  where  and  are constants to be found.

Given that  is a factor of , factorise  completely.

Hence show that the equation  has exactly 2 real roots.

June is to start training in order to run a marathon.
For the first week of training she will run a total of 3 miles.
Each subsequent week she’ll increase the total number of miles run by  miles.
June intends training for  weeks and will run a total distance of 570 miles during the training period.

Write down an expression in  for the number of miles June will run in the 10^th week of training.

Write down an equation in  and  for the total distance June will run during the training period.

Given that June runs twice as far in week 4 than in week 2, find the values of  and .

The points and lie on a circle.

Show that  

Deduce a geometrical property of the line segment AB.

Hence find the equation of the circle.

The second and fifth terms of a geometric series are 13.44 and 5.67 respectively.  The series has first term  and common ratio

By first determining the values of  and , calculate the sum to infinity of the series.

Calculate the difference between the sum to infinity of the series and the sum of the first 20 terms of the series. Give your answer accurate to 2 decimal places.

Find the -coordinates of the stationary points on the graph with equation

Find the nature of the stationary points found in part (a).

The diagram below shows a sketch of the curves with equations

  and

Find the x-coordinates of the points of intersection of the two graphs.

Use calculus to find the total shaded area enclosed by the two graphs.

The set of numbers S is defined as all positive integers greater than 5 and less than 10.

Prove by exhaustion that the square of all values in S differ from a multiple of 5 by 1.

Solve the equation  sintan   for  , giving your answers to 1 decimal place where appropriate.

Solve the equation  sin² cos for