Set 2 (Edexcel A Level Maths: Pure): Exam Questions

In triangle ABC, and    Point P divides BC in the ratio 3:2.

i)

Write down vector in terms of a and b.

ii)

Find in terms of a and b.

Solve the equation

giving your answer correct to 3 significant figures.

In the expansion of , the coefficient of the  term is 19 440. Given that  is a positive integer find the value of .

Solve the equation .

Solve the equation .

Write    in the form   , where and  are integers to be found.

The diagram below shows the graph of , where is the function defined by

The points A and B are maximum and minimum points, respectively.

Find the difference between the -values of the coordinates of  and , giving your answer correct to 3 decimal places.

The diagram below shows the graphs of and .

The iterative formula

is to be used to find an estimate for a root, , of the function.

Write down an expression for .

Using an initial estimate, , show, by adding to the diagram above, which of the two points (S or T) the sequence of estimates will converge to. Hence deduce whether   is the -coordinate of point S or point T.

Find the estimates and , giving each to three decimal places.

Confirm that α = 4.146 correct to three decimal places.

. Given that  and : 

find the values of  and .

Factorise  completely.

A simple model for the acceleration of a rocket, , is given as

where  is the time in seconds after lift-off.   is a constant.

What does the constant  represent?

After 10 seconds, the acceleration is . Find the value of .

Find how long it takes for the acceleration of the rocket to reach 

By letting , use the identity for to derive an expression for in terms of tan .

Hence, or otherwise, solve the equation

On the same axes, sketch the graphs of   and    where

Label the points at which the graphs intersect the coordinate axes.

Solve the equation .

The diagram below shows a sketch of the curve defined by the parametric equations

(i)

Write down the equations of the two horizontal tangents to the curve.

(ii)

Write down the equations of the two vertical tangents to the curve.

The four tangents from part (a) create a rectangle around the curve as shown below.

Find the percentage of the area of the rectangle enclosed by the curve

(the shaded area on the diagram).

It is given

Write down the domain and range of the function f(x).

 Sketch the graph of  y = f(x), stating the coordinates of any intersections with the coordinate axes. (You do not need to give the coordinates of any turning points.)

The points A (2, -21) and B (-5, 3) are the two endpoints of the diameter AB of a circle. Find the equation of the circle in the form , where a, b, c and d are integers to be found.

A geometric series has first term 9, and the sum of the first three terms of the series is 19.  The common ratio of the series is .

Show that .

Find the two possible values of .

Given that the series converges, find the sum to infinity of the series.

Fully factorise .

Prove that, if n is odd, is odd and that if n is even,  is even.