Methods in Calculus (Edexcel A Level Further Maths: Core Pure)

Exam Questions

39 mins5 questions

4 marks

$f (x) = \frac{x + 2}{x^{2} + 9}$

(a)

Show that

$\int f (x) d x = A \ln (x^{2} + 9) + B \arctan (\frac{x}{3}) + c$

where

c

is an arbitrary constant and

A

and

B

are constants to be found.

How did you do?

3 marks

(b)

Hence show that the mean value of

f (x)

over the interval [0, 3] is

$\frac{1}{6} \ln 2 + \frac{1}{18} π$

How did you do?

2 marks

(c)

Use the answer to part (b) to find the mean value, over the interval [0, 3], of

$f (x) + \ln k$

where

k

is a positive constant, giving your answer in the form

p + \frac{1}{6} \ln q,

where

p

and

q

are constants and

q

is in terms of

k

How did you do?

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Methods in Calculus (Edexcel A Level Further Maths: Core Pure)

Exam Questions

1. Complex Numbers

1.1 Complex Numbers & Argand Diagrams

1.2 Exponential Form & de Moivre's Theorem

2. Matrices

2.1 Properties of Matrices

2.2 Transformations using Matrices

3. Further Algebra & Functions

3.1 Roots of Polynomials

3.2 Series

3.3 Maclaurin Series

4. Hyperbolic Functions

4.1 Hyperbolic Functions

5. Further Calculus

5.1 Volumes of Revolution

5.2 Methods in Calculus

6. Further Vectors

6.1 Vector Lines

6.2 Vector Planes

7. Polar Coordinates

7.1 Polar Coordinates

8. Differential Equations

8.1 First Order Differential Equations

8.2 Second Order Differential Equations

8.3 Simple Harmonic Motion

9. Proof

9.1 Proof by Induction