1.1 Functions and mappings

Transformation of graphs

Example 1

Example 2 Combined Transformations

1.2 Composite functions

1.3 Inverse functions

The inverse trig functions

The inverse trig functions only exist when we restrict the domain of the original functions. So that they become 1:1 mappings

1.4 The modulus function and inequalities

Curve Sketching

Laws of Logarithms

2.1 Definitions, equations & graphs

Definitions & Graphs

2.2 Modelling with exponential functions

3.1 The Reciprocal Functions

3.2 The Compound & Double Angle Formulae

Double Angle Formula

3.3 The forms r cos(x +/- y), r sin(x +/- y)

4.1 The Chain Rule

4.2 The Product Rules

4.3 The Quotient Rules

Inverse Functions

Exponentials & Logs

Further example

Further example

5.1 Integration by substitution

Integration by inspection

Integration of Exponentials & Logarithms

5.2 Volumes of revolution

Change of Sign Methods

To find the root of a function f(x), if

f(a) > 0f(b) < 0

and the function is continuous, then there is a root between a and b.

We can narrow this down by successively halving the size of the interval, until we get an answer to the required accuracy.

Example

6.1 Numerical Methods

We can continue this method indefinitely, to whatever accuracy we require

This method is useful for confirming the existence of a root between two given values. It can be unreliable however, sometimes failing to find a

root(s) when they are very close together, or ‘finding’ a root that doesn’t exist.

Iterative Methods

(there are many other re-arrangements you could have done)

Then start at any value (it will be given in the question; here we use x=0, and show 3 iterations)

This method continues until it converges on the solution x = 0.276 (to 3 dp)

Iterative methods will often fail to find the root for given re-arrangements. If this is the case, you must try a different re-arrangement.

In this example, yn = y8

1.1 Transformations 1 Question 1

6.2 Numerical Integration

(5)Question 1 insert

Question 2

Total / 10 �1.2 Composite Functions 1

Question 1

Question 2

Total / 10 �1.3 Inverse Functions 1

Question 1

Question 2

Total / 10 �

1.4 Modulus function & inequalities 1

Question 1

Question 2

Total / 10 �2.1 Log Equations & Graphs 1

Question 1

Question 2

Total / 10 �2.2 Modelling 1

Question 1

Question 2

Total / 14 �3.1 The Reciprocal Functions 1

Question 1

Question 2

Total / 10 �

3.2 Compound & Double-angle formulae 1

Question 1

Question 2

Total / 10 �

3.3 The forms rcos(x+/-y), rsin(x+/-y) 1

Question 1

Question 2

Total / 12 �4.1 The Chain Rule 1

Question 1

Question 2

Question 3

Total / 15 �4.2 The Product Rule 1

Question 1

Question 2

Total / 10 �4.3 The Quotient Rule 1 Question 1

(3)

Question 2

Total / 10 �5.1 Integration by Substitution 1

Question 1

Question 2

Total / 11 �5.2 Volumes of revolution 1 Question 1

Question 2

Total / 10 �6.1 Numerical Methods 1

Question 1

Question 2

Total / 10 �6.2 Numerical Integration 1 Question 1

Question 2

Total / 8 �

1.1 Transformations 1 Solutions Question 1

(5)Question 1 insert

Question 2

Total / 10 �1.2 Composite Functions 1 Solutions

Question 1

Question 2

Total / 10 �

1.3 Inverse Functions 1 Solutions Question 1

Question 2

Total / 10 �

1.4 Modulus function & inequalities 1 Solutions

Question 1

Question 2

Total / 10 �2.1 Log Equations & Graphs 1 Solutions Question 1

Question 2

Total / 10 �2.2 Modelling 1 Solutions Question 1

Question 2

Total / 14 �3.1 The Reciprocal Functions 1 Solutions Question 1

Question 2

Total / 10 �3.2 Compound & Double-angle formulae 1 Sols Question 1

Question 2

Total / 10 �3.3 The forms rcos(x+/-y), rsin(x+/-y) 1 Solutions Question 1

Question 2

Total / 12 �

4.1 The Chain Rule 1 Solutions Question 1

Question 2

Question 3

Total / 15 �

4.2 The Product Rule 1 Solutions

Question 1

Question 2

Total / 10 �4.3 The Quotient Rule 1 Solutions Question 1

(3)

Question 2

Total / 10 �

5.1 Integration by Substitution 1 Solutions

Question 1

Question 2

= 3.5 + 4ln2

Total / 11 �5.2 Volumes of revolution 1 SolutionsQuestion 1

Question 2

Total / 10 �

6.1 Numerical Methods 1 Solutions Question 1

Question 2

Total / 10 �6.2 Numerical Integration 1 Solutions Question 1

Question 2

Total / 8