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Edexcel C3

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Personalised Revision Tool for

Edexcel C3

Aims

This Revision Tool aims to make your revision smarter and more effective. It aims

to:-

Identify gaps in your understanding and knowledge.

Give a short summary & example for each sub-topic.

Provide hyperlinks to MyMaths lessons for most sub-topics.

Using the short tests

There are 2 mini-assessments for each sub-topic.

Use the first test to identify which topics you need to work on. If you get a good

mark you will not need to use the second test on this topic.

Use the second test to measure the level of improvement after remedial work has

been undertaken.

This PRT is not a substitute for, or an alternate to, doing past papers.

A programme of completing whole past papers is essential for success.

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Topic Sub-topic with link to examples MyMaths T1 A1 T2 A2

1 Algebra & Functions

1.1 Rationalising

expressions

Rationalising expressions

1.2

Transformations Functions and mappings

Transformation of functions.

The modulus function & inequalities

Sketching curves

1.3 Composite functions

Composite functions

1.4 Inverse functions

Inverse functions

Inverse trig functions

2 Trigonometry

2.1 The Reciprocal

Functions

The Reciprocal Functions

2.2 The Compound and

Double angle formulae

Compound angle formulae

Double angle formulae

2.3 The forms

rcos(x+/-y), rsin(x+/-y)

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

3 Exponentials & Logarithms

3.1 Definitions , equations

& graphs

Laws of logarithms

Definitions

Solving equations

Graphs

3.2 Modelling Modelling with exponential functions

4 Differentiation

4.1 The Chain Rule The chain rule

Rates of Change

Exponentials & logs

Trigonometric functions

4.2 The Product Ruke The Product Rule

4.3 The Quotient Rule The Quotient Rule

5 Numerical Methods

5.1 Numerical Methods Change of sign methods

Iterative Methods

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1.1 Rationising Expressions

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1.2 Functions and mappings

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Transformation of graphs

Example 1

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Example 2 Combined Transformations

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1.3 Composite functions

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1.4 Inverse functions

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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

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The modulus function and inequalities

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Curve Sketching

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2.1 The Reciprocal Functions

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2.2 The Compound & Double Angle Formulae

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

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Laws of Logarithms

3.1 Definitions, equations & graphs

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Definitions & Graphs

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3.2 Modelling with exponential functions

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4.1 The Chain Rule

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4.2 The Product Rules

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4.3 The Quotient Rule

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Exponentials & Logs

Further example

Trig Functions

Further example

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Change of Sign Methods

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

f(a) > 0

f(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

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.

5.1 Numerical Methods

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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.

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1.1 Rationalising expressions/solving equations 1

Question 1

Question 2

Question 3

Total / 10

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1.2 Transformations 1

Question 1

(5) Question 1 insert

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Question 2

Question 3

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1.3 Composite Functions 1

Question 1

Question 2

Total / 10

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1.4 Inverse Functions 1

Question 1

Question 2

Total / 10

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2.1 The Reciprocal Functions 1

Question 1

Question 2

Total / 10

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2.2 Compound & Double-angle formulae 1

Question 1

Question 2

Total / 10

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

Question 1

Question 2

Total / 12

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3.1 Log Equations & Graphs 1

Question 1

Question 2

Total / 10

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3.2 Modelling 1

Question 1

Question 2

Total / 14

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4.1 The Chain Rule 1

Question 1

Question 2

Question 3

Total / 15

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4.2 The Product Rule 1

Question 1

Question 2

Total / 10

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4.3 The Quotient Rule 1

Question 1

Question 2

Total / 10

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5.1 Numerical Methods 1

Question 1

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Question 2

Total / 10

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1.1 Rationalising expressions/solving equations 1 sol

Question 1

Question 2

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Question 3

Total / 10

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1.2 Transformations 1 Solutions

Question 1

(5) Question 1 insert

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Question 2

Question 3

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Total / 16

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1.3 Composite Functions 1 Solutions Question 1

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Question 2

Total / 10

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1.4 Inverse Functions 1 Solutions

Question 1

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Question 2

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Total / 10

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2.1 The Reciprocal Functions 1 Solutions Question 1

Question 2

Total / 10

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2.2 Compound & Double-angle formulae 1 Sols

Question 1

Question 2

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Total / 10

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

Question 1

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Question 2

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Total / 12

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3.1 Log Equations & Graphs 1 Solutions

Question 1

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Question 2

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Total / 10

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3.2 Modelling 1 Solutions

Question 1

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Question 2

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Total / 14

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4.1 The Chain Rule 1 Solutions

Question 1

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Question 2

Question 3

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Total / 15

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4.2 The Product Rule 1 Solutions

Question 1

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Question 2

Total / 10

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4.3 The Quotient Rule 1 Solutions

Question 1

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Question 2

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Total / 10

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5.1 Numerical Methods 1 Solutions

Question 1

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Question 2

Total / 10

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1.1 Rationalising expressions/solving equations 2

Question 1

(3)

(3)

Question 2

(4)

Total / 10

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1.2 Transformations 2

Question 1

Question 2

(7)

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(2)

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Question 3

Total / 15

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1.3 Composite Functions 2

Question 1

Question 2

(4)

Total / 10

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1.4 Inverse Functions 2

Question 1

Question 2

Total / 10

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2.1 The Reciprocal Functions 2

Question 1

Question 2

Question 3

Total / 12

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2.2 Compound & Double-angle formulae 2

Question 1

Question 2

(3)

Total / 10

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2.3 The forms rcos(x+/-y), rsin(x+/-y) 2

Question 1

Question 2

Total / 13

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3.1 Log Equations & Graphs 2

Question 1

Question 2

Question 3

Solve

(3)

Total / 10

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3.2 Modelling 2

Question 1

Question 2

Total / 14

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4.1 The Chain Rule 2

Question 1

Question 2

Question 3

(3)

Total / 15

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4.2 The Product Rule 2

Question 1

(4)

Question 2

(3)

Question 3

Total / 10

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4.3 The Quotient Rule 2

Question 1

Question 2

(2)

Total / 10

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5.1 Numerical Methods 2

Question 1

Total / 8

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1.1 Rationalising expressions/solving equations 2 sol

Question 1

(3)

(3)

Question 2

(4)

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Total / 10

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1.2 Transformations 2 Solutions

Question 1

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Question 2

(7)

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Question 3

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Total / 15

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1.3 Composite Functions 2 Solutions

Question 1

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Question 2

(4)

Total / 10

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1.4 Inverse Functions 2 Solutions

Question 1

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Question 2

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Total / 10

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2.1 The Reciprocal Functions 2 Solutions

Question 1

Question 2

Question 3

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Total / 12

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2.2 Compound & Double-angle formulae 2 Sols

Question 1

Question 2

(3)

Total / 10

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2.3 The forms rcos(x+/-y), rsin(x+/-y) 2 Solutions

Question 1

Question 2

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Total / 13

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3.1 Log Equations & Graphs 2 Solutions

Question 1

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Question 2

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Question 3

Solve

(3)

Total / 10

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3.2 Modelling 2 Solutions

Question 1

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Question 2

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4.1 The Chain Rule 2 Solutions

Question 1

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Question 2

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Question 3

(3)

Total / 15

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4.2 The Product Rule 2 Solutions

Question 1

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Question 2

(3)

Question 3

Total / 10

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4.3 The Quotient Rule 2 Solutions

Question 1

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Question 2

(2)

Total / 10

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5.1 Numerical Methods 2 Solutions

Question 1

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Total / 8