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Each app in this series covers the essential topics for the module, presenting them in short video tutorials and explained in a clear mathematical style so as you can progress quickly and smoothly through the topics. There are further supplementary exercises and worked solutions from past papers for you to try, essential to improving your grade.

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Module Content

Algebra and Series:

- Rational expressions
- Simplifying
- Exam Questions
- Addition and subtraction
- Exam Questions

- Functions
- Notation
- f(x) notation
- Domain and Range
- Combining Functions
- Inverse Functions
- Finding an inverse
- Graphical relationships
- between f(x) and its inverse
- Exam Questions

- Transformations of Graphs (Revision of C1 work)
- Basic graphs used in transformations
- Translations
- y = f(x ± a) and y = f(x) ± a
- Why does the transformation do this?
- translation parallel to the x-axis
- translation parallel to the y-axis
- Reflections
- y = - f(x) and y = f(-x)
- Why does the transformation do this?
- Stretches
- y = af(x)
- Why does the transformation do this?
- y = f(ax)
- Why does the transformation do this?
- Exam Questions on transformations
- Exam questions from C1 papers

- Modulus Functions
- The modulus function
- Graph y=|f(x)|
- Graph y=f(|x|)
- Exam Questions
- Modulus Equations
- Modulus Inequalities

- The Exponential Function e^x
- What is it?
- Sketching graphs (reflections)
- Sketching graphs (translations)
- Sketching graphs (stretches)

- The Natural Log Function ln x

Trigonometry:
- Secant, Cosecant and Cotangent
- graphs
- Inverse trig. functions
- arcsin x
- arccos x
- arctan x

- Identities
- Pythagorean type
- Introduction and Proof
- Examples

- Addition type
- sin(A±B), cos(A±B), tan(A±B)
- Using the formulae to get exact values
- Proving identities

- Double angles
- sin2A, cos2A, tan2A
- Half angles
- Applications - Triple angles
- cos 3θ
- sin 3θ

- Factor Formulae
- A cos x ± B sin x type

- Solving Equations using
- the Pythagorean identities
- the double angle identities
- the A cos x ± B sin x identities
- Exam Questions
- Miscellaneous Exam Practice
- Exam Questions

Differentiation:
- Using the Formula Book
- e^x, ln x, sin x, cos x, tan x

- The Chain Rule
- polynomial to a rational power types
- exponential types
- natural log types
- trigonometric types

- The Product Rule

- The Quotient Rule

- A Special Result
- Using the result dy/dx = 1 ÷ dx/dy

- Exam questions on Methods
- Exam questions - tangents, normals, stationary points
- Exam questions on Exponential Rates of change

Numerical methods:
- Solution of Equations by
- Graphical methods
- Change of sign
- Iteration
- The method
- How it works
- Exam Questions