OCR C3

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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 OCR and other exam boards past papers for you to try, essential to improving your grade.

It is like having your own personal tutor but at a fraction of the cost. You can pause, rewind, play again and again and learn at your own pace. Learn on the go or place a video in your favourites to view later.

This is a valuable resource that will work side by side with a text book and should help you to get the grade you want, whether you are at school, college or just studying on your own.

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Module Content

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

- Modulus Functions
- The modulus function
- Graph y=|f(x)|
- Graph y=f(|x|)
- 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
- Miscellaneous Exam Practice

Differentiation:
- The exponential function e^x
- The natural log function ln(x)

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

- Connected rates of change

Integration:
- (ax+b)^n types
- The exponential functions e^x, e^ax and e^(ax+b)
- Reciprocal Functions 1/x and 1/(ax+b)
- Integrals of the form f'(x)/f(x)
- Applications
- Volume of Revolution about the x axis
- Volume generated between two curves
- Volume of revolution about the y-axis
- Volume generated between curves

Numerical methods:
- Solution of Equations by
- Graphical methods
- Change of sign
- Iteration
- Numerical Integration
- Simpsons Rule