# C3 Worksheets – Core Advanced Mathematics

The C3 Worksheets have questions on the following topic areas: Algebraic Fractions, Domain & Range or Composite & Inverse Functions, Logarithms & Exponentials, Numerical Methods for Finding Roots, The Mod Function and Transformations, More Trigonometric Functions, More Trigonometric Identities and More Differentiation.

Although the C3 Worksheets are based on the C3 module as taught in the UK, it can be used anywhere. See below to find out what core maths content is in each question.

## C3 Worksheet 1

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## C3 Worksheet 2

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## C3 Worksheet 3

Available soon in 2014

The C3 Worksheets have 8 questions on the following topic areas, note that a working knowledge of the C1 and C2 syllabus is assumed:

1. Algebraic Fractions – perform operations with algebraic fractions. Simplify and use remainder theorem to divide them.
2. Domain & Range or Composite & Inverse Functions – find valid value intervals for the domain and range of a function. Apply a function to a function including at specific values and find inverses.
3. Logarithms & Exponentials – know what the graph of a number to the power of x looks like. Know what $e$ is and use the natural to invert the exponential function.
4. Numerical Methods for Finding Roots – understand that a function has a root on an interval where it changes from negative to positive. Rearrange equations and use iteration to approximate roots.
5. The Mod Function and Transformations – know what the mod function does and apply transformations. Solve equations involving mod functions.
6. More Trigonometric Functions – Know the sec, cosec and cotan functions and their graphs. Know the inverse functions of the standard trig functions and their graphs.
7. More Trigonometric Identities – derive identities involving the new trig functions. Know how to use double angle and composite angle formulae.
8. More Differentiation – know how to differentiate the new functions. Use the product, quotient and chain rule to differentiate various combinations of standard functions.

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