# Further Mathematics F3

When studying pure mathematics at AS and A2 level you will be extending your knowledge of such topics as algebra and trigonometry as well as learning some brand new ideas such as calculus. While many of the ideas you will meet in pure mathematics are interesting in their own right, they also serve as an important foundation for other branches of mathematics, especially mechanics and statistics.

### Unit Content

1. Chapter 1 Hyperbolic Functions (F3) In this session, you will learn about Hyperbolic Functions, one of the 6 topics you need to be knowledgeable in to master the Unit F3 paper in Further Mathematics. ​After completing this session, you will be able to write down the definitions of the hyperbolic functions sinh $$x$$ and cosh $$x$$, and tanh $$x$$, sech $$x$$, cosech $$x$$, and coth $$x$$ in terms of sinh $$x$$ and cosh $$x$$, sketch the graphs of the six hyperbolic functions and know their properties, establish identities for hyperbolic functions, solve equations involving hyperbolic functions, using definitions or identities, understand and use inverse hyperbolic functions, as well as understand and use the logarithmic equivalents of the inverse hyperbolic functions.
0 Concepts, 0 Quizzes
2. Chapter 2 Further Coordinate Systems (F3) In this session, you will learn about Further Coordinate Systems, one of the 6 topics you need to be knowledgeable in to master the Unit F3 paper in Further Mathematics. After completing this session, you will be able to identify an ellipse or a hyperbola from its Cartesian or parametric equations, find tangents and normals to these curves, find the focus and directrix for an ellipse or a hyperbola, as well as solve simple loci questions.
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3. Chapter 3 Differentiation (F3) In this session, you will learn about Differentiation, one of the 6 topics you need to be knowledgeable in to master the Unit F3 paper in Further Mathematics. After completing this session, you will be able to find the derivatives of hyperbolic functions and expressions involving them and find the derivatives of inverse trigonometric and hyperbolic functions.
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4. Chapter 4 Integration (F3) In this session, you will learn about Integration, one of the 6 topics you need to be knowledgeable in to master the Unit F3 paper in Further Mathematics. After completing this session, you will be able to integrate hyperbolic functions, functions requiring trigonometric or hyperbolic substitutions, functions involving quadratic surds, inverse trigonometric and inverse hyperbolic functions, derive and use reduction formulae, as well as use integration to calculate the length of an arc of a curve, the area of a surface of revolution.
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5. Chapter 5 Vectors (F3) In this session, you will learn about Vectors, one of the 6 topics you need to be knowledgeable in to master the Unit F3 paper in Further Mathematics. ​After completing this session, you will be able to find the vector product $$a \times b$$ of two vectors $$a$$ and $$b$$, find the triple scalar product $$a.b \times c$$ of three vectors $$a, b$$ and $$c$$, interpret $$|a \times b|$$ as an area and $$a.b \times c$$ as a volume write the vector equation of a line in the form $$(r - a) \times b = 0$$, write the equation of a plane in the form $$r.n = p$$, or in the form $$r = a + sb + tc$$, as well as use vectors in problems involving points, lines and planes and use the equivalent Cartesian forms for the equations of lines and planes.
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6. Chapter 6 Further Matrix Algebra (F3) In this session, you will learn about Further Matrix Algebra, one of the 6 topics you need to be knowledgeable in to master the Unit F3 paper in Further Mathematics. After completing this session, you will be able to find transposes, determinants and inverses of 3 X 3 matrices, represent linear transformations by 2 X 2 and 3 X 3 matrices, find eigenvalues and eigenvectors of 2 X 2 and 3 X 3 matrices, as well as reduce symmetric matrices to diagonal form.
0 Concepts, 0 Quizzes

### Prerequisites and Requirements

Students who have achieved a grade of 'C' or higher in their IGCSE, GCSE, or any other equivalent 'O' Level Mathematics.

### What's Next?

Core Mathematics
C12
Edexcel International A Level Mathematics