# Further Mathematics F1

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 Complex Numbers (F1) In this session, you will learn about Complex Numbers, one of the 8 topics you need to be knowledgeable in to master the Unit F1 paper in Further Mathematics. After completing this session, you will be able to add, subtract, multiply, and divide complex numbers, find the modulus and argument of a complex number, show complex numbers on an Argand diagram, as well as solve equations that have complex roots.
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2. Chapter 2 Roots of Quadratic Equations (F1) In this session, you will learn about Roots of Quadratic Equations, one of the 8 topics you need to be knowledgeable in to master the Unit F1 paper in Further Mathematics. After completing this session, you will be able to understand the sum of roots and product of roots of a quadratic equation, manipulate expressions involving the sum of roots and product of roots, as well as form quadratic equations with new roots.
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3. Chapter 3 Numerical Solution of Equations (F1) In this session, you will learn about Numerical Solution of Equations, one of the 8 topics you need to be knowledgeable in to master the Unit F1 paper in Further Mathematics. After completing this session, you will be able to find approximations to the solutions of equations of the form $$f(x) = 0$$ using interval bisection, linear interpolation, and the Newton-Raphson process.
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4. Chapter 4 Coordinate Systems (F1) In this session, you will learn about Coordinate Systems, one of the 8 topics you need to be knowledgeable in to master the Unit F1 paper in Further Mathematics. After completing this session, you will be able to plot and sketch a curve expressed parametrically, work with the Cartesian equation and parametric equations of a parabola and a rectangular hyperbola, understand the focus-directrix property of a parabola, and find the equation of the tangent and the equation of a normal to a point on a parabola and on a rectangular hyperbola.
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5. Chapter 5 Matrix Algebra (F1) In this session, you will learn about Matrix Algebra, one of the 8 topics you need to be knowledgeable in to master the Unit F1 paper in Further Mathematics. After completing this session, you will be able to add, subtract and multiply matrices, find inverses of 2 X 2 matrices, represent some geometrical transformations with 2 X 2 matrices, as well as use matrices to solve linear simultaneous equations.
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6. Chapter 6 Transformations Using Matrices (F1) In this session, you will learn about Transformations Using Matrices, one of the 8 topics you need to be knowledgeable in to master the Unit F1 paper in Further Mathematics. After completing this session, you will use linear transformations of column vectors in two dimensions and their matrix representation, the application of 2 X 2 matrices to represent geometrical transformations, understand the combinations of transformations, as well as use the inverse (if it exists) of a given transformations or combinations of transformations.
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7. Chapter 7 Series (F1) In this session, you will learn about Series, one of the 8 topics you need to be knowledgeable in to master the Unit F1 paper in Further Mathematics. After completing this session, you will be able to use the result for the sum of the first $$n$$ natural numbers, $$\displaystyle\sum_{r=1}^{n} r$$, use the results for the sum of the squares, and the sum of the cubes, of the first $$n$$ natural numbers $$\displaystyle\sum_{r=1}^n r^2$$ and $$\displaystyle\sum_{r+1}^n r^3$$ respectively, use the results for $$\displaystyle\sum_{r+1}^n 1, \displaystyle\sum_{r=1}^n r, \displaystyle\sum_{r=1}^n r^2$$ and $$\displaystyle\sum_{r=1}^n r^3$$ to sum series where the general term is a polynomial in $$r$$ of degree at most 3, e.g. $$\displaystyle\sum_{r+1}^n (2r^3 + r^2 – 3r + 6)$$, as well as become more familiar with the $$\sum$$ notation and know the result $$\displaystyle\sum_{r=1}^n 1 = n$$.
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8. Chapter 8 Proof (F1) In this session, you will learn about Mathematical Proof, one of the 8 topics you need to be knowledgeable in to master the Unit F1 paper in Further Mathematics. After completing this session, you will be able to use the method of mathematical induction to prove general statements which involve positive integers.
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### 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