# Further Mathematics F2

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 Inequalities (F2) In this session, you will learn about Inequalities, one of the 7 topics you need to be knowledgeable in to master the Unit F2 paper in Further Mathematics. After completing this session, you will be able to manipulate inequalities, determine the critical values of an inequality, as well as find solutions of algebraic inequalities.
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2. Chapter 2 Series (F2) In this session, you will learn about Series, one of the 7 topics you need to be knowledgeable in to master the Unit F2 paper in Further Mathematics. After completing this session, you will be able to sum simple finite series using the method of differences when the differences do not involve fractions, the differences involve fractions which as given, and use partial fractions to establish the difference. You will also be able to prove by using the method of difference for the following standard results from FP1: $$\displaystyle\sum_{r=0}^n r^0 = \displaystyle\sum_{r=1}^n 1= 1 + 1 + 1 … + 1 = n$$, $$\displaystyle\sum_{r=1}^n r = 1 + 2 + 3 … + n = \frac{n}{2}(n + 1)$$, $$\displaystyle\sum_{r=1}^n r^2 = 1^2 + 2^2 + 3^2 ... + n^2 = \frac{n}{6}(n+1)(2n+1)$$, and $$\displaystyle\sum_{r=1}^n r^3 = 1^3 + 2^3 + 3^3 ... + n^3 = \frac{n^2}{4}(n+1)^2$$.
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3. Chapter 3 Further Complex Numbers (F2) In this session, you will learn about Further Complex Numbers, one of the 7 topics you need to be knowledgeable in to master the Unit F2 paper in Further Mathematics. After completing this session, you will be able to write down a complex number, $$z$$, in modulus-argument form as either $$z=r(cos\theta+i sin\theta)$$ or $$z=re^{i\theta}$$, where $$r$$ is the modulus of $$z$$ and $$\theta$$ is the argument of $$z$$, and $$-\pi < \theta \leq \pi$$, apply the de Moivre's theorem to find trigonometric identities and to find the nth roots of a complex number, represent loci and regions in an Argand diagram, as well as apply transformations from the z-plane to the w-plane.
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4. Chapter 4 First Order Differential Equations (F2) In this session, you will learn about First Order Differential Equations, one of the 7 topics you need to be knowledgeable in to master the Unit F2 paper in Further Mathematics. After completing this session, you will be able to solve first order differential equations by separation of variables and sketch members of the family of solution curves, solve first order differential equations by the use of an integrating factor, as well as use a given substitution to transform a differential equations into one that can be solved.
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5. Chapter 5 Second Order Differential Equations (F2) In this session, you will learn about Second Order Differential Equations, one of the 7 topics you need to be knowledgeable in to master the Unit F2 paper in Further Mathematics. After completing this session, you will be able to find general solutions of linear second order differential equations of the form $$a \frac{d^2y}{dx^2} + b\frac{dy}{dx} + cy = f(x)$$, use boundary and initial conditions to find specific solutions, as well as use a given substitution to transform a second order differential equation into one that can be solved.
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6. Chapter 6 Maclaurin and Taylor Series (F2) In this session, you will learn about Maclaurin and Taylor Series, one of the 7 topics you need to be knowledgeable in to master the Unit F2 paper in Further Mathematics. After completing this session, you will be able to find and use higher derivatives, derive and use Maclaurin's series for simple functions, derive and use Taylor's series for simple functions, as well as use the Taylor series method to find a series solution to a differential equation.
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7. Chapter 7 Polar Coordinates (F2) In this session, you will learn about Polar Coordinates, one of the 7 topics you need to be knowledgeable in to master the Unit F2 paper in Further Mathematics. After completing this session, you will be able to convert between polar coordinates and Cartesian coordinates in simple cases, sketch simple curves given in polar coordinates, find tangents parallel or perpendicular to the initial line for polar curves, as well as find areas using polar coordinates.
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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