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### What I will learn?

• Use the relations between the roots and coefficients of polynomial equations e.g. to evaluate symmetric functions of the roots or to solve problems involving unknown coefficients in equations; restricted to equations of degree 2, 3 or 4 only.
• Use a substitution to obtain an equation whose roots are related in a simple way to those of the original equation
• Sketch graphs of simple rational functions, including the determination of oblique asymptotes, in cases where the degree of the numerator and the denominator are at most 2.
• Use the standard results for to find related sums and use the method of differences to obtain the sum of a finite series.
• Carry out operations of matrix addition, subtraction and multiplication, and recognise the terms zero matrix and identity (or unit) matrix.
• Understand the use of 2 X 2 matrices to represent certain geometric transformations in the x-y plane.
• Understand the meaning of ‘invariant’ as applied to points and lines in the context of transformations represented by matrices, and solve simple problems involving invariant points and invariant lines.
• Understand the relations between Cartesian and polar coordinates, and convert equations of curves from Cartesian to polar form and vice versa.
• Use equations of lines and planes, together with scalar and vector products where appropriate, to solve problems concerning distances, angles and intersections.
• Use the method of mathematical induction to establish a given result.
• Recognise situations where conjecture based on a limited trial followed by inductive proof is a useful strategy, and carry this out in simple cases.

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### A course by Walter Chatyoka
Maths Tutor

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### Requirements

• A desktop or laptop computer is recommended for optimum user experience. However, a phone or tablet can also be used as an alternative.
• A reliable internet connection for the duration of the course
• Have good foundational knowledge of Mathematics (IGCSE level).
• Ideally the student must have studied the majority of the Cambridge International AS & A Level Mathematics (9709).

### Target Audience

• Cambridge AS/A Level students