Outlined below are topics covered for the Pure maths A-Level

## I am slowly moving all the videos to my YouTube channel. Please use the Playlists to get to the videos in any topic. This work is ongoing.

## Contents for Pure Maths A-Level Tutorials

## Prior Knowledge

## Algebra Basics – Playlist

- Expanding a single bracket
- Expanding two or more brackets
- Squaring a bracket
- Terms in expressions and equations
- Identity or equation – what is the difference?
- Linear equations with a positive x-term
- Linear equations with a negative x-term
- Linear equations with two x-terms
- Linear equations with brackets
- Fractional linear equations

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## Algebra and Functions : 1 – Playlist

## Indices – Playlist

- Introduction to indices (exponents)
- Multiplication rule for indices
- Division rule for indices
- Negative indices
- Fractions raised to a negative index
- Rational (fractional) indices
- Simplifying terms with negative powers
- Expressing terms in the form ax
^{n } - Equations in which the power has to be found
- Summary of indices
- Exam Questions: Indices – Playlist

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## Quadratic Equations – Roots and Discriminant – Playlist

- Roots and discriminant of a quadratic equation
- Exam Questions: Roots and discriminant – Playlist

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## Rational Expressions: Simplifying – Playlist

- Simplifying rational expressions
- Addition and subtraction of algebraic fractions
- Exam Questions: Addition and Subtraction of algebraic fractions – Playlist
- Multiplication of algebraic fractions
- Further simplifying of ‘stacked fractions’
- Division of algebraic fractions
- Exam Questions: Algebraic long division – Playlist

## Coordinate Geometry: – Playlist

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## Exam Questions – Straight Lines

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## Parametric Equations – Playlist

- Parametric equations
- Converting to Cartesian form
- Exam Questions: Parametric to Cartesian equations – Playlist
- Sketching parametric graphs
- Parametric equations of circle, ellipse, parabola and hyperbola
- Finding points of intersection between a parametric and Cartesian equation
- Exam Questions: Parametric equations – Playlist

## Algebra and Functions : 2 – Playlist

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## Sequences and Series: – Playlist

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## Trigonometry: – Playlist

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## Exam Questions – Mixed trigonometry – Playlist

## Logarithmic and Exponential Functions: – Playlist

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## Differentiation: – Playlist

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## Exam Questions – Differentiation – Playlist

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## Integration: – Playlist

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## Integration – Common Functions – Playlist

- Integration:(ax+b)
^{n}types - Exam Questions: Integration:(ax+b)
^{n}types – Playlist - Integrating exponential functions e
^{x}, e^{ax}and e^{(ax+b)} - Exam Questions: Integrating exponential functions e
^{x}, e^{ax}and e^{(ax+b)}– Playlist - Integrating reciprocal functions 1/x and 1/(ax+b)
- Exam Questions: Integrating reciprocal functions 1/x and 1/(ax+b ) – Playlist
- Integrals of the form : f ‘(x)/f(x)
- Integrals of the form : f'(x)e
^{f(x)}

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## Integration by Substitution – Playlist

- Integration by substitution
- Square root types
- Integration of trigonometric functions by substitution
- Integration of exponential types by substitution
- Integration by substitution using limits
- Integration of trigonometric functions by substitution with limits
- Exam Questions: Integration by substitution – Playlist

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## Numerical Methods: – Playlist

## Vectors: – Playlist

## Vectors – Playlist

- What is a vector and a scalar quantity?
- Vector notation 2-dimensions
- Vector notation
- Position vectors 2-dimensions
- Position vectors
- Equal and negative vectors
- Multiplying a vector by a scalar 2-dimensions
- Multiplying a vector by a scalar
- Addition and subtraction of vectors 2-dimensions
- Addition and subtraction of vectors
- Magnitude of a 2 dimensional vector
- Magnitude of a 3 dimensional vector
- Unit vectors

## Past Papers

For further revision and practice I have past papers, some with worked solutions – Check them out for:

- circles
- chain rule
- change of sign
- completing the square
- connected rates of change
- coordinate geometry
- cosine rule
- cubic graph

- decreasing functions
- differential equations:
- solving
- forming
- differentiation:
- chain rule
- connected rates of change
- implicit
- parametric
- product rule
- quotient rule
- differentials:
- a
^{x} - e
^{x} - ln x
- sin, cos, tan(x)
- sec, cosec, cot(x)
- discriminant
- domain – functions

- implicit differentiation
- increasing functions
- indices
- inequalities
- integration
- by parts
- common functions
- general methods
- partial fractions
- substitution
- trigonometric
- definite
- integration applications
- area under a curve
- iteration
- intersection – graphs
- inverse functions

- parametric:
- differentiating
- equations
- partial fractions
- product rule
- proof

- quadrant rule
- quadratics:
- discriminant
- equations
- graphs
- quotient rule

- sector
- segment
- sequences and series
- sigma notation
- simultaneous equations
- sine rule
- stationary points
- straight lines
- surds

- tangents to curves
- transformations:
- graphs
- trapezium rule
- trigonometric:
- equations
- graphs
- ratios 30°, 60°, 45°
- trigonometry
- cosine rule
- cosec, sec and cot θ
- inverse functions
- sine rule
- small angles
- trigonometry – identities:
- addition formulae
- double angle formulae
- half angle formulae
- harmonic formulae
- Pythagorean
- triple angle formulae