A video revising the techniques and strategies for all of the topics that you need to achieve a grade A in AS Pure Mathematics.
These topics are all of the essential topics that appear on the AS Pure Maths curriculum. This however is not ALL of the question styles within the A Level. Further videos can be found on the channel for a more in depth look at some of these topics.
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? Timestamps?
00:00 What topics are covered?
01:09 How to use the video
02:27 Intro
02:45 Expanding Brackets
04:55 Simplifying Algebraic Fractions
07:17 Factorising Quadratics
09:02 Index laws
11:47 Harder Index laws
16:04 Surds
18:45 Rationalising the Denominator
20:42 Solving Quadratics
22:31 The Quadratic Formula
25:37 Completing the Square
28:45 Solving Equations by Completing the Square
32:05 Negative Quadratics
37:20 The Discriminant Explained
42:19 Solving Problems with the Discriminant
48:47 Modelling with Quadratics
57:19 Linear Simultaneous Equations
59:39 Quadratic Simultaneous Equations with a Circle Meets a Line
01:06:06 Quadratic Simultaneous Equations with a Curve Meets a Line
01:11:08 Graphical Simultaneous Equations
01:20:31 Linear Inequalities using Set Notation
01:28:24 Quadratic Inequalities
01:31:02 Regions
01:35:35 Sketching Cubic Graphs
01:38:15 Sketching Quartic Graphs
01:41:27 Reciprocal Graphs and Asymptotes
01:45:22 Intersecting Graphs Problems
01:53:34 Using Desmos Graphing Calculator
01:55:13 Graph Transformations Explained
01:59:42 Translating Functions
02:04:16 Equation of a Line
02:06:16 Perpendicular Lines
02:08:27 Area with Coordinate Geometry
02:13:48 Modelling with Linear Graphs
02:19:02 Midpoints and Perpendicular Bisectors
02:23:13 Equation of a Circle
02:25:25 Equation of a Circle to Find the Centre
02:32:44 Intersections of Linear Graphs and Circles
02:36:16 Tangents to a Circle
02:39:53 Chord Properties
02:43:31 Algebraic Fractions
02:44:51 The Factor Theorem
02:49:12 Methods of Proof with Inequalities
02:52:39 Methods of Algebraic Proof
02:58:13 Binomial Expansion Explained
03:07:38 The Binomial Expansion
03:12:47 Solving Binomial Problems
03:17:25 Binomial Estimation
03:24:17 The Cosine Rule
03:28:39 The Sine Rule
03:33:41 Areas of Triangles
03:36:08 Solving Triangle Problems with Bearings
03:44:58 Transforming Trigonometric Graphs
03:48:04 Graphs of Sine, Cosine and Tangent
03:55:12 Exact Values of Trigonometric Ratios
03:56:18 Trigonometric Identities
03:58:28 Trigonometric Equations
04:04:39 Equations and Identities
04:14:22 Harder Trigonometric Equations
04:27:49 Vectors
04:32:18 Representing Vectors
04:35:56 Magnitude and Direction of Vectors
04:40:10 Position Vectors
04:50:04 Solving Geometric Problems
04:57:15 Modelling with Vectors
05:10:53 Differentiation Explained
05:13:19 Differentiation from First Principles
05:15:59 Differentiating Quadratics
05:17:08 Harder Differentiation
05:19:43 Gradients of Tangents and Normals
05:22:34 Increasing and Decreasing Functions
05:24:54 Second Order Derivatives
05:25:34 Stationary Points
05:31:39 Modelling with Differentiation
05:41:20 Integration Explained
05:45:08 Indefinite Integrals
05:47:29 Finding Functions by Integrating
05:52:55 Definite Integrals
05:56:09 Areas Under Curves
06:00:40 Areas Under the x-axis
06:08:17 Areas Between Curves and Lines
06:14:08 Logarithms Explained
06:17:27 Laws of Logarithms
06:19:30 Solving Simple Equations Using Logarithms
06:21:10 Laws of Logs (Adding)
06:25:53 Laws of Logs (Subtracting)
06:30:02 Laws of Logs (Multiplying)
06:34:36 Solving Harder Logarithmic Equations
06:39:21 Exponential Functions
06:41:29 Differentiating e^x
06:42:35 Solving Exponential Equations using Natural Logarithms
06:44:17 Solving Exponential Quadratics with Natural Logarithms
06:46:39 Modelling with Exponentials
06:54:49 Well done, Please Like, Comment and Subscribe
06:54:49 Outro
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Disclaimer: It would be impossible to cover every single topic in the maths curriculum in this timeframe, the topics chosen here are the fundamental topics that I work on with my own students studying for the AS Pure exam. You should always conduct your own subject analysis using your revision guides and teachers to ensure that you cover any aspects of topics not mentioned in this particular video.
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