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1. Algebraic Methods

This chapter reviews a lot of prior knowledge from GCSE Maths. This is essential practice for you because A-level maths requires a high skill level in algebra. Fluent algebraic manipulation is essential to high grades.

Learning Objective	Revision Videos	Practice
Know and apply indices laws.	Revision Page: Laws of Indices	See revision page.
Be able to expand and factorise brackets. Including: Basic linear factors Quadratics Difference of 2 Squares	Algebra Playlist Factorising Quadratics Difference of 2 Squares Factorising Harder Quadratics	Difference of 2 Squares Transum Factorising Harder Quadratics Transum Mixed Algebra Practice from Addvance Maths
Understand how to manipulate surds and simplify surd expressions.	Surds Revision Page	See revision page.
Be able to rationalise the denominator of a fractional surd.	See above.	See above.

2. Quadratic Equations and Functions

Learning Objective	Revision Videos	Practice
Be able to solve quadratic equations by: Factorising The quadratic formula Completing the square	Quadratics Revision Page Deriving the Quadratic Formula Video Completing the Square Video	Transum Practice: Solving Quadratic Equations Quadratic: Algebra Practice (Dr Austin Maths) Markscheme for Above Completing the Square Questions Markscheme for Above
Understand functions and inverse functions.	Composite Functions Video Inverse Functions	Functions Introduction: Transum Composite Functions: Transum Inverse Functions: Transum
Understand the concept of Domain and Range of a function.	Domain and Range Video	Domain and Range: Corbett Maths
Be familiar with the features of a quadratic graph, and solve problems associated with the graphs.	Plotting Quadratic Graphs Video Quadratic Graphs Video
Understand what the discriminant is and solve problems using the discriminant.		Dr Austin Maths Discriminant Questions Markscheme for Above Dr Oliver Maths: Discriminant Markscheme for Above

3. Equations and Inequalities

Learning Objective	Revision Videos	Practice
Be able to solve linear simultaneous equations.	Simultaneous Equations Video	Extension: Comparing Method of Solving Simultaneous Equations
Be able to solve simultaneous equations on graphs.	Simultaneous on a Graph Video
Be able to solve equations on graphs, understanding that the points of intersection are the solutions.	Solving Equations using Graphs Video
Be able to solve quadratic simultaneous equations.	Quadratic Simultaneous Equations Video
Know how to solve linear inequalities.	Inequalities Video
Know how to solve quadratic inequalities.	Quadratic Inequalities Video
Understand regions and inequalities on graphs.	Inequalities Regions Video

4. Graphs and Transformations

Learning Objective	Revision Videos	Practice
Be familiar with cubic and quartic graphs, and know their features.	Cubic Graphs Revision Video
Know the general shape and features of a reciprocal graph.	Reciprocal Graphs Video
Solve problems involving points of intersection of two graphs.	Solving Equations using Graphs Video
Know and understand that rules for graph transformations.	Graph Transformations Page	Mathsgenie Practice for all of Topci 4 Markscheme Naiker Maths: Practice Questions Markscheme

5. Straight Line Graphs

Learning Objective	Revision Videos	Practice
Be familiar with the equation of a straight line graph: y=mx+c	Straight Line Graphs Revision Page
Be able to find the gradient of a straight line.	Straight Line Graphs Video
Know that parallel lines have the same gradient, but perpendicular graphs have the negative reciprocal gradient.	Video Coming Soon
Be able to solve problems and model scenarios using straight line graphs.	Video Coming Soon	Mathsgenie Practice for all of 5. Markscheme

6. Circles

Learning Objective	Revision Videos	Practice
Understand how to find the midpoint between two points, and solve problems involving midpoints.
Be able to find the equation of a perpendicular bisector on a graph.
Know that the general form of a circle equation is (x-a)2+(y-b)2=r2	Circle Equations Video
Be able to solve problems involving circle equations and their graphs.	See Above	Mathsgenie: Circle Equations Markscheme NaikerMaths: Circle Questions Markscheme

7. Algebraic Methods

Learning Objective	Revision Videos	Practice
Be able to simplify algebraic fractions.	Algebraic Fractions Video
Be able to solve equations involving algebraic fractions.	See above.
Divide polynomials using algebra.
Understand the factor theorem.		Mathsgenie: The Factor Theorem and Algebraic Division Markscheme for Above Dr Oliver Maths: Factor Theorem Dr Oliver Maths: Solutions
Use mathematical proof to prove mathematical facts.	Algebraic Proof Video
Understand various methods of proof.

8. The Binomial Expansion

Learning Objective	Revision Videos	Practice
Understand how to use binomial expansion, and be able to expand brackets efficiently.	Binomial Expansion Video
Solve problems using the binomial theorem.	Binomial Expansion Problems Video	Mathsgenie: The Binomial Expansion Markscheme for Above
Estimate calculations using an appropriate binomial expansion.	Binomial Approximations

9. Trigonometric Ratios

Learning Objective	Revision Videos	Practice
Revision: Revise all of GCSE SOHCAHTOA and Pythagoras Theorem.	Trigonometry Revision Page
Be able to use the sine and cosine rules to solve problems involving non-right angle triangles.	Sine Rule Video Cosine Rule Video
Be able to use the formula for the area of a triangle with sine to solve problems.	Area of a Triangle with Sine Video
Know the graphs of sine, cosine and tan.	Sin, Cos and Tan graphs Video
Know how to transform trigonometric graphs.	Transformations of Trigonometric Graphs Video Modelling with Trig Graphs Video

10. Trigonometric Identities and Equations

Learning Objective	Revision Videos	Practice
Be able to solve basic trigonometric equations.
Know the exact trigonometric values, and the special triangles.	Special Triangles Video
Know the trig identities, and use them to solve problems.	Trigonometric Identities Video
Be able to use a CAST diagram to calculate repeated solutions to trigonometric equations.	Introduction to CAST Diagrams Solving Trig Equations Using Trig	MathsGenie: Solving Trigonometric Equations Markscheme

11. Vectors

Learning Objective	Revision Videos	Practice
Understand vector notation.	Vector Notation Video
Understand the concept of vector magnitude, and be able to calculate the magnitude of a vector.	Video Coming Soon
Be able to apply vector facts to solve vector problems.	Video Coming Soon
Be able to model with vectors.	Video Coming Soon	MathsGenie: Vectors Markscheme

12. Differentiation

Learning Objective	Revision Videos	Practice
Understand how to differentiate from first principles.	Differentiation from First Principles Video	MathsGenie: Differentiation from First Principles MarkScheme
Be able to differentiate using the power rule.	Differentiation Video	MathsGenie: Differentiation Questions Markscheme
Use differentiation to find the gradient of a curve at a particular coordinate.	See below
Use differentiation to find the equation of a tangent of a curve at a coordinate.	Finding the Equation of Tangent Video	Naiker Maths: Tangent Questions Markscheme
Use differentiation to find the equation of a normal of a curve at a coordinate.	See above
Understand the concept of a second derivative.	Second Derivative Video
Analyse a curve to see whether it is increasing or decreasing at a particular point.	See above
Find the coordinates of stationary points using differentiation.	Maximum and Minimums Video
Be able to model using differentiation.	Coming Soon	NaikerMaths: Modelling with Differentiation Markscheme

13. Integration

Learning Objective	Revision Videos	Practice
Be able to integrate using the reverse power rule.	Introduction to Integration Video	Transum: Integration MathsGenie: Integration Markscheme
Be able to find the equation of a function from the equation of a gradient using integration.	Coming Soon
Use integration to find areas beneath and between curves.	Integration: Finding Areas Video	Naiker Maths: Integration and Areas Markscheme

14. Exponentials and Logarithms

Learning Objective	Revision Videos	Practice
Understand the general shape an exponential graph.	Coming Soon
Use exponential equations to model real life situations.	Modelling with Exponentials Video
Understand the concept of a logarithm.	Coming Soon	Transum: Logarithms MathsGenie: Exponentials and Logarithms Questions Markscheme
Know the laws of logarithms and how to use them to solve equations involving exponents.	Coming Soon
Understand how to use logarithms to model non-linear data.	Coming Soon

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