MEI Pure Maths AS Tutorials

Algebra Basics

1. Expanding a single bracket
2. Expanding two or more brackets
3. Squaring a bracket
4. Terms in expressions and equations
5. Identity or equation - what is the difference?
6. Linear Equations with a positive x term
7. Linear equations with a negative x-term
8. Linear equations with two x-terms
9. Linear equations with brackets
10. Fractional linear equations
11. f(x) notation
12. Polynomials

Polynomials

1. Polynomials

Pythagoras’ Theorem

1. Pythagoras' theorem

Trigonometry Introduction

1. Introduction to trigonometry
2. Finding the length of a side
3. Finding an angle

Indices

1. Introduction to indices (exponents)
2. Multiplication rules for indices
3. Division rule for indices
4. Negative indices
5. Fractions raised to a negative index
6. Rational (fractional) indices
7. Simplifying terms with negative powers
8. Expressing terms in the form axⁿ
9. Equations in which the power has to be found
10. Summary of indices
11. Exam Questions - Indices

Surds

1. Surds - introduction & simplifying
2. Addition and subtraction of surds
3. Multiplying surds
4. Dividing surds
5. Rationalising surds
6. Exam Questions - Surds

Functions

1. f(x) notation

Factorising

1. Introduction to factorising
2. Highest common factor (HCF)
3. Factorising by grouping
4. Factorising quadratic expressions
5. Mixed Exercise - Factorising
6. Exam Questions - Factorising

Completing the Square

1. Completing the square
2. Applications of completing the square
3. Exam Questions - Completing the square

Quadratic Equations

1. Solve by factorising
2. Solve by completing the square
3. Solve by the quadratic formula
4. Exam Questions - Solved by the quadratic formula
5. Solving equations with equal terms on both sides (Common error)
6. Solving quadratic equations in some function of x

Quadratic Equations – Roots and Discriminant

1. Roots and discriminant of a quadratic equation
2. Exam Questions - Roots and discriminant

Quadratic Graphs

1. Sketching quadratic graphs

Simultaneous Equations

1. Elimination method for linear equations
2. Substitution method for linear and non-linear equations
3. Exam Questions - Simultaneous equations

Inequalities

1. Linear inequalities
2. Rules for reversing the inequality sign
3. Solving a linear type
4. Solving a double inequality
5. Exam Questions - Solving a double inequality
6. Quadratic inequalities
7. Exam Questions - Quadratic inequalities
8. Exam Questions - Simultaneous inequalities

Algebraic Long Division

1. Algebraic long division

Factor Theorem

1. The factor theorem
2. Exam Questions - Factor theorem

Gradient of Straight Lines

1. Line segment
2. Parallel lines
3. Perpendicular lines

Straight Lines

1. Equation of a straight line: y=mx+c
2. Equation of a line given the gradient and point
3. Distance between two points
4. Mid-point of a line segment
5. Equation of a parallel line
6. Equation of a perpendicular bisector

Intersection of Graphs

1. Intersection of two straight lines
2. Intersection of a straight line and a parabola
3. Intersection of a straight line and a hyperbola
4. Nature of the intersection

Circles

1. Equation of a circle
2. Finding the centre and radius
3. Circle properties
4. Equation of a tangent to a circle
5. Equation of a circle through 3 points
6. Exam Questions - Circles

Sketching Cubic and Reciprocal Curves

1. Sketching cubic curves
2. Sketching reciprocal curves of the form y = k/x

Graph Transformations

1. Basic graphs used in transformations
2. Translations of graphs
3. Reflections of graphs
4. Stretches of graphs
5. Exam Questions - Graph transformations

Asymptotes

1. Asymptotes - horizontal and vertical types

Binomial Expansion

1. Binomial expansion
2. Exam Questions - Binomial expansion for positive integer powers
3. Exam Questions - Binomial expansion, comparing coefficients
4. Exam Questions - Binomial expansion, estimating a value
5. Exam Questions - Binomial expansion, other

Trigonometric Ratios

1. Trigonometric ratios for 30°, 45° and 60°

Trigonometric Graphs and Transformations

1. Trigonometric graphs
2. Translations of trig graphs
3. Reflections of trig graphs
4. Stretches of trig graphs
5. Combining transformations
6. Exam Questions - Trigonometric graphs and transformations

Applications of Trigonometry

1. Area of a triangle - Given two sides and an included angle
2. Sine rule
3. Exam Questions - Sine rule
4. Cosine rule

Trigonometric Equations

1. Quadrant rule to solve trig equations
2. Trig equations with different ranges
3. Trig equations with multiple angles
4. Trig equations that factorise
5. Solving equations with equal terms on both sides (Common error)

Trigonometric Identities

1. Using the identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1
2. Using the identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)
3. Solving equations using identities
4. Exam Questions - Trigonometric identities

Exponential Functions and Logarithms

1. Exponential functions: what they are and their graphs
2. What do we mean by a log?
3. Rules of logs
4. Simplifying and expanding
5. Converting between Logarithmic and Power (Exponential) equations
6. Modelling exponential growth and decay
7. Modelling exponential equations | Exam Questions
8. Exponential and log equations
9. Solving inequalities
10. Exam Questions - Logarithms

The Exponential Function e^x and Natural Log Functions

1. The exponential function e^x
2. Sketching exponential graphs based on transformations
3. The natural logarithmic function, ln x
4. Exam Questions - Natural log functions

Modelling Curves of the form y=kxⁿ and y=ka^x

1. Modelling curves - Converting to linear form

Differentiation – Introduction

1. The gradient function dy/dx
2. Differentiation - terms of the form axⁿ
3. The second derivative
4. Exam Questions - Differentiation: introduction

Tangents and Normals

1. Equations of tangents and normals
2. Exam Questions - Tangents and normals

Stationary Points

1. Stationary points
2. Nature of a stationary point
3. Exam Questions - Stationary points
4. Applications of stationary points
5. Exam Questions - Applications of stationary points

Increasing and Decreasing functions

1. Increasing and decreasing functions
2. Exam Questions - Increasing and decreasing functions

Integration – Introduction

1. Integration - Terms of the form axⁿ
2. Exam Questions - Integration: introduction

Equations of Curves

1. Finding the equation of a curve given the gradient function
2. Exam Questions - Equations of curves

Definite Integration

1. Definite integration

Vectors

1. What is a vector and a scalar quantity?
2. Vector notation 2d
3. Position vectors 2d
4. Equal and negative vectors
5. Multiplying a vector by a scalar 2d
6. Addition and subtraction of vectors 2d
7. Magnitude of a 2 dimensional vector
8. Unit vectors
9. How to solve vector geometry problems

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