Topic module: Pure Maths AS OCR

Solving equations with equal terms on both sides (Common error)

Modelling exponential equations | Exam Questions

Modelling exponential growth and decay

Converting between Logarithmic and Power (Exponential) equations

How to solve vector geometry problems

Vector geometry problems In this tutorial, we learn how to solve vector geometry problems using a logical approach

Exam Questions – Proof By Counter Example

Exam Questions – Definite Integration

Using a Counter-Example

Proof by Exhaustion and Deduction

Proving Identities

Mixed Exercise – Pythagoras and Trigonometry

Trig ratios for multiples of 30°, 45° and 60°

Shading regions for a linear inequality

How to solve a cubic equation

Logarithms – Change of Base

Simultaneous equations

Multiplying a vector by a scalar 2d

Addition and subtraction of vectors 2d

Position vectors 2d

Vector notation 2d

Exam Questions – Applications of stationary points

Exam Questions – Binomial expansion, other

Exam Questions – Binomial expansion, estimating a value

Exam Questions – Binomial expansion, comparing coefficients

Exam Questions – Simultaneous inequalities

Identity or equation – what is the difference?

Modelling curves – Converting to linear form

Mixed Exercise – Factorising

Summary of indices

Exam Questions – Sine rule

Exam Questions – Straight lines

Exam Questions – Solving a double inequality

Exam Questions – Natural log functions

Exam Questions – Increasing and decreasing functions

Exam Questions – Stationary points

Exam Questions – Trigonometric identities

Exam Questions – Trigonometric graphs and transformations

Exam Questions – Binomial expansion for positive integer powers

Exam Questions – Circles

Exam Questions – Logarithms

Exam Questions – Factor theorem

Exam Questions – Equations of curves

Exam Questions – Integration: introduction

Exam Questions – Tangents and normals

Exam Questions – Differentiation: introduction

Exam Questions – Graph transformations

Exam Questions – Quadratic inequalities

Exam Questions – Simultaneous equations

Exam Questions – Roots and discriminant

Exam Questions – Solved by the quadratic formula

Exam Questions – Completing the square

Exam Questions – Factorising

Exam Questions – Surds

Exam Questions – Indices

Nature of a stationary point

Using the identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)

Trig equations with multiple angles

Trig equations with different ranges

Stretches of trig graphs

Equation of a line given the gradient and point

Asymptotes – horizontal and vertical types

Sketching reciprocal curves of the form y = k/x

Sketching cubic curves

Magnitude of a 2 dimensional vector

Equal and negative vectors

Unit vectors

What is a vector and a scalar quantity?

The natural logarithmic function, ln x

Sketching exponential graphs based on transformations

The exponential function e^x

Simplifying algebraic fractions

Definite integration

Increasing and decreasing functions

Applications of stationary points

Stationary points

Solving equations using identities

Using the identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1

Trig equations that factorise

Quadrant rule to solve trig equations

Cosine rule

Sine rule

Area of a triangle – Given two sides and an included angle

Combining transformations

Reflections of trig graphs

Translations of trig graphs

Trigonometric graphs

Trigonometric ratios for 30°, 45° and 60°

Binomial expansion formula

Binomial expansion

Circle properties

Equation of a circle through 3 points

Equation of a tangent to a circle

Finding the centre and radius

Equation of a circle

Solving inequalities

Exponential and log equations

Simplifying and expanding

Rules of logs

What do we mean by a log?

Exponential functions: what they are and their graphs

The factor theorem

Algebraic long division

Finding the equation of a curve given the gradient function

Integration – Terms of the form axⁿ

Equations of tangents and normals

The second derivative

Differentiation – terms of the form axⁿ

The gradient function dy/dx

Intersection of a straight line and a hyperbola

Nature of the intersection

Intersection of a straight line and a parabola

Intersection of two straight lines

Equation of a perpendicular bisector

Equation of a parallel line

Mid-point of a line segment

Distance between two points

Equation of a straight line: y=mx+c

Perpendicular lines

Parallel lines

Line segment

Quadratic inequalities

Solving a double inequality

Solving a linear type

Rules for reversing the inequality sign

Linear inequalities

Substitution method for linear and non-linear equations

Elimination method for linear equations

Fractional linear equations

Finding an angle

Finding the length of a side

Introduction to trigonometry

Pythagoras’ theorem

Linear equations with brackets

Linear equations with two x-terms

Linear equations with a negative x-term

Linear Equations with a positive x term

Terms in expressions and equations

Squaring a bracket

Expanding two or more brackets

Expanding a single bracket

Stretches of graphs

Reflections of graphs

Translations of graphs

Basic graphs used in transformations

Polynomials

Sketching quadratic graphs

Roots and discriminant of a quadratic equation

Solving quadratic equations in some function of x

Solve by the quadratic formula

Solve by completing the square

Solve by factorising

Applications of completing the square

Completing the square

Factorising quadratic expressions

Factorising by grouping

Highest common factor (HCF)

Introduction to factorising

f(x) notation

Addition and subtraction of surds

Rationalising surds

Dividing surds

Surds – introduction & simplifying

Multiplying surds

Equations in which the power has to be found

Simplifying terms with negative powers

Rational (fractional) indices

Fractions raised to a negative index

Negative indices

Division rule for indices

Multiplication rules for indices

Expressing terms in the form axⁿ

Introduction to indices (exponents)