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
Increasing and decreasing sequences
In this tutorial, we show you how to prove whether a sequence is increasing or decreasing using algebra.
Exam Questions – Definite Integration
Exam Style Questions – Geometric Series and Progressions
Convergent and Divergent Integrals
Radians
Mixed Exercise – Pythagoras and Trigonometry
Trig ratios for multiples of 30°, 45° and 60°
How to solve a cubic equation
Logarithms – Change of Base
Simultaneous equations
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?
Mixed Exercise – Factorising
Summary of indices
Exam Questions – Sine rule
Exam Questions – Straight lines
Exam Questions – Solving a double inequality
Exam Questions – Trapezium rule
Exam Questions – Area bound by a curve and x-axis
Exam Questions – Increasing and decreasing functions
Exam Questions – Stationary points
Exam Questions – Trigonometric identities
Exam Questions – Arcs, sectors and segments
Exam Questions – Binomial expansion for positive integer powers
Exam Questions – Geometric series
Exam Questions – Circles
Exam Questions – Logarithms
Exam Questions – Remainder theorem
Exam Questions – Factor theorem
Exam Questions – Equations of curves
Exam Questions – Integration: introduction
Exam Questions – Tangents and normals
Exam Questions – Differentiation: introduction
Examsolutions Beastie – Arithmetic progressions
Exam Questions – Arithmetic sequences and series
Exam Questions – Sigma notation
Exam Questions – Recurrence relationships
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
Multiplication of algebraic fractions
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
Equation of a line given the gradient and point
Working with consecutive terms
Finding a and d given two terms
Definition and finding the nth term
Sketching reciprocal curves of the form y = k/x
Sketching cubic curves
Trapezium rule
Area bound by a curve and x-axis
Infinite integrals
In this tutorial I show you how to handle integrals where a limit is infinite as in the example below. Example:
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
Arcs, sectors and segments
Cosine rule
Sine rule
Area of a triangle – Given two sides and an included angle
Trigonometric ratios for 30°, 45° and 60°
Binomial expansion formula
Binomial expansion
Sum to infinity
Proof of sum of first n terms, Sn
Geometric series
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 remainder theorem
The Remainder Theorem Rule to remember: If a polynomial is divided by then the remainder is . In the video tutorial I demonstrate this. Finding the remainder when a cubic polynomial is divided by x+1 In the videos that follow, I run through some typical remainder theorem questions that you are likely to encounter. I […]