Implicit functions with product rule
Modelling exponential growth and decay
Converting between Logarithmic and Power (Exponential) equations
Differentiating arctan(x/a) or inverse tan(x/a) example
In this video, we go through an example of how to Differentiate arctan(x/a) or inverse tan(x/a)
Differentiating arctan(x/a) or inverse tan(x/a)
In this video we learn how to Differentiate arctan(x/a) or inverse tan(x/a)
Complex numbers specimen questions (mixed exam boards)
Complex numbers In this tutorial, we solve problems from different exam boards involving complex numbers. The idea is to give you a more rounded approach to solving different topic problems. Edexcel A-Level Further Maths Specimen Paper 1 Q3 (Core Pure 1) 9 MARKS IB Maths AA HL Specimen Paper 1 (Section B) a) 5MARKS b) […]
Increasing and decreasing sequences
In this tutorial, we show you how to prove whether a sequence is increasing or decreasing using algebra.
Exam Questions – Small Angle Approximations
Exam Questions – Double Angles
Integrating products of the form f[g(x)]g'(x) by inspection
Integration – General Methods
Harmonic identities – Max and Min
How to solve a cubic equation
Identities – Addition type – Equations
Logarithms – Change of Base
Simultaneous equations
Square root types
Exam Questions – Finding roots
Exam Questions – Partial fractions with the binomial expansion
Shortest distance of a point to a line
Shortest distance from a point to a plane
Geometrical effects of conjugating a complex number
Modelling curves – Converting to linear form
Shortest distance between two skew lines
Vector product form of a line
Denominator contains 1 linear and 1 quadratic factor
Exam Questions – Parallel intersecting and skew lines
Exam Questions – Integration
Proof of the formula – Integration by parts
Exam Questions – Trigonometric types
Exam Questions – Integrating reciprocal functions 1/x and 1/(ax+b)
Exam Questions – Integrating exponential functions ex, eax and e(ax+b)
Using partial fractions with the binomial expansion
Exam Questions – Harmonic identities and equations
Exam Questions – Modulus equations
Exam Questions – Modulus functions graphing
Solving quartic equations
Solving cubic equations
Solving quadratic equations with complex roots
Square roots of a complex number
Exam Questions – Loci in the complex plane
Exam Questions – Further complex numbers
Exam Questions – Complex numbers
Exam Questions – Trapezium rule
Exam Questions – Forming differential equations
Exam Questions – Integration by parts
Exam Questions – Integration by substitution
Exam Questions – Integrals involving partial fractions
Exam Questions – Integration:(ax+b)n types
Exam Questions – Implicit functions
Exam Questions – Parametric functions
Exam Questions – Binomial expansion for rational and negative powers
Exam Questions – Partial fractions
Exam Questions – Iteration
Exam Questions – Natural log functions
Exam Questions – Modulus inequalities
Exam Questions – Logarithms
Exam Questions – Remainder theorem
Exam Questions – Factor theorem
The angle between two planes
The equation of the line of intersection between two non parallel planes
Finding the point of intersection between a line and a plane
Scalar product forms of a plane
Cartesian form of a plane
Parametric vector form of a plane
Cartesian form of a line
Working with constants in log types
Differential Equations – Finding a general and a particular solution
Using complex numbers to represent regions on an Argand diagram
The locus of a point moving on the arc of a circle
The locus of a point moving along a half-line
The locus of a point moving along a perpendicular bisector
The locus of a point moving in a circle
Multiplication and division rules for mod and argument of two complex numbers
Exponential Form (Euler’s relation)
sin2x and cos2x types
Integrals Using Trigonometric Identities
The reciprocal function of dy/dx
The trig functions, sec(x), cosec(x) and cot(x)
The trig functions sin(x), cos(x) and tan(x)
The natural log function, ln(x)
Solving problems with complex numbers
Modulus and argument of a complex number
Argand diagrams
Division of a complex number by a complex number
Complex conjugates
Addition, subtraction and multiplying complex numbers and simplifying powers of i
Real and imaginary numbers
Closest point to a line and shortest distance from the origin
Intersecting and skew lines
Parallel lines
Angle between two lines
Vector equation of a line
Trapezium rule
Newton’s law of cooling
Inverse proportion type
Direct proportion type
Differential Equations – Exponential and trig type
Mixed Examples – Integration
Integration by parts (ln types)
Integration by parts using limits
Integration by parts
Integration of trigonometric functions by substitution with limits
Integration by substitution using limits
Integration of exponential types by substitution
Integration of trigonometric functions by substitution
Integration by substitution
Integrals involving partial fractions
Integrals of the form sin(ax+b), cos(ax+b), sec² (ax+b) types
Integrals of sin x, cos x, sec² x
Integrals of the form : f'(x)ef(x)
Integrals of the form : f ‘(x)/f(x)
Integrating reciprocal functions 1/x and 1/(ax+b)
Integrating exponential functions ex, eax and e(ax+b)
Integration:(ax+b)n types
Stationary points
In this tutorial I show you how to find stationary points to a curve defined implicitly and I discuss how to find the nature of the stationary points by considering the second differential. Both methods involve using implicit differentiation and the product rule. Example: Nature of the Stationary Points
Tangents and normals
Implicit functions
Stationary points
In this video you are shown how to find the stationary points to a parametric equation.
Tangents and normals
Differentiation: Parametric functions
Validity
Binomial expansion for rational powers
Denominator contains repeated factors
Denominator contains 2 or 3 linear factors
Partial fractions
Iteration
Change of sign
Graphical methods
The quotient rule
The product rule
Chain rule: Trigonometric types
Chain rule: Natural log types
Chain rule: Exponential types
Chain rule: Polynomial to a rational power
Exponential function ex
Equations using harmonic identities
Harmonic Identities Rsin(x ± α), Rcos(x ± α)
Examples using half angle identities
Solving equations using double angle identities
Examples using double angle identities
Identities for sin2A, cos2A and tan2A
Proving identities using the addition formulae
Using the Addition formulae to get exact values
sin(A±B), cos(A±B) and tan(A±B)
Solving equations using Pythagorean identities
sin²x + cos²x ≡1 , 1 + tan²x ≡ sec²x , 1 + cot²x ≡ cosec²x
Graphs of sec θ, cosec θ and cot θ
Trig functions sec θ, cosec θ and cot θ
The natural logarithmic function, ln x
Sketching exponential graphs based on transformations
The exponential function ex
Modulus inequalities
Modulus equations
Graphing y=f(|x|)
Remember: f(|x|) reflects the graph to the right of the y-axis in the y-axis. Ignore the left hand side part of the graph In this video I show you how to draw graphs of the form y=f(|x|) using the modulus function and give you three graphs to try. Examples in the video: Sketch the following
Graphing y=|f(x)|
The modulus function
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 […]