 # Geometry Lectures by Nigel Simmons

Lectures from 2014-2015 from teacher Nigel Simmons.

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Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Geometry Lectures by Nigel Simmons
- Nigel Simmons
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A couple of questions that have appeared in the past years
Topic: induction
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finally a look at the inequality type of induction problem
Topics: induction, inequality
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Deriving formulae for use with geometric aeries.
Topics: series, geometric
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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The alternate segment
Topic: alternate segment
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the means of numbers
Topics: series, means
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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A quick look at the generalistion of the sum & difference formulae
Topic: sum & difference formulae
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Calculating a series
Topic: series
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Solving problems using calculus
Topic: calculus
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Introducing the useful theorem
Topic: integration
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Key features to look for when sketching polynomials
Topics: polynomials, curve sketching
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Calculating areas if irregular shapes
Topics: integration, areas
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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How to find areas for functions too difficult to integrate
Topic: integration
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Inequalities involving two variablss
Topic: regions
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding sides and angles in non-right angled triangles
Topic: trigonometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Expanding on the idea of transforming the basic curves.
Topic: curve sketching
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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The first of the angle theorems
Topic: circle geometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Deriving the double angle formulae
Topics: trigonometry, double angles
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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The chord joing the points of contcat of the tangents drawn from an external point.
Topics: chord, parametrics
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Solving optimisation problems using calculus.
Topics: calculus, maxima, minima
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Circles and tangents
Topic: geometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Introducing sigma notation
Topics: series, sum
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Defining the quadratic and how to find its important features.
Topics: quadratic, curve sketching
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Some alternative ways of finding the features of quadratics
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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When two quadrtics are "congruent", the coefficients an be matched.
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Results concerning polynomials
Topic: polynomials
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the valueof integrals for curves that can't be integrated!!
Topics: integration, approximations
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Deriving the inverse trig derivatives!!!
Topic: inverse trig
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Applying the general term of a binomial to probability problems
Topics: binomial, probability
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Introducing the binomail theorem
Topic: binomial
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Looking at the pattewrn of the coefficients in a binomial expansion
Topic: binomial
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Raising complex numbers to powers
Topics: complex numbers, de moivres
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Defining the parametric coordinates of the ellipse and finding the tangent and normal.
Topics: conics, parmeters, ellipse
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Defining the family of conics and more specifically, te ellipse.
Topics: conics, ellipse
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the volume of solids with non circular cross sections
Topics: volumes, parallel cross sections
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Expanding on the idea from Extension 1
Topics: polynomials, roots, coefficients
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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A hyperbola whose asymptotes are perpendicular
Topics: conics, hyperbola
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Working with surds
Topic: surds
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Techniques for solving basic equations/
Topics: algebra, equations
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Defining te sine rule for use in non-right angled triangles, as well as a formuls for finding the area of a triangle without having to know the perpendicular height.
Topics: trigonometry, sine rule, area
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Three diferent levels of inequality questions
Topic: inequations
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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solving trig equations
Topic: trigonometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Making the use of the symmetry of odd and even functions to make integration simpler.
Topics: integration, odd & even functions
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Solving inequality problems using graphs
Topic: inequalities
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Manipulating the roots of unity
Topics: complex numbers, roots of unity
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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A rule which allows us to differentiate without expanding out
Topic: calculus
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Using the derivative to solve rates of change problems
Topics: calculus, rates of change
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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The basic algebraic operations
Topics: algebra, indices
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the area under a curve
Topics: integration, area
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Looking at divisibility types of induction problems
Topics: induction, divisibility
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the equation of a line that pase through the intersection of two given lines and another point.
Topics: linear function, lamda formula
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Looking at the specific case of the locus as a parabola
Topics: parabola, locus
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Introducing the logarithmic function
Topics: logarithms, log laws
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Solving trig equations
Topics: trigonometry, trig equations
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Polynomial results that assist when factorising
Topic: polynomial
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Differentiating a function divided by a function
Topics: calculus, quotient rule
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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An alternative way of solving simultaneous equations.
Topics: algebra, matrices
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Deriving the sine rule
Topic: trigonometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Creating quadraticfactors from complex roots
Topics: complex numbers, factorising
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the equation of the chord of contact and other geometric properties of the conic sections.
Topics: conics, chord of contact, geometric properties
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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investigating the forces involved with a conical pendulum
Topics: dynamics, conical pendulum
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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How to operate numbers in polar form
Topics: complex numbers, mod arg
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Functions and the Argand Diagram
Topics: complex numbers, locus
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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When te order is unimportamt....
Topic: combination
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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What happens when some of the objects being arranged are the same?
Topics: probability, permutations
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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How do we differentiate inverse trig functions?
Topics: inverse trig, calculus
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Standard integrals involving inverse trig
Topics: inverse trig, calculus
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the greatest coefficient/term without expanding the binomial
Topic: binomial
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Introducing the terms and basic ideas of probabiolity
Topic: probability
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Motion that oscillates between two points is known as Simple Harmonic Motion (SHM)
Topic: simple harmonic motion
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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How do the arrangements change when arranging in a circle?
Topic: permutation
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Finding the relationships & patterns of binomial coefficients
Topics: binomial theorem, coefficients
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Generalising the expansion using Pascal's Triangle for the binomial coefficients.
Topic: binomial theorem 