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Geometry Lectures by Nigel Simmons

Lectures from 2014-2015 from teacher Nigel Simmons.



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Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Angular velocity vs linear velocity
Topic: circular motion
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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INtroducing the conic sections
Topics: conics, ellipse
Geometry Lectures by Nigel Simmons
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The parametric form of the hyperbola
Topic: hyperbola
Geometry Lectures by Nigel Simmons
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Turning quadratics into trig functions
Topic: integration
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Solving locus problems by eliminating the parameters
Topics: parabola, locus, parametrics
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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When te order is unimportamt....
Topic: combination
Geometry Lectures by Nigel Simmons
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Introducing the quadratic function
Topic: quadratic
Geometry Lectures by 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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What happens when some of the objects being arranged are the same?
Topics: probability, permutations
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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finding the greatest coefficient/term in a binomial expansion
Topics: binomial theorem, greatest coefficient
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Techniques for how to approach factorising
Topics: algebra, factorising
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Differentiating a second time
Topics: calculus, second derivative
Geometry Lectures by Nigel Simmons
audio

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Mathematical inverse of graphs
Topic: functions
Geometry Lectures by Nigel Simmons
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The idea behind solving quadratics
Topics: algebra, quadratic
Geometry Lectures by Nigel Simmons
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If the product of factors is zero, then at least one factor must be zero.
Topic: quadratic
Geometry Lectures by Nigel Simmons
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Start with the basic curve and transform it to a new curve.
Topic: curve sketching
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
audio

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A key procedure when dealing with surds is making the denominator a rationsl nuber.
Topics: surds, rationalising the denominator
Geometry Lectures by Nigel Simmons
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A basic principle of mathematics is used for solving surdic equalities.
Topic: surds
Geometry Lectures by Nigel Simmons
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Rationals and irrationals do not mix!!
Topic: surds
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Using symmetry to sketch graphs
Topic: curve sketching
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Using the symmetry of functions to help sketching
Topic: Symmetry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Selecting the objects when order is NOT important
Topic: combination
Geometry Lectures by Nigel Simmons
audio

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The shortest distance between a point and a line
Topic: cartesian geometry
Geometry Lectures by Nigel Simmons
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Finding the shortest distance between a point and a lne.
Topics: linear function, perpendicular distance
Geometry Lectures by Nigel Simmons
audio

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Calculating the acute angle between two lines
Topics: linear function, angle between lines
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Waht if some of the objects we are arranging look the same?
Topic: permutation
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Geometry theorems involving triangles
Topics: geometry, triangle theorems
Geometry Lectures by Nigel Simmons
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Using te counting techniques to solve probability problems.
Topics: permutations, combinations, probability
Geometry Lectures by Nigel Simmons
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Investigating the linear function (straight line)
Topic: linear function
Geometry Lectures by Nigel Simmons
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Dividing intervals in ratios other than 1:1
Topic: coordinate geometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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How to deal with the product of functions
Topic: calculus
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Application of similar triangles
Topics: geometry, transversals
Geometry Lectures by Nigel Simmons
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Proving Pascal Triangle relationships using the binomial theorem
Topic: binomial theorem
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Using the discriminant to investigate the roots of a quadratic
Topics: discriminant, quadratic
Geometry Lectures by Nigel Simmons
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Looking at some properties of the parabola
Topics: parabola, parametrics
Geometry Lectures by Nigel Simmons
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The technique of inducing a proof.
Topics: mathematical induction, series
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Using the first derivative to help sketch curves.
Topics: calculus, curve sketching
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Describing the locus of points
Topics: locus, parabola
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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How to use the second derivative to help curve sketching
Topics: concavity, calculus
Geometry Lectures by Nigel Simmons
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Solving inequalities vis induction
Topics: induction, inequalities
Geometry Lectures by Nigel Simmons
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Introducing number patterns
Topic: arithmetic series
Geometry Lectures by Nigel Simmons
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generalising the factorisation of two terms to the same index
Topic: factorisation
Geometry Lectures by Nigel Simmons
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Using the theory to solve the problems
Topic: series
Geometry Lectures by Nigel Simmons
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Using series to solve finance problems
Topics: series, finance
Geometry Lectures by Nigel Simmons
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Calculating the mean of different types of wequences.
Topics: mean, series
Geometry Lectures by Nigel Simmons
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Using the induction technique for prrof of a sum of series
Topics: series, induction
Geometry Lectures by Nigel Simmons
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Defining some terms that are used with polynomials.
Topic: polynomials
Geometry Lectures by Nigel Simmons
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Looking at a couple of past questions
Topic: induction
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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The reaminder and factor theorems
Topics: polynomials, factor theorem, remainder theorem
Geometry Lectures by Nigel Simmons
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What happens when we can't find an integral?
Topics: integration, approximation
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Using integration to find area.
Topics: integration, area
Geometry Lectures by Nigel Simmons
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Using the patterns of series to solve problems.
Topics: series, geometric series, arithmetic series
Geometry Lectures by 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
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Standard integrals involving inverse trig
Topics: inverse trig, calculus
Geometry Lectures by Nigel Simmons
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Defining the inverse trig functions.
Topic: inverse trig
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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An extension to Pythagoras Theorem
Topics: trigonometry, cosine rule
Geometry Lectures by Nigel Simmons
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Putting the different ideas together in order to solve probability problems
Topic: probability
Geometry Lectures by Nigel Simmons
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Representing inequalities on the number plane.
Topic: regions
Geometry Lectures by Nigel Simmons
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The steps involved in solviong trig equations.
Topics: trigonometry, equations
Geometry Lectures by Nigel Simmons
- Nigel Simmons
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Deriving the sine rule
Topic: trigonometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Converting between different angular measures
Topic: radians
Geometry Lectures by Nigel Simmons
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A different way of measuring angles
Topics: radians, trigonometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Defining and using the t results
Topic: t results
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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The first look at some angle theorems
Topics: geometry, ange theorems
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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differentiation via the method of first principles
Topics: calculus, first principles
Geometry Lectures by Nigel Simmons
audio

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Similar triangle proofs are similar to congruent riangle proofs
Topics: geometry, similarity
Geometry Lectures by Nigel Simmons
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Taking a cartesian approach to parabola questions.
Topics: parabola, parametrics, tangents, normals
Geometry Lectures by Nigel Simmons
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Using a cartesian approach to find tangents and normals
Topics: parabola, tangets, normals
Geometry Lectures by Nigel Simmons
audio

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Using the theorems in reverse
Topic: geometry
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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A parametric approach to tangent and normal problems.
Topic: parametriv parabola tangent normal
Geometry Lectures by Nigel Simmons
- Nigel Simmons
audio

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Creating the double angle formulae
Topics: trigonometry, double angles
Geometry Lectures by Nigel Simmons
audio

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How to find the slope of a tangent when you only know one point.
Topic: tangent
Geometry Lectures by Nigel Simmons
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Differentiating a function divided by a function
Topics: calculus, quotient rule
Geometry Lectures by Nigel Simmons
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Deriving functions diveded
Topics: calculus, quotient