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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
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THe importance of prime numbers and recurring decimals
Topic: numbers
Geometry Lectures by Nigel Simmons
by NIgel Simmons
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Transversals will always cut parallel lines in the same ratio
Topics: geometry, transversals
Geometry Lectures by Nigel Simmons
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Finding the integral of exponential functions.
Topics: exponentials, integration
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Placing imaginary numbers on a graph
Topics: complex numbers, argand diagram
Geometry Lectures by Nigel Simmons
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Describing complex numbers as vectors and points
Topic: complex numbers
Geometry Lectures by Nigel Simmons
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Looking at lines in the complex plane
Topics: complex numbers, locus
Geometry Lectures by Nigel Simmons
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Partial fractions is the reverse of combining algebraic fractions.
Topics: integration, partial fractions
Geometry Lectures by Nigel Simmons
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Angular velocity vs linear velocity
Topic: circular motion
Geometry Lectures by Nigel Simmons
by 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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Looking further into the relationship between the roots and coefficients of a polynomial and extending on the Extension 1 style of question
Topics: polynomials, roots & coeffcients
Geometry Lectures by Nigel Simmons
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Creating quadraticfactors from complex roots
Topics: complex numbers, factorising
Geometry Lectures by 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
by Nigel Simmons
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investigating the forces involved with a conical pendulum
Topics: dynamics, conical pendulum
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Defining trig terms
Topic: trig
Geometry Lectures by Nigel Simmons
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De Moivre put the mod arg relations into a theorem
Topics: complex numbers, de moivre
Geometry Lectures by Nigel Simmons
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Defining the rectangular hyperbola
Topics: hyperbola, conics, rectangular hyperbola
Geometry Lectures by Nigel Simmons
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Finding the volume of solids with circular cross-sections by taking slices parallel to the axis of rotation
Topic: volumes
Geometry Lectures by Nigel Simmons
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Some properties of conics
Topic: conics
Geometry Lectures by Nigel Simmons
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Testing for multiple roots of a polynomial
Topics: polynomials, roots
Geometry Lectures by Nigel Simmons
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moving curves around the number plane
Topic: curve sketching
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Looking at some different induction questions
Topic: induction
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Newton's laws of motion and their use in solving motion problems.
Topics: motion, acceleration
Geometry Lectures by Nigel Simmons
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Taking into account resistance
Topics: motion, resistance
Geometry Lectures by Nigel Simmons
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How to operate numbers in polar form
Topics: complex numbers, mod arg
Geometry Lectures by Nigel Simmons
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Functions and the Argand Diagram
Topics: complex numbers, locus
Geometry Lectures by Nigel Simmons
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Finding the equation of a parabola from its geometrical description
Topics: locus, parabola
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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Sketching the inverse trig graphs
Topic: inverse trig
Geometry Lectures by Nigel Simmons
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Defining the inverse trig functions.
Topic: inverse trig
Integrating functons that result in a lo9garthmic function
Topics: logarithms, integration
Geometry Lectures by Nigel Simmons
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Finding solutions to difficult equations
Topic: approximations
Geometry Lectures by Nigel Simmons
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Finding the greatest coefficient/term without expanding the binomial
Topic: binomial
Geometry Lectures by Nigel Simmons
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Introducing the terms and basic ideas of probabiolity
Topic: probability
Geometry Lectures by Nigel Simmons
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How do the arrangements change when arranging in a circle?
Topic: permutation
Geometry Lectures by Nigel Simmons
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Finding the relationships & patterns of binomial coefficients
Topics: binomial theorem, coefficients
Geometry Lectures by Nigel Simmons
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Generalising the expansion using Pascal's Triangle for the binomial coefficients.
Topic: binomial theorem
Geometry Lectures by Nigel Simmons
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Techniques for how to approach factorising
Topics: algebra, factorising
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Differentiating a second time
Topics: calculus, second derivative
Geometry Lectures by Nigel Simmons
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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
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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
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Selecting the objects when order is NOT important
Topic: combination
Geometry Lectures by Nigel Simmons
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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
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Calculating the acute angle between two lines
Topics: linear function, angle between lines
Geometry Lectures by Nigel Simmons
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Waht if some of the objects we are arranging look the same?
Topic: permutation
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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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
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Putting the different ideas together in order to solve probability problems
Topic: probability
Geometry Lectures by Nigel Simmons
by 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
by Nigel Simmons
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Using the first derivative to help sketch curves.
Topics: calculus, curve sketching
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Describing the locus of points
Topics: locus, parabola
Geometry Lectures by Nigel Simmons
by 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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Polynomial results that assist when factorising
Topic: polynomial
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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What happens when we can't find an integral?
Topics: integration, approximation
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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How to induce a solution
Topics: induction, series
Geometry Lectures by Nigel Simmons
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Looking at a couple of past questions
Topic: induction
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Using integration to find area.
Topics: integration, area
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Using symmetry to sketch graphs
Topic: curve sketching
Geometry Lectures by Nigel Simmons
by Nigel Simmons
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Using the symmetry of functions to help sketching
Topic: Symmetry
Geometry Lectures by Nigel Simmons
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An extension to Pythagoras Theorem
Topics: trigonometry, cosine rule