Bayes Theorem A basic introduction to Bayes theorem through a simple example plus an alternative derivation of the expression.
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Bernouilli numbers a very simple method to calculate them.
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curvature An initial stab at a topic that is clearly a lot deeper than I realised with a first result that seems to make a simple idea more complicated.
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differentiating trig functions A simple explanation of the actual effect of differentiating a trig function and deriving the periodicity of sin and sinh.
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dividing fractions When dividing by a fraction why do we invert then multiply. Acknowledgments to Osomnofu Online Maths. Check him out
Lizzie's Method for factorising quadratics. A rediscovery by an American HIgh School girl of Vieta's Theorem that baffled her teacher.
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exponential function A clear explanation of the exponential function and a neat derivation of Euler's equation.
logarithms The twelve rules of logarithms explained in one consistent logical sequence using consistent algebra. This is a world's first.
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normal distribution Differentiating the normal distribution curve function helps understand its characteristics
negative numbers My PGCE submission for a lesson on negative numbers
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Fitzgerald Lorentz contraction A basic derivation of the Lorentz factor by investigating swimmers crossing a river.
locating quartiles A full explanation of exactly how to locate a quartile in all circumstances - it's a cycle of 4.
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physics_equations A clear derivation of the equations of motion, force, work and energy that students at degree level still get wrong.
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proof God Godël's proof of the existence of God with symbol meaning. There's just no arguing about this anymore.
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solving_quadratics_1 A clear explanation how to derive the quadratic formula by "completing the square".
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solving_quadratics_2 An investigation of quadratics using the TI-83/84 to consolidate a clear understanding.
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standard_integrals.pdf A summary of 9 standard integrals giving inverse trig functions with log equivalents including complex forms.
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theory of equations Manipulating roots is not as tricky as it looks if we use a bit of clear notation.
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trig calculus summary A summary sheet of the differential and integral of all 24 functions including domains.
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trigonometric functions A narrative explanation of the 24 trigonometric functions
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units_measurement a simple summary sheet of the Imperial and SI base quantities and key derived units. Did you know Imperial is also metric?
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further trig relationships Derivation of four more trig equations.
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log_differentiation Deriving the first differential of some of the more interesting functions using logs
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double_angle_formula Why does an asymmetry arise between cosine and sine which is most apparent in the double angle formulae
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Inverse trigonometric functions Determining the relationship between inverse circular and hyperbolic function requires clear thinking
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reduction formulae Deriving of the main trig reduction formulae.
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two variable statistics A straightforward one page summary explaining how we determine the correlation between two variables whether from tables or plots.
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speeding Yes I had to attend a speeding course to avoid points. I was interested in the effects of speeding if it came to hitting a child outside a school. A frightening result.
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