Maths Core 3

Maths Core 3

1. Functions

   • y = f(x)
     • Composite function fg(x) can be worked out by f(g(x))
   • Transformations of graphs

2. e and ln

   • y=e^x is the same as x = ln(y)
     • ln rules
       • ln(A) + ln(B) = ln(A+B)
       • ln(A) - ln(B) = ln(A/B)
       • nln(A) = ln(A^n)
   • f(x) = e^x
   • f(x) = ln(x)

3. Triganometary

   • Minor trig functions
     • cosec(x) = 1/sin(x)
     • sec(x) = 1/cos(x)
     • cot(x) = 1/tan(x)
       • tan(x) = sin(x)/cos(x)
       • cot(x) = cos(x)/sin(x)
   • Identities
     • Compound angle formulae
       • sin(A±B) = sin(A)cos(B) ± cos(A)sin(B)
       • cos(A±B) = cos(A)cos(B) ∓ sin(A)sin(B)
       • tan(A±B) = [tan(A) ± tan(B)] / [1 ∓ tan(A)tan(B)]
     • Double angle formulae
       • sin(2A) = 2sin(A)cos(A)
       • cos(2A) = cos^2(A) - sin^2(A)
         • cos(2A) = 2cos^2(A) - 1
         • cos(2A) = 1- 2sin^2(A)
       • tan(2A) = [2tan(A)] / [1 - tan^2(A)]
     • Pythagorean identities
       • sin^2(x) + cos^2(x) = 1
         • sin^2(x) = 1 - cos^2(x)
         • cos^2(x) = 1 - sin^2(x)

4. Differentiation

   • Chain rule
     • y = f(g(x)) => dy/dx = f'(g(x)) . g'(x)
     • dy/dy = dy/du . du/dx
   • Differentials
     • y => dy/dx
     • f(x) => f'(x)
     • x^n => nx^(n-1)
     • e^x => e^x
     • ln(x) => 1/x
     • sin(x) => cos(x)
     • cos(x) => -sin(x)
     • tan(x) => sec^2(x)
     • cosec(x) => -cosec(x)cot(x)
     • sec(x) => sec(x)tan(x)
     • cot(x) => -cosec^2(x)

5. Modulus Function

   • y = |x|
     • graph
       • to draw graph just reflect at the point where it crosses the x axis

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