MHF4U Formulae

MHF4U Formulae

1. Unit 1: Polynomial Functions

   • k=a(n!)
   • instantaneous rate of change
   • average rate of change
   • a, k, d and c of exponential functions

2. Unit 2: Polynomial Equations and Inequations

   • quotient form
   • factor form
   • Remainder Theorem: P(x)/(x-b), P(b)=R
   • Factor Theorem: If P(b/a)=0, b is a factor of the constant term and a is a factor of the lead coefficient

3. Unit 3: Rational Functions

   • reciprocal of a linear
   • linear over a linear
   • c/k V.A.
   • -d/c V.A.
   • a/c H.A.

4. Unit 4: Trigonometry*

   • the trig triangles
   • a=θr arc length
   • Pythagorean Identity: sin2 θ+cos2 θ=1
   • Compound Angle Formulae
     • sin(A+B)=sinAcosB+sinBcosA
     • cos(A+B)=cosAcosB-sinAsinB
   • Double Angle Formulae
     • cos2A
       • =2cos^2A-1
       • =cos^2A-sin^2A
       • =1-2sin^2A
     • sin2A
       • =2sinAcosA

5. Unit 5: Trigonometric Functions*

   • f(x)=asin[k(x-d)]+c
   • f(x)=acos[k(x-d)]+c
   • P=2π/k
   • a=(max-min)/2
   • c=(max+min)/2

6. Unit 6&7: Logarithms

   • y=logbx^n
   • y=alog[k(x-d)]+c
   • Power Law of Logarithms: y=nlogbx
   • bye method: b^x=n, logbn=x
   • Product Law: log(xw)=logx+logw
   • Quotient Law: log(x/w)=logx-logw

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