Mathematics

• Scientific notation


  A method of writing numbers that takes advantage of powers of ten.

  
• 1/0.02


  50 == 1 / (1/50)---> 1/1 *50/1
• Estimations in division?


  While in multiplication, we adjusted each number in opposite directions...

  
  

  In division, make adjustments in the same direction. (multiplication, opposite directions)

  
  

  For example, 15.4 / 3.8 = 4.05

  
  

  16 / 4 = 4
• X^0


  X^0 = 1
• Multiplication of exponents?

  
  

  X^A x X^B = ?

  Exponents can be multiplied directly, as long as base number is the same.

  
• Division of exponents?

  
  

  X^A / X^B

  subtract

  
• Exponents of exponents?

  
  

  (X^A)^B

  multiply

  
• Fraction raised to an exponent?

  
  

  (X/Y)^A

  each number is raised to exponent ie) X^A/Y^A

  
• Negative exponets?

  
  

  X^-A


  Represent the inverse function:

  
• Fractional exponets?

  
  

  X^(A/B)


  Keep A, B root

  
  

  ie) B-root of X^A

  
• Square roots (1-20)

  
• √(2) = ?


  1.414
• √(3) = ?


  1.732
• Logarithms


  The inverse function of exponents, follow many of the same rules.
• Log rules:


  Also useful to know "p" is a shorthand for - log.

  
  

  For example, pH = -log [H+], or pKa = -log Ka

  
• Log(A)1


  0
• Log(A)A


  1
• Log[AxB]


  LogA + Log B
• Log[A/B]


  LogA - LogB
• Log[A^B]


  BlogA
• Log[1/A]


  -logA
• How to convert natural logarithms into common logarithms?

  divide lnX/2.303

  
• Estimating logarithms?


  Log[Ax10^B] = B+0.A

  
• Estimating pH ie) Log[A x 10^B]


  [B-1] . [10-A]
• Log scale 1-10 values:

  log[1]= 0

  log[2]= .30

  log[3]= .48

  log[4]= .60

  log[5]= .70

  log[6]= .78

  log[7]= .85

  log[8]= .90

  log[9]= .95

  log[10] = 1
• Trigonometric ratios Mnemonic:


  SOH CAH TOA:

  
• Trigonometric value range


  The values of

  
  

  - Sin and Cosine range form -1 to +1

  
  

  Sine starts at 0

  Cosine starts at 1

  
  

  -Tangent = -infinity to +infinity
• What is pi/2 in degrees

  90
• sine (pi/2)


  1
• Special right triangles?

  (list values)

  
• All trigonometric ratios:

  
• Trig ratio Mnemonic

  
• Fahrenheit conversion

  (C and K)

  
• 45-45-90 Triangle


  All sides are equal, sin/cos(tan) = √2/2, tan = 1