Math for CS Review

Note - Khan Academy Math is a good resource to look up and refresh general math knowledge. Khan Academy AP CS Principles and Khan Academy Computing also have some content related to math embedded within them.

Memorize

These are things you need to memorize.

• Order of operations: first parenthesis, then exponents, then multiplication/division/modulus, then addition and subtraction. And left to right.
• Powers/exponents
  • 2¹⁰ = 1024, roughly 1 thousand
  • 2^a+b = 2^a * 2^b
  • y^a+b = y^a * y^b
  • 2^-a = 1 / (2^a)
  • 2²⁰ = 1024 × 1024, roughly 1 million
  • 2³⁰ = 1024 × 1024 × 1024, roughly 1 billion
• Logarithms
  • log_bx = y, means b^y = x, for any b > 1
  • log₁₀1000 = 3
  • log₂1024 = 10
  • log_bx = log_cx / log_cb, for any b > 1, c > 1
  • log₂10 is about 3.32
  • log_b(x^y) = y log_b x, for any b > 1
  • log_b(x y) = log_b x + log_b y, for any b > 1
• Formulae
  • Arithmetic Sum: (1 + 2 + ... + n) = n * (n+1) / 2
  • Geometric Sum: 1 + r + r² + r³ + ... + rⁿ = (rⁿ⁺¹-1) / (r-1)
• Boolean logic
  • Possible values - true, false - can mean on, off - often represented by 1, 0
  • and, or, not - read about in Khan academy
  • De Morgan's laws: not (A and B) is equivalent to (not A) or (not B). not (A or B) is equivalent to (not A) and (not B).
  • Also, A and (B or C) is equivalent to (A and B) or (A and C). And, A or (B and C) is equivalent to (A or B) and (A or C).
  • Should be able to answer questions about truth tables for and / or / not, and evaluate expressions of and's / or's / not's