# 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
• 2a+b = 2a * 2b
• ya+b = ya * yb
• 2-a = 1 / (2a)
• 220 = 1024 × 1024, roughly 1 million
• 230 = 1024 × 1024 × 1024, roughly 1 billion
• Logarithms
• logbx = y, means by = x, for any b > 1
• log101000 = 3
• log21024 = 10
• logbx = logcx / logcb, for any b > 1, c > 1
• log210 is about 3.32
• logb(xy) = y logb x, for any b > 1
• logb(x y) = logb x + logb 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