Revision as of 01:24, 7 January 2020

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(xy) = y log_b x, 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).
- Should be able to answer questions about truth tables for and / or / not, and evaluate expressions of and's / or's / not's

@@ Line 22: / Line 22: @@
 ** Possible values - true, false - can mean on, off - often represented by 1, 0
 ** and, or, not - read about in [https://www.khanacademy.org/computing/ap-computer-science-principles/computers-101/logic-gates-and-circuits/a/logic-gates 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).
 ** Should be able to answer questions about truth tables for and / or / not, and evaluate expressions of and's / or's / not's