CLEP Algebra Study Guide
solving a matrix
(1st x 4th) minus (2nd x 3rd)
what are the 5 types of numbers in order (with acronym)
(New Ways Including Rat Reels) Natural (1, 2, 3..) Whole (+0) Integers (+ negatives) Rational (+ anything that can be a fraction) Real or irrational(+ everything else)
associative property
(a + b) + c = a + (b + c) (ab) x c = a x (bc) The way in which numbers are grouped does not change their sum or product
how to find the lowest common multiple?
1. factor 2. find LCM of coefficients first 3. find LCM of rest
identity property
2 + 0 = 2 2 x 1 = 2 the sum of any number and 0 is that number the product of 1 and any number is that number
commutative property
a + b = b + a ab = ba 2 or more numbers can be added or multiplied in any order without changing the result
perfect square trinomial
a trinomial that is the square of a binomial
Distributive Property
a(b + c) = ab + ac
inverse property
a+(-a)=0 the sum of a number and its opposite is 0
difference of 2 squares
a2-b2=(a-b)(a+b)
difference of 2 cubes
a^3-b^3=(a-b)(a^2+ab+b^2)
geometric sequence formula
an = a1 (r)^n-1 r= common ratio an= nth term a1= 1st term n= term position
arithmetic sequence formula
an = a1 + (n-1)d d= common difference an= nth term a1= 1st term n= term position
Types of mathematical sequences
arithmetic: what is added/subtracted is constant geometric: what is multiplied/divided is constant
when testing for a, b, or c, and you dont have an x value, what do you use?
b^2 - 4ac > 0
what are the 5 mathematical properties
commutative associative distributive identity inverse
how can you tell a graph/equation/points represents a function
graph: pass vertical line test equation: enter into calculator to graph points: no repeating x value
rules of logarithms
loga(1) = 0 log a(A) = 1 log (A X B) = log A + Log B log (A / B) = log A - Log B log (A^B) = B *log A log (1/A) = - log A
log to exponential form
loga(b) = c a^c = b
inverse functions
replace x's with y's
how to find domain?
set denominator equal to zero
imaginary numbers
square roots of negative numbers i^0 = 1 i^1 = i i^2 = -1 i^3 = -i i^4 = 1
when to flip sign when solving inequality
when multiplying or dividing by a negative number
quadratic formula
x = -b ± √(b² - 4ac)/2a
