Download Name:_____________________________________________ Date:________ Period:______ Regents & Final Study Guide

Name:_____________________________________________
Date:________ Period:______
Regents & Final Study Guide
Algebra 2
Regents & Final Study Guide
Important Information to Remember:
Equations:
Quadratic Formula:
Discriminant: “nature of the roots” formula: b2 – 4ac
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b2 – 4ac < 0 : imaginary roots
b2 – 4ac = 0 : real, rational, and equal roots
b2 – 4ac > 0 & a perfect square: real, rational, and unequal
b2 – 4ac > 0 & a non-perfect square: real, irrational, and unequal
Sum of the roots:
Product of the roots:
Axis of Symmetry:
How to find a quadratic equation using sum & product of roots: x2 – (sum)x + (product) = 0
Equation of a circle (center-radius form): (x – h)2 + (y – k)2 = r2 where (h,k) = center and r = radius
If you are given an equation of a circle in standard form and need to write it in center-radius form, you
must perform completing the square twice. Remember to group the x’s and y’s together.
Rational Expressions:
Simplifying a Complex Fraction: find an LCD, then multiple each “little” fraction by the LCD. Once that is
completed, factor both the numerator & denominator then reduce.
Rational Equations: To solve these, you must find an LCD. Multiply each fraction by the LCD to reduce
out the denominator. Then solve like a regular equation. You must check your answer to make sure that
the fraction is not undefined.
Adding & Subtracting Rational Expressions: To simplify , first factor the denominators, then find an LCD.
Once you find an LCD, multiply each fraction by what is “missing”. Then, combine like terms across the
numerator, leaving the denominator as the LCD. All answers must be in simplest form.
Multiplying Rational Expressions: Factor every numerator and denominator. Simplify the expression by
reducing any numerator with any denominator. Rewrite as one fraction.
Dividing Rational Expressions: Change a division problem into a multiplication one by multiplying by the
reciprocal. Then complete the problem as you would a multiplication one.
Radicals:
Fractional Exponents:
or
To Solve Radical Equations: Isolate the radical. Then square both sides. Make sure you check your
answers.
Simplifying Radicals: Look for perfect powers. For example, if you are taking a square root, look for
perfect squares.
Functions:
Domain: set of all of the x-values
Range: set of all the y-values
One-to-One: none of the elements in the range is used more than once.
Onto: all the elements in the range are used.
Vertical Line Test: used to tell if a graph is a function. If a vertical line intersects the graph more than
once, then it is not a function.
Horizontal Line Test: used to tell if a graph of a function is one-to-one. If a horizontal line intersects the
graph more than once, then it is not a one-to-one function.
Trig Functions:
Soh – Cah – Toa
Cofunctions:
x + y = 90
Radians  Degrees:
Arc Measure:
arcsin x = sin-1x
Degrees  Radians:
, where s = arc length,
arccosx = cos-1x
= angle, in radians, and r = radius
arctanx = tan-1x
Reference Angles:
You are looking for
the reference angle.
Trig Equations:
For all trig equations you must find the reference angle and quadrants that the angle terminates in.
Then, use the reference angle to find your answer.
QI: Angles in QI are their own RA
QII: 180 – RA
QIII: 180 + RA
QIV: 360 - RA
Trig Identities:
Trig Graphs:
y = asinbx
y = acosbx
|a| = amplitude
|b| = frequency
frequency: how many complete cycles you see from 0o – 360o period: how long it takes to complete 1 full
cycle
y = a sin (b(x – c)) + d
y = a cos (b(x – c)) + d
c: horizontal shift
d: vertical shift
Exponential Functions & Logs:
The inverse of an exponential function is a log. The inverse of a log is an exponential function.
is equal to
Log Rules:
(1)
(2)
(3)
Probability & Statistics:
Bernoulli’s Theorem: nCr sr fn-r
where n = # of trials, r = “exactly” # times, s = probability of success, f = probability of failure
s + f = 1 (therefore s and f must be written as either a fraction or a decimal)
at least # of trials: you must find the probability of that number and everything greater than it,
until you reach the total number of trials.
at most # of trials: you must find the probability of that number and everything less than it, until
you reach the exact probability of 0.
Binomial Expansion: find the rth term: nCr – 1 an – (r – 1) br – 1