Mr. Visca – Algebra 2 with Trigonometry Finals Class Notes
***FINAL: June _____ @ ___________; Room #: ______________ ***
Solving for Absolute Values
 1st: Get absolute value by itself; 2nd: drop abs val bars and set equal to both +
and – answer; 3rd: solve for each
 Ex: |2x – 6| + 10 = 22
 Inequalities Ex: |2x – 6| + 10 > 22
o Flip sign when negating your one answer
Domain and Range
 Domain = all possible ___________ of equation/graph
 Range = all possible ____________ of equation/graph
Direct/Indirect Variation
 Direct: Set up 2 _____________ equal to each other, proportions
o Ex:
 Indirect: set up 2 _______________ equal to each other
o Ex:
Correlation
 In graph, positive correlation means positive ___________
 In graph, negative correlation means negative ___________
 Numerically, correlation # should be between -1 ≤ x ≤ 1
 IN CALCULATOR: stat edit; stat calc LinReg(ax+b); vars stat EQ r;
Trig Functions:
Sin
Csc (inverse of Sin) = 1/sin
Cos
Sec (inverse of Cos) = 1/cos
Tan = sin/cos
Cot (inverse of Tan) = 1/tan OR cos/sin
Unit Circle
For any point on the unit circle, (x,y),
x = __________, and y = ______________
Radians vs Degrees Conversion
 Radians to Degrees – multiply by
 Degrees to Radians – multiply by
180
𝜋
𝜋
, then add the o symbol
, (careful if π is in radians to start or
180
not!!!)
o Simply fraction IN CALCULATOR – math enter enter
Graphing Functions:
 Amplitude – half the distance from the bottom to the top OR from the
middle to the top OR from the middle to the bottom
 Frequency – number of cycles in __________________
 Period – distance (in degrees or radians) of __________
o y = a sin bx
o a = _____________ ; b = _______________ ; 360/b = __________
Sine, Cos, Tan curves/graphs
 Moving graphs…
Quadratic Regression
 Just like Linear Regression IN CALCULATOR but use “QuadReg” instead of
LinReg;
o IN CALCULATOR: stat edit; stat calc QuadReg(ax+b);
Completing the Square:
Steps:
1) get your x’s alone on one side
2) divide by number in front of x2 if you
3) take number in front of x (not x2), divide it by 2 then square it
4) take the number from step 3 and add it to both sides, not proceed to solve
Ex) 3x2 + 12x + 6 = 0
The Quadratic Formula:
x=
Ex. x2 + 9x + 20 = 0
The imaginery #
 a negative under the radial
o √−16
√−50
 i0 = _______
 i1 = _______
 i2 = _______
 i3 = _______
Binomial Theorem
Expand: (2a + b)4
Radicals
 Simplifying exponents under radical, even numbers, divide by 2
o √16𝑥 4
√18𝑥 7 𝑦 5
 Simplify fractions w radical in bottom (composite)
o
 Rational Exponents
o 𝑥
3
4
Multiple Functions
 (f○g)(5)
f(x) = 2x + 1
g(x) = x – 2
 Inverse functions: just switch x and y and solve for y
Logs:
 Natural logs (Ln) – brings exponent down
o 32 = 2
𝑥
3
 Logs: 52 = 25 is equivalent to log525 = 2
 Properties:
simplify:
Trig Identities:
 The expression (sec2Ө) (cot2Ө)(sinӨ) is equivalent to:
 Remember to check your reference sheet on the exam; it will
contain a lot of your trig identities!
 Area of Triangle, Law of Sines and Law of Cosines are all on
reference sheet
1
o Area∆ = 𝑎𝑏𝑆𝑖𝑛𝐶
2
o Law of sines:
𝑎
𝑠𝑖𝑛𝐴
=
o Law of cosines: 𝑐 =
𝑏
=
𝑐
𝑠𝑖𝑛𝐵
𝑠𝑖𝑛𝐶
√𝑎2 + 𝑏 2 −
2𝑎𝑏𝐶𝑜𝑠𝐶
Probability
 Permutations – order matters, no repetition
𝑛!
o nPr = (𝑛−𝑟)!
 Combinations – order doesn’t matter
o nCr =
𝑛!
𝑟!(𝑛−𝑟)!
 Permutation and Combinations in calculators: math, PRB
 Binomial Probability:
o nCrprq(n-r) + nC(r+1)pr+1q(n-r+1) + nC(r+2)pr+2q(n-r+2) + ...
o p = percent, q = percent to not happen (1 – p)
Standard Deviation / Normal Bell Curve
 enter info in calculator…
o enter data in stat, edit
o stat, calc, 1-var stats, calculate
 Sx – is standard deviation for SAMPLE DATA
 σx – is standard deviation for POPULATION DATA
o to get sample or population variance, just square the Sx or σx
 Standard Bell Curve should be on reference sheet
Series and Sequence
 Series – a number pattern
o Arithmetic – common difference that is constant between all
numbers
o Geometric – common ratio, numbers are separated by some
ratio or multiple
 Can just count or use calculator
o Set mode to “SEQ”
o “y=”, nMin = 1, u(n) is your equation to your number pattern
o Look at the table to see all your numbers in that pattern
 Series
o The sum of a sequence
o You SHOULD use calculator
 Math, then option “0”