Review for Algebra 2 CC Radicals: r x p 1 r x p p r = x p r = x Imaginary Numbers: i = 1 Polynomials (to Solve) Try Factoring: i 2 = 1 Step 1: Greatest Common Factor Step 2: Count the number of terms If there are: 2 Terms: Difference of 2 Perfect Squares ( + )( - )
3 Terms: Trinomials: ax 2 + bx + c Find Factors of a and c and find the combination that adds to be c 4 Terms: Grouping -OR- Use Quadratic Formula if it s a quadratic (x 2 ) Use Long Division -OR- -OR- Graph and find where it intersects the x-axis
Conics Quadratics: y = ax 2 + bx + c Vertex Form: y = a(x h) 2 + k Vertex: (h,k) a = 1 where p is the distance from the vertex 4p to the focus or the directrix Circles: (x h) 2 + (y k) 2 = r 2 Center: (h,k) Radius: r
To put into Center-Radius form or Vertex Form Use Completing the Square: Step1: Set Variables = Constants Step 2: ADD ( b 2 )2 to both sides Step 3: Factor Exponentials: y = ab x a = initial value b = base if b>1 then increasing (growth) if 0<b<1 then decreasing (decay) To Solve for x Use LOGS
Word Problems F = A(1 ± r) t F = Future Value A = Initial Value r = Rate of Increase (+) or Decrease (-)(decimal) t = time F = A (1 + r nt n ) F = Future Value A = Initial Value r = Interest Rate (decimal) n = Number of Compoundings t = time
Logarithms (Inverse of Exponentials) To Solve put into Exponential Form log b N = e b e = N Log Rules log(xy) = log x + log y log x y = log x log y log(x) y = y log x Functions f(x) = y Is it a function? No repeating x-values No y 2 Vertical Line Test
Is it a One-to-One Function? No repeating x or y-values No x 2 or y 2 Vertical and Horizontal Line Tests Domain: x-values that can be plugged into function (where is it not defined) Range: y-values of the function (look at graph) Inverse: Switch x and y Even Function: f(x) = f( x) and Symmetric about the y-axis Odd Function: f( x) = f(x) and symmetric about the origin
Sequences Recursive: (Prior term need to find next term) a 1 = number a n = some rule using a n 1 Arithmetic: (Common Difference (d) between Terms) Rule formula given on Reference Sheet Geometric: (Common Ratio (r) between terms) Formulas given on Reference Sheet Systems Solve Graphically if allowed To solve Algebraically use substitution
3 equations with 3 unknowns Use addition method to eliminate twice Rationals Simplify: Factor and Cancel To Solve: Multiply all terms by LCD to get rid of denominators Solving in general use inverse to eliminate to a single x value Polynomials: set = 0 and factor Rational Exponents: Raise both sides to a power of the reciprocal Exponentials: Use Logs Logs: Use Exponents
Trigonometry Point on the unit circle (x,y) = (cosx, sinx) tanx = sinx cosx cscx = 1 sinx cotx = 1 tanx = cosx sinx secx = 1 cosx sin 2 x + cos 2 x = 1 Positive Signs for Trig Functions
Special Angles tan30 = 3 3 tan45 = 1 tan60 = 3 Coterminal Angles: ±360 Reference Angles: angle measure to the x-axis s = θr (arc=angle * radius)
Convert from radians to degrees and degrees to radians (given on reference sheet) 1 radian 57 degrees Trig Graphs
Transformations: y = asin(bx c) + d y = acos(bx c) + d Amplitude = a (1/2 of total height) Frequency = b (how many cycles of curve from 0 to 2π) Period = 2π b (length of one cycle) Midline: y = d (vertical shift) Horizontal Shift: c
Probability P(A and B) = P(A) * P(B) P(A or B) = P(A) + P(B) P(A and B) P(A and B) P(A B) = P(B) Independent Events: P(A B) = P(A) P(A and B) = P(A) * P(B) Statistics z-score = x μ (how many standard deviations σ from the mean your data is) p(1 p) standard devation = n Margin of Error: ±2standard deviations