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Algebra 2 & Trigonometry Regents Review Sheet Regents Date (Fill in):
EQUAL Roots IMAGINARY Roots 2 UNEQUAL Roots Solving Linear/Quadratic Systems: 1.Set both equations to “y=” form. 2.Then set both equations equal to each other. 3.Solve the remaining quadratic equation for the x values.
- Substitute x back in to find y values. 2 2 2 6 5 2 2 7 3 0 (2 1)( 3) 0 1 , 3 2 2.5, 5 x x x x x x x x x y y − + = + − + = − − = = = = = 2
y x x
y x
Absolute Values Ex. Equations: Set up 2 cases: Positive case (copy over as is) Negative case: set = to negation of each term on the right Inequalities: Set up 2 cases: Positive case (copy over as is) Negative case: set = to negation of each term on the right Ex.
x x
x x x x
x x
x x
x x x x
x x
x
Less than: arrows in towards each other “AND” Greater than: arrows away from each other “OR” *CHECK all answers! Radical Equations
- Isolate the radical
- Square BOTH sides
- Solve for x. OR Solve GRAPHICALLY! Left side into Y1, right side into Y Zoom Standard (#6)
Wednesday June 18
th
, 11am
Arc Length
= Arc Length
= Central angle (in Radians)
r = radius
S r
S
θ θ
= g
Cofunctions (sin-‐cos, sec-‐csc, tan-‐cot) Cofunctions of Complementary Angles are Equal Sin (x) = cos (90 – x) Ex. sec (2x + 10) = csc (x – 40) 2x + 10 + x – 40 = 90 3x – 30 = 90 3x = 120 X = 40 Trig Graphs Y = a sin (bx) + c A = amplitude (dist from midline to max) B = frequency (how many cycles occur 0 -‐ 2 π) C = midline (average of max and min values) Period = 2π/Freq Freq = 2π/Per Setting up your axes: X-‐Axis: 4 tick marks spaced 3 boxes apart Y-‐Axis: 3 tick marks spaced 2 boxes apart π/2, π, 3π/2, 2π (same as 90, 180, 270, 360 deg) Show your work! List Amp, freq, period and midline for each graph. Label your graphs!!!
Probability
nCr (Failure)
(n-‐r)(Success)r
n = Total # of trials r = Exactly # of trials Failure = Prob of failure (for one time only) Success = Prob of success (for one time only) Binomial Expansion nCr (First Term)
(n-‐r)(Second Term)r
n = exponent r = the # of the term (one less if numerical)
Entering Data: STAT -‐> CALC -‐> 1 Var Stats L1, L
Complex Numbers +, -‐, x, / All operations can be done on calculator! Rationalize the denominator: Multiply by the conjugate of the denominator! Graphing a Complex Number: a + b i is graphed using the coordinate (a, b) Draw an arrow from the origin to the coordinate 1 2 3 4
i i
i
i i
i
Complex Fraction Multiply each “little” fraction by the common denominator Variance = (standard deviation)^2 Interquartile Range = Q3 – Q1. Regressions
- Enter data into L1 and L2.
- Turn on your scatterplot (2nd^ Y=, StatPlot 1 ON)
- Hit Zoom Stat (#9)
- Find your regression equation: hit STAT -‐
CALC, then select the appropriate regression from the list based on the question, hit enter.
- Tyoe the equation into Y1.
- Answer the questions based on the eqution in Y1 (2nd^ Trace Value or 2 nd^ Trace Intersect w/ Y2) Solving Equations GRAPHICALLY: ANY equation can solved graphically by typing the left side of the equation into Y1 and the right side of the equation into Y2. Set up an appropriate window (sometimes your ZOOM features will help you establish a good window) to graph and find the intersections (2nd^ Trace -‐> Intersect (enter, enter, enter) This will work for all quadratic, exponential, logarithmic (base 10 or “e”) trigonometric, power, etc… functions!
