CH 8
What are the roots and what should "happen" at them for the following equation?
y= 0.5-x3(x+2)(x-3)4
x=0, wiggle
x= -2, cross
x=3, bounce
Someone is stuck on The Screamer 30 ft below ground level. What possible angles of rotation are they at?
197.45° and 342.55°
Write the summation notation for the following sequence:
50, 53, 56, ... , 83
12
∑ 50+3(n-1) or 47+3n
n=1
Simplify and write the exclusions:
15x-20 / (x-5)
TIMES
x2-2x-15 / 3x2+5x-12
simplify: 5
x ≠ 5, -3, 4/3
Expand the binomial:
(2y-3)4
16y4-96y3+216y2-216y+81
What is the end behavior for this equation?
y= -0.5x3(x+2)(x-3)4
As x approaches positive infinity, y approaches negative infinity
As x approaches negative infinity, y approaches negative infinity
Name one positive and one negative coterminal angle for 225°.
585° and -135°
Find the sum of the series:
50+12.5+3.125+...
66 and 2/3
Which option is better for Northwood if they want to deposit $200 in a bank, and keep it there for all 4 years of high school?
Option 1: 9% annual interest compounded quarterly
Option 2: 8% annual interest compounded monthly
Option 3: 8.8% annual interest compounded continuously
BEST: Option 1
Option 1: $285.52
Option 2: $275.13
Option 3: $284.38
What are the 3 criteria in order to calculate the finite sum of an infinite series?
1. It is a geometric series.
2. It is an infinite series.
3. The multiplier is less than 1, or it is a decreasing, infinite, geometric series.
Divide with polydoku or long division:
x3+x2-14x+3 / (x-3)
x2+4x-2 - (3/(x-3))
a) Convert 5pi/3 to degrees.
b) Convert 420° to radians.
a) 300°
b) 7pi/3 radians
Find the sum of the following series:
2+6+18+...+ 39366
59048
Simplify and write the exclusions:
x2-3x-10 / x2-4x-5
DIVIDE BY
x2-7x-18 / 2x2-5x-7
simplify: 2x-7 / x-9
x ≠ 9, -2, 5, -1, 7/2
Write the summation notation for the following sequence:
3, 6, 12, ... , 96
6
∑ 3(2)n-1
n=1
Determine all the roots of
3x3-4x2-9x+10
x=1
x=2
x= -5/3
List all the positive and negative signs for sine, cosine, and tangent in each quadrant.
Quadrant 1:
Sin: + Cos: + Tan: +
Quadrant 2:
Sin: + Cos: - Tan: -
Quadrant 3:
Sin: - Cos: - Tan: +
Quadrant 4:
Sin: - Cos: + Tan: -
Find the sum of the following series:
5+8+11+...+41
299
Simplify and write the exclusions:
4 / 2x+3
PLUS
x2-x-2 / 2x2+5x+3
simplify: x+2 / 2x+3
x ≠ -1, -3/2
Find the standard form equation for a polynomial that has the roots: x=3/4, x=-1-i, and goes through the point (0,-12)
y=8x3+10x2+4x-12
Factor out the following equation:
x4+5x2-36
roots:
x = 3i and -3i
x= 2 and -2
List all 6 trigonometric values for 5pi/6 radians.
sin = 1/2
cos = -sqrt3/2
tan = -sqrt3/3
csc = 2
sec = -2sqrt3/3
cot = -sqrt3
Expand the following binomial:
(3-2i)3
-9-46i
Simplify and write the exclusions:
6x-4 / 3x2-17x+10
SUBTRACT
1 / x2-2x-15
simplify: 2x+5 / (x+3)(x-5)
x ≠ -3, 2/3, 5
Graph or list the 5 descriptions of the equation below: (midline, amplitude, starting point for cosine, vertical shift, and period)
y=-2cos[1/4(x-pi)]-2
k/midline = -2
a/amplitude = -3
cos -> start at bottom amplitude
horizontal shift = pi
period = 2pi/(1/4)= 8pi