Statistical Analyses for Research I
2014-2015
Two Main Differential Tools
ANOVA
T-tests
There are many other statistical tools that are
possible and maybe needed but you will more
than likely use one of these tests
Null Hypothesis
You have been taught
Normal Distribution
Objective
The student will be able to:
s
identify properties of normal distribution
apply mean, standard deviation, and zscores
to the normal
distribution graph
determine probabilities based on z-scores
Normal Distribution
Curve
A n
Math IV HW Rational Functions
MT) ft I
Name 20 cfw_IL/Lin f
I. Find. the domain, intercepts, holes and asymptotes for each of the following:
Functions:
L ./
X.th q L3! M 3) 314111; :17
VA X 1" f hole(s)
HA 3 one 3%
m cm 42/
X f
x w 5
2 5x kt: (K
Doma
Section 9.2 The Law of Sines
Up until now we have dealt only with right triangles.
But obviously there are triangles (called oblique
triangles) that do not contain a right angle. An oblique
triangle can have all three angles acute (less than 90)
or one ob
Name: _
Class: _
Date: _
ID: A
Directions for all problems on this test: Round your decimals to three decimal places. You must show
your work. Attach all work to the back of the test when you turn it in.
Trig Test #2 Review: Non-right triangle trig
1. Giv
Verifying Trigonometric Identities
Process: make one side look exactly like the other using a combination of
trigonometric identities and algebra. You can work with only one side at a
time.
1. Algebra techniques utilized
a. FOILing
example 1
b. FOILing
ex
UNIT CIRCLE TRIGONOMETRY
The Unit Circle is the circle centered at the origin with radius 1 unit (hence, the unit
circle). The equation of this circle is x 2 + y 2 = 1 . A diagram of the unit circle is shown
below:
y
x2 + y2 = 1
1
x
-2
-1
1
2
-1
-2
We hav
Notes
Name_
To solve oblique triangles, you can use the Law of Sines and the Law of Cosines:
A
Use Law of Sines when given ASA, AAS, or SSA
(ambiguous case).
b
C
c
a
Use Law of Cosines when given SSS or SAS.
B
Law of Sines:
Law of Cosines:
Examples: Solve
Trigonometric Identities
1
Trigonometric Identities
Basic Identities:
y
sin = r
(1)
x
cos = r
(2)
y sin
tan = x =
cos
(3)
r
y
x cos
1
cot = y =
=
sin
tan
r
1
sec = x =
cos
2/3
x
(4)
r
1
csc = y =
sin
(5)
(6)
Unit Circle
/2, 90
/3, 60
/4, 45
3/4
/6,
Radians
RadiansanAlternativeMeasureforAngles
In science and engineering, radians are much more convenient (and common) than degrees. A
radian is defined as the angle between 2 radii (radiuses) of a circle where the arc between them has
length of one radiu
Acc. Math III
Practice Exam for Trig Graphing
Name_
Quiz A
Per_
Date_
1. Write an equation for the sine graph below:
2. Graph one period of f(x). Make sure to label all x-coordinates for peaks and valleys and zeros (if any)
on the final graph. Also state
Math IV Unit 4 Test 2 Study Guide Name
Know How To:
- Convert -orn degrees to radians or radians to degrees
- Determine the quadrant in which the terminal side of an angle (in degrees or radians) lies
- Determine exact trig values (all six) at a certain
Math IV Practice for Test 2, Unit 5 Name 33 (U frag
Graph 2 neriods of each of the following trigonometric functions:
0:3 .-
1. C(xfmh-y per Nu phaseshi .21?" midlineeq. 3 250.5
n.
- r , - " -77
2. T'O-s cfw_55(2yog)amp r 3 per '17,: phase shift I =
6.3. Geometric sequence.
A sequence in which each term after the first is a constant multiple of the preceding term
is called a geometric sequence.
Definition of a Geometric Sequence:
A sequence is geometric if each term after the first is obtained by mul
Accelerated Math 3 Nameg J3
Geometric Sequences & Series Date: .
A sequence is geometric if the ratios of consecutive terms are the same. This ratio (r) is called the
common ratio. In geometric sequences, the common ratio can be found by dividing any term
Acc. Math III/Math IV
Sequences and Series
Semester Exam Review Unit 2
1. Find the next term of the arithmetic sequence.
8, 9, 26, 43.
2. Find the next term of the geometric sequence.
Name_
8, 32, 128, 512.
3. A landscaper is designing a wall made of whit
Name: t +7 U 3 Mat IV/Accelerated Math 3
Class Perio : Adapted from Acc Math 3 State Task Unit 4
What is a Radian? Learning Task
-_.
.m
L
a
Take a piece of string and measure the radius of the circle. Cut the string to exactly the length of the
radius