The Number of total goals scored in an NHL game for the year of 2015 (NHL.com)
Data
<-Population indicated in title
Upper Limits
1
3
5
7
9
3
5
2
7
8
5
5
5
4
9
2
3
3
Sample Size:
30
Sample Error (90%)
0.6
Sample Error (95%)
0.7
4
3
90% Confidence Interval
Unit 5 Lesson 8
Chapter 12.6 Products, Quotients, Powers and Roots of Complex Numbers
Products of Complex Numbers
Using exponent laws multiply the following
[5 2 ][2 2 ]
What does this mean in general?
[1 1 ][2 2 ]
This follows for polar form
[1 (cos 1 +
Unit 3 Lesson 13
Chapter 3.4 The Graph of a Function
When graphing any functions with a table of values you must be aware of any
restrictions you may encounter.
Restrictions with a variable in a denominator (create vertical asymptote)
Restrictions of a sq
Unit 5 Lesson 7
Chapter 12.5 Exponential Form of a Complex Number
Another important form of an complex number is the Exponential form
rej = (cos + sin )
NOTE: must be in radians [ (
180
)]
Convert the following to exponential form.
a) 575(cos 135 + sin 13
Unit 4 Lesson 4
Chapter 10.4 Graphs of = , = , = , =
Complete the following table for =
Complete the following table for =
Complete the following table for =
Unit 3 Lesson 11
Chapter 7.3 Quadratic Formula
Solving Quadratics through use of the Quadratic Formula
Note the 2 4 is called the discriminant and tells us how many roots
( ) a quadratic has. We use the discriminant to check our solutions
and we can use t
Unit 2 Lesson 6
Chapter 8.1 Signs of the Trigonometric Functions
The ASTC Rule
Examples
1) Find the sign of the 6 trigonometric functions of if the terminal side of
passes through the following points.
a) (1,1)
b) (4, 3)
2) Determine the sign of the give
Unit 4 Lesson 7
Chapter 11.3 Simplest Radical Form
Radical Product Rule: =
This means if there is one radicand that is two numbers that and
multiplied under one root symbol, then you can separate them into two
separate radicals. Also two separate radical
Unit 1 Lesson 8
Chapter 5.2 Graphs of Linear Functions
Graphing by the Intercept Method
Definitions
- an Intercept is where a line crosses an axis or line
-an intercept ( ) is where the line crosses the axis
-a intercept ( ) is where the line crosses the
Unit 3 Lesson 9
Chapter 7.1 Quadratic Equations; Solutions by Factoring
When we solved Linear systems of equations we were interested in finding
the , or the point of intersection(POI). With Quadratics we are
interested in finding the intercepts (there co
Unit 4 Lesson 8
Chapter 11.4 Addition and Subtraction Radicals
Adding and subtracting radicals have many of the same characteristics
as adding and subtracting variable expressions. Recall Collecting like
terms; we would add or subtract the coefficients an
Unit 5 Lesson 1
Chapter 13.3 Properties of Logarithms
The Exponential Function
An exponential function is of the form = and has the following basic
characteristics.
1. The domain is all values of . The Range is > 0.
2. The is a horizontal asymptote of the
Unit 4 Lesson 6
Chapter 11.2 Fractional Exponents
3
Radicals are square roots ( ) , cubed roots (
) and
roots ( , ). Radicals are tools to
find the root of a number.
For example the square root of 9 is 3 or 9 = 3. Another way to
look at this tool is fin
MTH 128
Unit 4 Test
=
%
Name:_
1) Graph one period of the following functions. (if radians are given, you must use radians)
1
1
a) = 3 cos (2 45)
) = 1.8 sin (2 + 2 )
3
b) = 2 csc
(must use radians)
2) Simplify the following using exponent rules.
310
a)
Question 1
Factor the following:
There are 3 of them (first worth 4, second + third worth 3 marks)
Question 2
Simplify the following
There will be fractions (reduce, multiply, divide, add or subtract) a) 3 marks, b)4
marks, c)6 marks, d)4 marks
Question 3
Unit 1 Lesson 4
Chapter 1.9 Division of Algebraic Expressions
Dividing Polynomials by a Monomial
Remember to divide each term in the numerator by the denominator.
Example Problems
Simplify the following
2
a) (6 + 2) 2
c)
18 2 5 3 3 4 6 2
3 2
b)
95 122 +39
Unit 2 Lesson 12
Chapter 9.5 Oblique Triangles, the Law of Sines
Cosine LAW (use when given SSS or SAS )
1. To find a side in a triangle (SAS)
use;
2 = 2 + 2 2 cos
where 2 is the unknown side squared
2. To Find an angle in a triangle (SSS)
use;
2 + 2 2
Unit 4 Lesson 9
Chapter 11.5 Multiplication and Division of Radicals
Recall
Product Rule: =
and
Radical Quotient Rule: =
If there are coefficients with the radicals then multiply/divide the
coefficients and radicals separately. (see example 1 and 2 below
Unit 3 Lesson 3
Chapter 6.3 Factoring Trinomials
Factoring Easy Trinomials
Easy Trinomials are as follows: 1 2 + +
We will know these are easy trinomials since the coefficient of 2 is one.
Steps to Factoring Easy Trinomials using this general case; 1 2 +
Unit 3 Lesson 5
Chapter 6.5 Equivalent Fractions
Simplifying Rational Expressions
Recall
Simplify the following: a)
15
b)
25
125
c)
142
15 9 9
15 9 9
Now we will look at more difficult rational expressions. i.e.
)
+5
)
+5
17 2 5
)
17 2 5
When canceling in
Unit 5 Lesson 2
Chapter 13.6 Exponential and Logarithmic Functions
Recall
= =
> 0 , 1
And
= , =
> 0 , 1
Steps to solving Logarithmic Equations (with a constant)
1. If there is a constant, move all of the Logarithms to one side and use the
properties
Unit 3 Lesson 4
Chapter 6.4 Sum and Difference of Cubes
Sums and Differences of cubes
+
Expand
( + )(2 + 2 )
Now that we see that the above expansion is 3 + 3 then we can go in the other
direction.
3 + 3 = ( + )(2 + 2 )
As a starting point for the formu
Unit 5 Lesson 3
Chapter 12.1 Basic Definitions
In elementary algebra we can represent most numbers, however there are a few
exceptions that we cannot. One of which is the complex number which comes
from the negative square root.
We represent any negative
Unit 4 Lesson 5
Chapter 11.1 Simplifying Expressions with Integral Exponents
Exponent Laws
Law of Exponent Multiplication (LEM)
When multiplying two powers with the same base, keep the base
the same and add the exponents.
= (+)
Law of Exponent Division (
Unit 2 Lesson 2
Chapter 4.2 Defining Trigonometric Functions
Similar Triangles
Similar triangles are triangles that have the same shape but are not the same size.
Properties of Similar Triangles
a) Corresponding angles are equal
b) Corresponding sides are
Unit 5 Lesson 5
Chapter 12.3 Graphical Representation of Complex Numbers
The Complex Plane
The Complex Plane looks much like the Cartesian Plane (, )
with one exception. The Complex Plane points are only one
number consisting of (, ) portions. The
Cartesi