Week 1 - Trigonometry

Day 1

1.Course Guidelines

2. Critical Path to Success

Critical Path to Success!!
A student who wants to succeed in this course will:

• Always be on time for class.


• Always arrive to class prepared to work with all the materials
needed.


needed.

Notebooks


needed.

Pencil

Notebooks


needed.

Pencil

Notebooks

Pen(s)


• Always attempt ALL their homework assignments.


• Review their class notes every night before going to bed.

The Curve of Forgetting...

Describes how we retain or get rid of information that
we take in.
It´s based on a one-hour lecture.


• Always ask LOTS of questions about anything they don’t
understand.


• Always gets extra help from the
teacher when they feel they
are falling behind.

3. Opener
2
a) What polynomial do you subtract from 3x − 8 to
get 5x −10 ?
b) Distribute: −2x 2 (4 x 5 − 5)
c) Simplify:
€ €
4 2 5 −2 ⎛10x ⎞−3
€ (5x ) (5x ) ⎜ 3 ⎟
⎝ 5x ⎠

d) What does Manero’s Steakhouse in Greenwich, CN, offer to
€ any baby born in the restaurant?
€

Day 2
1. Opener.
1. What is the first step in any factoring problem?

2. What is the first step to factor -x2 + 8x - 15?

3. On a test, Luis Gonzalez wrote the following, but the
teacher considered it to be incomplete. Explain why

15x2 - 21x - 18 = (5x + 3)(3x - 6)

4. What appetizer is most requested with a last meal?

Before we start...

1. What is a prime number?

Before we start...


2. What’s factoring?

Before we start...


2. What’s factoring?

3. Why do we need factoring?

3. Factoring Strategy.

Step 1. Always check for the _____________________ first.

3. Factoring Strategy.

greatest common factor
Step 1. Always check for the _____________________ first.

Step 2.Is the expression a -termed expression?
If yes, then try one of these three forms:

1. _______________________________:

2. _______________________________:

3. _______________________________:

Step 2.Is the expression a two -termed expression?

1. _______________________________:

2. _______________________________:

3. _______________________________:

a2 - b2 = (a + b)(a - b)
1. _______________________________:

2. _______________________________:

3. _______________________________:

a2 - b2 = (a + b)(a - b)
1. _______________________________:

a3 + b3 = (a + b)(a2 - ab + b2)
2. _______________________________:

3. _______________________________:

a2 - b2 = (a + b)(a - b)
1. _______________________________:

a3 + b3 = (a + b)(a2 - ab + b2)
2. _______________________________:

a3 - b3 = (a - b)(a2 + ab + b2)
3. _______________________________:

Step 3.If it is a -termed expression (or trinomial), it may fall into one
of these groups:
1.The coefficient of is 1. Example: ________________. Find two
numbers whose sum is ______ and whose product is ______.
They are ______ and ______:

Step 3.If it is a three -termed expression (or trinomial), it may fall into one
of these groups:
1.The coefficient of is 1. Example: ________________. Find two
They are ______ and ______:

of these groups:
1.The coefficient of x is 1. Example: ________________. Find two
They are ______ and ______:

of these groups:
x2 - 17x - 60
They are ______ and ______:

of these groups:
x2 - 17x - 60
-17
They are ______ and ______:

of these groups:
x2 - 17x - 60
-17
numbers whose sum is ______ and whose product is ______. -60
They are ______ and ______:

of these groups:
x2 - 17x - 60
-17
-20
They are ______ and ______:

of these groups:
x2 - 17x - 60
-17
-20 3
They are ______ and ______:

2. The coefficient of is not 1. Example: ________________.
a. Find the product of first and last coefficients: ___________
= _____.
b. Look for two numbers whose product is ______ and whose
sum is _____: _____ and ______.
c. Write the expression as four terms:

d. Proceed to use Step 4 as follows:

2. The coefficient of x is not 1. Example: ________________.
= _____.
sum is _____: _____ and ______.


6x2 - 7x - 3
= _____.
sum is _____: _____ and ______.


6x2 - 7x - 3
(6)(-3)
= _____.
sum is _____: _____ and ______.


6x2 - 7x - 3
(6)(-3)
-18
= _____.
sum is _____: _____ and ______.


6x2 - 7x - 3
(6)(-3)
-18
= _____.
-18
sum is _____: _____ and ______.


6x2 - 7x - 3
(6)(-3)
-18
= _____.
-18
-7
sum is _____: _____ and ______.


6x2 - 7x - 3
(6)(-3)
-18
= _____.
-18
-7 -9
sum is _____: _____ and ______.


6x2 - 7x - 3
(6)(-3)
-18
= _____.
-18
-7 -9
sum is _____: _____ and ______. 2


6x2 - 7x - 3
(6)(-3)
-18
= _____.
-18
-7 -9
sum is _____: _____ and ______. 2
6x2 - 9x +2x - 3

Step 4.If it is a -termed expression, try factoring by grouping.

Example:

Step 4.If it is a four-termed expression, try factoring by grouping.

Example:

Step 4.If it is a four-termed expression, try factoring by grouping.

Example: 2x2 - 3xy - 4x + 6y

4. Exercises
Factor each expression completely.

4 2 3
1. x − 9x 2. x − 27
3 2
3. x + 8 4. 4t + 16t + 16
2 2
5. y − 9y + 20 6. 6m + 5m − 4

Homework 1.

Baldor, Algebra:

Exercise 106, Problems 9, 18, 27, 36, 47, 54, 73, 83, 91, 98, 109
and 128, p. 171

Day 3

1. Opener
A person is standing at the top of a building, and throws a
ball upwards from a height of 60 ft, with an initial velocity
of 30 ft per second. How long will it take for the ball to
reach a height of 25 ft from the floor?
1 2
Use the formula h = − gt + v0t + h0
2

2. Quadratic Formula
If ax2 +bx + c = 0 and a ≠ 0, then

2
−b ± b − 4ac
x=
2a

3. Exercises.
Solve the equations:

2
1. y + 3y + 2 = 0
2
2. 2m + 3m − 35 = 0
2
3. 9b = −12b − 4
2
4. 2x − 6x − 5 = 0
2
5. 2x − 5x + 1 = 0

Day 4
1. Opener

1. True or False:

a) A function is a set of ordered pairs.

b) A relation is a set of ordered pairs where the first
element of each ordered pair is never repeated.

2. What is the most recognizable ad icon of the 20th
century?

Are the following relations functions, or just relations?


f = {(1, 2), (3, 4), (5, 6)}


f = {(1, 2), (3, 4), (5, 6)}

f = {(3, 3), (3, 2), (4, 3)}


f = {(1, 2), (3, 4), (5, 6)}
Relations

f = {(3, 3), (3, 2), (4, 3)}


f = {(1, 2), (3, 4), (5, 6)}
Relations

f = {(3, 3), (3, 2), (4, 3)}

Functions


Vertical Line Test.
Sweep a vertical line across the graph of the function. If
the line crosses the graph more than once it is not a
function, only a relation.

Day 7
1. Domain and Range.
What is the domain and range of the following function?

Day 7

Domain.
Is the set of "input" or argument values for which the
function is defined.

Day 7

Domain.
Is the set of "input" or argument values for which the
function is defined.

Range.
Refers to the output of a function.

2. Examples.
What is the domain and range of the following functions?

1. f (x) = 4 − x
1
2. g(x) =
2x + 3
3. y = 1− 2x

1. Quiz 1.
Factor the following, completely:
2
1. x − 3x − 40
2. 2x 2 + 3x − 35
2
3. x − 49
2
4. z + 12z + 36
3
5. x + 8
Use the cuadratic formula to solve:
2
5x − 2x + 7 = 0

Week 1 - Trigonometry

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