Dif calc10week1

1. Course Guidelines.

2. Course Procedures.

3. Why do we study Math?

4. Who Am I?

Factoring Review.

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).

Factoring Strategy.

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 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 ______:

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:

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

Example:

Exercises.

Factor each expression completely.

Homework #1.

Exercise106, Problems 9, 18, 27, 36, 47, 54, 73, 83, 91, 98, 109 and 128, p. 171

Baldor, Algebra.

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?

Use the formula

Quadratic Formula.

If ax2 + bx + c = 0 and a ≠ 1, then

Exercises.Solve the equations. Use the quadratic formula.

Homework #2.

Exercise 266, Odd numbered problems, p. 450.

Baldor, Algebra.

Opener.

1. Consider equations and

Do their solutions have to be the same? Explain your answer.

2. Consider and

Are the solutions the same for both equations? Explain.

3. What is a Reference Angle?

The Reference angle for θ is the acute angle θR that the terminal side of θ makes with the x-axis.

Trigonometry Review.

Find the reference angle θR for θ, and sketch θ and θR in standard position.

a) θ = 315o b) θ = -240o

y

x

y

x

y

x

c) θ = 5π/6

Multiply degrees by to get radians.

Multiply radians by to get degrees.

Find the exact values of sin θ, cos θ and tan θ if(a) θ = 5π/6 (b) θ = 315o

Verifying Trigonometric Identities.

The fundamental identities.

1. The Reciprocal Identities.

2. The Tangent and Cotangent Identities.

3. The Pythagorean Identities.

Examples.

Show that the following equation is an identity by transforming the left-hand side into the right-hand side:

Exercises.