Estas con las transparencias, en Keynote, de la primera semana de mi curso de Cálculo diferencial.

1. Day 1
1. Course Guidelines
2. Critical Path to Success

2. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always be on time for class.

3. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials needed.

4. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials needed.

5. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials needed.
Notebooks

6. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials needed.
Notebooks

7. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials needed.
Pencil
Notebooks

8. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials needed.
Pencil
Notebooks

9. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always arrive to class prepared to work with all the materials needed.
Pencil
Notebooks
Pen(s)

10. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always attempt ALL their homework assignments.

11. Critical Path to Success!!
A student who wants to succeed in this course will:
• Review their class notes every night before going to bed.

12. 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.

13. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always ask LOTS of questions about anything they don’t understand.

14. Critical Path to Success!!
A student who wants to succeed in this course will:
• Always gets extra help from the teacher
when they feel they are falling
behind.

15. Factoring Review.

16. Before we start...

17. Before we start...
1. What is a prime number?

18. Before we start...
1. What is a prime number?
2. What’s factoring?

19. Before we start...
1. What is a prime number?
2. What’s factoring?
3. Why do we need factoring?

20. Day 2
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)

21. Factoring Strategy.
Step 1.
Always check for the ___________________ first.

22. Factoring Strategy.
greatest common factor
Step 1.
Always check for the ___________________ first.

23. Factoring Strategy.
Step 2.
Is the expression a -termed expression?
If yes, then try one of these three forms:
1. ________________________:
2. ________________________:
3. ________________________:

24. Factoring Strategy.
Step 2.
Is the expression a two -termed expression?
If yes, then try one of these three forms:
1. ________________________:
2. ________________________:
3. ________________________:

25. Factoring Strategy.
Step 2.
Is the expression a two -termed expression?
If yes, then try one of these three forms:
1.
a2 - b2 = (a + b)(a - b)
________________________:
2. ________________________:
3. ________________________:

26. Factoring Strategy.
Step 2.
Is the expression a two -termed expression?
If yes, then try one of these three forms:
1.
a2 - b2 = (a + b)(a - b)
________________________:
2.
a3 + b3 = (a + b)(a2 - ab + b2)
________________________:
3. ________________________:

27. Factoring Strategy.
Step 2.
Is the expression a two -termed expression?
If yes, then try one of these three forms:
1.
a2 - b2 = (a + b)(a - b)
________________________:
2.
a3 + b3 = (a + b)(a2 - ab + b2)
________________________:
a3 - b3 = (a - b)(a2 + ab + b2)
3. ________________________:

28. Factoring Strategy.
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 ______:

29. Factoring Strategy.
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 numbers whose sum is ______ and whose
product is ______. They are ______ and ______:

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

31. Factoring Strategy.
Step 3.
If it is a three -termed expression (or trinomial), it may
fall into one of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________.
Find two numbers whose sum is ______ and whose
product is ______. They are ______ and ______:

32. Factoring Strategy.
Step 3.
If it is a three -termed expression (or trinomial), it may
fall into one of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________.
-17
Find two numbers whose sum is ______ and whose
product is ______. They are ______ and ______:

33. Factoring Strategy.
Step 3.
If it is a three -termed expression (or trinomial), it may
fall into one of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________.
-17
Find two numbers whose sum is ______ and whose
-60
product is ______. They are ______ and ______:

34. Factoring Strategy.
Step 3.
If it is a three -termed expression (or trinomial), it may
fall into one of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________.
-17
Find two numbers whose sum is ______ and whose
-60 -20
product is ______. They are ______ and ______:

35. Factoring Strategy.
Step 3.
If it is a three -termed expression (or trinomial), it may
fall into one of these groups:
x2 - 17x - 60
1.The coefficient of x is 1. Example: ________________.
-17
Find two numbers whose sum is ______ and whose
-60 -20 3
product is ______. They are ______ and ______:

36. Factoring Strategy.
2. T h e c o e f f i c i e n t o f 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:

37. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
________________.
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:

38. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
6x2 - 7x - 3
________________.
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:

39. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
6x2 - 7x - 3
________________.
a. Find the product of first and last coefficients:
(6)(-3)
___________ = _____.
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:

40. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
6x2 - 7x - 3
________________.
a. Find the product of first and last coefficients:
(6)(-3)
___________ = _____. -18
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:

41. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
6x2 - 7x - 3
________________.
a. Find the product of first and last coefficients:
(6)(-3)
___________ = _____. -18
-18
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:

42. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
6x2 - 7x - 3
________________.
a. Find the product of first and last coefficients:
(6)(-3)
___________ = _____. -18
-18
b. Look for two numbers whose product is ______ and
-7
whose sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:

43. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
6x2 - 7x - 3
________________.
a. Find the product of first and last coefficients:
(6)(-3)
___________ = _____. -18
-18
b. Look for two numbers whose product is ______ and
-7 -9
whose sum is _____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:

44. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
6x2 - 7x - 3
________________.
a. Find the product of first and last coefficients:
(6)(-3)
___________ = _____. -18
-18
b. Look for two numbers whose product is ______ and
-7 -9
whose sum is _____: _____ and ______. 2
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:

45. Factoring Strategy.
2. T h e c o e f f i c i e n t o f x i s n o t 1 . E x a m p l e :
6x2 - 7x - 3
________________.
a. Find the product of first and last coefficients:
(6)(-3)
___________ = _____. -18
-18
b. Look for two numbers whose product is ______ and
-7 -9
whose sum is _____: _____ and ______. 2
c. Write the expression as four terms:
6x2 - 9x +2x - 3
d. Proceed to use Step 4 as follows:

46. Factoring Strategy.
Step 4.
If it is a -termed expression, try factoring by grouping.
Example:

47. Factoring Strategy.
Step 4.
If it is a four -termed expression, try factoring by grouping.
Example:

48. Factoring Strategy.
Step 4.
If it is a four -termed expression, try factoring by grouping.
Example: 2x2 - 3xy - 4x + 6y

49. 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

50. Homework 1.
Baldor, Algebra:
Exercise106, Problems 9, 18, 27, 36, 47, 54, 73, 83, 91, 98, 109 and
128, p. 171

51. Day 3
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

52. Quadratic Formula.
If ax2 +bx + c = 0 and a ≠ 1, then
2
−b ± b − 4ac
x=
2a

53. Exercises.
Solve the equations. Use the quadratic formula:
2 2
t + 8t + 8 = 0 x = 2x − 3

54. Trigonometry review.
What is a reference angle?

55. Trigonometry review.
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.

56. Trigonometry review.
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.

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

59. Find the reference angle θR for θ, and sketch θ and θR in standard
position.
a) -240o

60. Find the reference angle θR for θ, and sketch θ and θR in standard
position.
a) -240o b) θ = 5π/6

61. Homework 2.
Baldor, Algebra:
Exercise 266, odd numbered problems, p. 450

62. Day 4
Find the exact values of sin θ, cos θ and tan θ if
(a) θ = 5π/6 (b) θ = 315o

63. The Fundamental Identities.
1. The Reciprocal Identities.
1 1 1
csc α = sec α = cot α =
sin α cos α tan α
2. The Tangent and Cotangent Identities.
sin α cos α
tan α = cot α =
cos α sin α
3. The Pythagorean Identities.
sin 2 α + cos 2 α = 1

64. Verifying Trigonometric Identities.
Show that the following equation is an identity by
transforming the left-hand side into the right-hand side:
(sec x + tan x )(1− sin x ) = cos x

65. tan x + cos x
= sec x + cot x
sin x

66. Day 5
Class Activity.