Part I: Some basics

A. Factor the following polynomials

1. 3.

3. 4.

B. Solve the following polynomials

5. 6.

7.

C. Simplify the following terms (make sure there are no negative exponents)

8. 9.

10. 11.

D. Simplify and combine like terms

12. -3(10b + 10) + 5 (b+2)13. -7(n+3) – 8(1+8n)

14. 2xy ( 1 + 2x) – 4 (3x + 4x2y) – 6y

Part II: Functions

Given and find the following

15. f(5)16. g(9)

17. f(-1)18. g(11)

19. (f + g)(4)20. (g – f)(9)

21. (f∙ g)(1)22.

23a). f◦ g(x) [also seen as f (g(x))]23b.)g◦ f (x)

23c.)What is the domain of 23 and 24?

Find the inverse of the following:

24. f(x) = 2x2 + 7

25a) f(x) = 3x – 4

25b) f(x) =

Part III: Polynomials

26. Given g(x) = 4x – 5

26a) find a line parallel to g(x) 26b) Find a line perpendicular to g(x) that passes through (1, 4)

27. Find the domain

  1. b.

Given

28a. Evaluate f(-2) 28b. Evaluate f(4)28c. Evaluate f(6)

29) Find the zeros of the polynomial by factoring:

  1. 5x2 + 10x = 0b. x2 – 6x – 27 = 0c. 2x2 + 5x – 3 = 0

d. x2 – 2x – 15 = 0e. x4 + x3 – 16x2 – 16x = 0

30) Kenzie is awesome at softball so she throws the ball off a cliff that is 200ft above the water. The heigh of the ball is given by the function h(x) = -32x2 + 45x + 200.

a) When does the ball hit the ground?

b) What is the y-intercept? What does it mean in the context of the problem?

c) What is the maximum height? When does it read the maximum height?

31. Describe the end behavior, find the roots, find the y-intercept of g(x) = x4 – 20x2 + 64

32. Suppose that the perimeter of a rectangle is 600ft. If x represents the width of the rectangle (in feet), then express the area of the rectangle as a function of x and find the width that will yield the maximum area.

33. Find the asymptotes (vertical, horizontal, slant if they exist) of

Part IV: Exponential

Use exponential growth, decay, continuous interest, or compounded interest to solve:

34) Find the account balance of the account that starts with $1000, has an annual rate of 4%, after 12 years.

35) During breathing, 12% of the air in your lungs is replaced after each breath. Write an exponential decay model for the original amount of air left in the lungs if the initial amount of air is 500mL. How much original air is left at 240 breaths?

36a) Find total investment if $7,300 is invested semi-annually at 7% for 3 years

36b) Find the balance of an account if $2,340 is invested at a rate of 3.1% compounded continuously after 3 years.

Part V: Conics

36. Classify each of the following conic sections (circle, ellipse, hyperbola, parabola)

37. Write each equation in standard form. For parabolas identify vertex, focus. For Ellipses and Hyperbolas identify the center, vertices and foci:

38. Given a conic in polar form, identity it’s graph as a parabola, hyperbola, ellipse:


Part VI Right-Angle Trigonometry

39). Findcsc θ if cotθ = 40)Find cos θ if tanθ =

41a). Find tan θ if sinθ = 41b)Find sec θ if cscθ =

For 42 – 44 Use law of sines and/or cosines to solve the triangle

42. 43.

44.

45. EOC questions similar to 5, 16, 25 from Spring 2013 and 6 from Fall 2014

Part VII: Solving Trigonometric Functions and identities

Verify each identity:

46. tan x sin x + cos x = sec x48.

49.

50. Solve the following trigonometric equations

a. 2 sin x – 1 = 0

b. sin x + = -sin x

c. Factor then solve:

Part VIII: Trigonometric Graphs

Describe the transformations from f(x) to g(x)

51a. f(x) = 2 sin (x) + 1

g(x) = sin (x) + 3

51b. f(x) =

g(x) =

51c. f(x) =

g(x) =

Part IX Parametric/Polar

52. Elimite the parameter:

X = 4t2 – 4

Y = 2

53. Convert from polar to rectangular

a) (-3, ) b) (2, )

Convert from rectangular to polar:

c) (2, 2) d) (-1, 3)

54. Convert to rectangular form:

Part X Series and Limits:

55a. Find n if

55b. Find the 10th term: -4, 12, -36, 108, -324, …

56. Find the first four terms in the sequence:

Determine if each geometric series converges or diverges

57.

58.

59.

Find the limits of the following:

60.

61.

62.