WELCOME TO AP CALCULUS AB!

This course is for students that plan on majoring in a STEM (Science, Technology, Engineering, and/or Math) field in college. Instruction will focus on preparing students for the AP exam. It is expected that all students will take the AP exam in May. Students receiving a 4 or 5 on the AP exam will earn up to 5 hours of college calculus credit.

Due to the rigorous content of this course, students are expected to be in attendance each day, committed to learning, complete all assignments, seek tutoring when needed, and prepare for unit exams. To prepare for the AP exam, there will be occasional study sessions during weekends and holidays.

If you need any assistance with this summer assignment, please email Mr. Stansbury. You are expected to turn this assignment in on the first day of school for 30 points. Points will be deducted for turning the assignment in late.

LOOKING FORWARD TO SEEING YOU IN AUGUST!

ENJOY YOUR SUMMER!!!

ALGEBRA REVIEW

Without a calculator, simplify each expression.

1. √𝑥𝑥

2. eln 3 3. ln e7 4. ln 1

5. ln e 6. e3 ln x 7. 272/3 8. 4-3/2

9. x3/2(x + x5/2 – x2) 10. 𝟒𝒙𝒚−𝟐

𝟏𝟐𝒙−𝟏𝟑 𝒚−𝟓

Solve each equation. Round answers to the nearest thousandth.

11. ex = 111 12. 10e2x = 42 13. 23 e-0.12x = 38

Evaluate the functions for the given values, if 𝑓(𝑥) = 2𝑥 − 2 𝑎𝑛𝑑 𝑔(𝑥) = 𝑥2 + 2𝑥.

14. 𝑓(2) 15. 𝑔(0) 16. 𝑓(−7) 17. 𝑓(ℎ + 1)

18. 𝑔(−5) 19. 𝑔(ℎ − 1) 20. 𝑓(ℎ+1)−𝑓(ℎ)(ℎ+1)−ℎ

If 𝑓(𝑥) = �3 𝑖𝑓 𝑥 < −2

2𝑥 − 1 𝑖𝑓 − 2 ≤ 𝑥 ≤ 4𝑥2 𝑖𝑓 4 < 𝑥 ≤ 20

�

21. 𝑓(−5) 22. 𝑓(0) 23. 𝑓(7) 24. 𝑓(20) 25. 𝑓(22)

Interpreting Graphs

26.

27.

29.

28.

Graph each function and clearly indicate units on the axes provided.

30. f x` a

= x 31. f x` a

= x 2 32. f x` a

= x 3 33. f x` a

= | x |

34. f x` a

= x3pwwwwwwwwwwwwwwwwwwwwwwwwww 35. f x` a

= e x 36. f x` a

= ln x 37. f x` a

= 1xffff

38. f x` a

= 1x 2ffffff 39. f x

` a= xpwwwwwwwwwwwwwwwwwwwwwwwwww 40. f x

` a= a 2@ x 2pwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww

where a is a constant

Generalize what is happening graphically (describe the shift or reflection) when using f(x) to graph each of the following:

41. f @ x` a

________________________________________________________

42. @ f x` a

_________________________________________________________

43. f x` a

+ c _______________________________________________________

44. f x@ c` a

________________________________________________________

Identify the vertical asymptotes, horizontal asymptotes, and/or holes. If the function is discontinuous, tell where each discontinuity occurs (the x-values) and identify the type of discontinuity.

45. f(x) = 46. f(x) = 47. f(x) =

48. f x` a

= 5x2x + 1fffffffffffffff 49. f x

` a= x2@ 3x@ 4

x2@ 16ffffffffffffffffffffffffffff 50. f x

` a= x

x 2@ 1ffffffffffffffff

Solve each of the inequalities.

51. x@ 2x + 1fffffffffffff< 0 52. x2@ x@ 6

x2@ 9fffffffffffffffffffffffff≥ 0

53. x2 + 3x@ 28 ≤ 0 54. 3x3@ 12x > 0

TRIG REVIEW

Without a calculator, determine the exact value of each expression.

1. sin 0 2. sin 3π2

3. csc 5π3

4. cos π 5. cos 3π4

6. sec 11π6

7. tan 7π4

8. cot 2π3

9. cos (Sin-1 ½ ) 10. Sin-1 (sin 7π6

)

Trig Values and Graphs

11. What is the sign (positive of negative) on each trig value in the given quadrant?

Quadrant Sine Cosine Tangent Cosecant Secant Cotangent I II III IV

12. List the 3 reciprocal identities 13. List the 2 Quotient Identities

14. List the 3 Pythagorean Identities

Find all angles, when 0 < x < 2π , for which the following are true.

15. sin x = 3pwwwwwwwwwwwwwwwwwwwwww

2fffffffff 16. cos x = -1/2 17. tan x = 1

18. cot x = 3pwwwwwwwwwwwwwwwwwwwwww

3fffffffff 19. sec x = 2 20. csc x = @ 2 3p

wwwwwwwwwwwwwwwwwwwwww

3fffffffffffffffffff

21. arcsin 12fff 22. cos -1 @

2pwwwwwwwwwwwwwwwwwwwwww

2fffffffff 23. tan -1 3p

wwwwwwwwwwwwwwwwwwwwww

Sketch each graph from [0,2π] and give the domain, range, amplitude and period.

24. y = sin x

Domain: _______________ Range: _____________Amplitude = ________Period = _________

25. y = cos x

Domain: _______________ Range: _____________Amplitude = ________Period = _________

26. y = tan x

Domain: ______________ Range: ____________ Period = ________

LIMITS REVIEW

Evaluate the limit using the table.

1. lim f(x) if f(x) = x – 1 ; x ≤ 2

Use the graph to evaluate the limits for #2 – 4.

5. lim f(x) 6. lim f(x) 7. lim f(x)

Evaluate each limit algebraically.

8. lim (3x2 – 4) 9. lim √𝑥2 − 4 10. lim

x 1.9 1.99 1.999 2.001 2.01 2.1 f(x)

x→2 2x – 3 ; x > 2

x→-2 x→2 x→-1

x→0

x→-2

x→2

x→-∞ x→4+ x→4

2. lim f(x)

3. lim f(x)

4. lim f(x)

11. lim 12. lim

13. lim 14. lim

15. lim 16. lim

x→25 x→4

x→0 x→3-

x→1 x→∞

17. lim 18. lim

For each of the following functions, determine:

a) limx→1- b) limx→1+ and c) limx→1

19. f(x) = x2 – 4x + 8 ; x ≥ 1 20. f(x) = 2 ; x = 1

x→∞ x→-∞

-x2 ; x < 1

6x – 4 ; x < 1 x – 2 ; x > 1

21. 22.