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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)
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)