ap calculus review packet 2013 - community school of naples
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Name__________________________________ Class__________________ (AB or BC)
AP Calculus Summer Review Packet
Please complete each problem in order, on notebook paper, and staple this packet to the front. All of your work will be collected and graded on the second day of school. This summer packet requires you to review many areas of mathematics. Expect to spend quite a few hours on this assignment. You are welcome to use old notes, books, or the internet (try Paul’s online notes or Khan Academy) to look up information that you may have forgotten. If you have difficulties with any of these topics, I encourage you to be very proactive in getting help at the beginning of the year as we will not be spending much time on these topics in class. Please note that the TI-‐Nspire CAS is the recommended calculator for this course. Instruction will be based on this calculator only.
Part 1: Mixed Topics
Part 2: Additional Trig Review. No Calculators allowed!! 1. Let θ be an acute angle of a right triangle. Find the values of the other five trigonometric functions of θ.
cos θ = 7
10
2. If is an acute angle of a right triangle and sin = 40
41
, what is tan ?
Express your answer as a reduced, improper fraction, if necessary.
3. Solve ABC. Round your answer to nearest hundredth, if necessary.
b = 32 A = 30 . 4. Let (2,−2) be a point on the terminal side of an angle in standard position. Evaluate the trigonometric function of . sin = ?
5. Find the reference angle ' for = 23
12
.
6. Evaluate the expression in radians. Express your answer, in radians, as a fraction, using the word pi for , if necessary.
sin−1 − 12
⎛⎝⎜
⎞⎠⎟
7. Evaluate the expression in radians. Express your answer, in radians, as a fraction, using the word pi for , if necessary.
cos−1
− 32
⎛
⎝⎜⎞
⎠⎟
8. Solve the equation cos θ = −0.5 where 180 θ 270 .
9. What is the general solution of sin3 x − 36 sin x = 0?
A. x = 2 n or x = + 2 n
B. x =
2
+ 2 n or x = + 2 n
C. x = + 2 n
D. x =
2
+ 2 n or x = 3
2
+ 2 n
10. Verify the identity tan x + cot x = sec x csc x . 11. Simplify the expression sec θ cos θ + tan2 θ.
12. Simplify the expression sin
2
− θ
sec θ
+ cos2 θ.
13. Write an equation of the graph of y = 4 sin x translated up 2 units and right units. 14. Graph y = 3 sin(4x) + 10. 15. Graph y = 4 cos(x − 4 ) . 16. Graph y = tan(x) 17. Graph y = arctanx and give the domain and range. 18. Graph y = arcsinx and give the domain and range. Now go back and check your answer to question 6. 19. Graph y = arccosx and give the domain and range. Now go back and check your answer to question 7. 20. Solve for x: Pay attention to given domain. 3sin2 x = cos2 x for 0 ≤ x< 2πcos2x − sin2 x = sin x for -π ≤ x < πtan x + sec x = 2cos x for -∞ < x < ∞
Part 4: Limits Review
1. Evaluate: 4
5 3lim4x
xx→
+ −
−
A. 0 B. 15 C. 1
6 D. DNE E. None of these
2. Evaluate: 21
18 3limn
n i
in n→∞
=
⎛ ⎞−⎜ ⎟⎝ ⎠
∑
A. 0 B.112 C. 33
2 D. 12 E. None of these
3. Evaluate: 2
5 3lim6 4x
xx→−∞
−
+
A. 52
− B. 54
− C. 54 D. 5
2 E. None of these
4. 32
3lim 23 −−−
→ xxx
x is
A. 0 B. 1 C 41 D E None of these
∞
Part 5: You must know the following properties/identities. They are assumed knowledge in an AP Calculus class. Study them! Logs:
Also:
Trigonometry: List of most commonly used identities in AP Calc
It is expected that you know the domain/range of the following inverse functions:
Of course, don’t forget about these special triangles. You must know your trig ratios of these angles in every quadrant! Also know your trig ratios of quadrant boundary angles such as
Special Triangles
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