WELCOME TO AP CALCULUS BC!
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 10 hours of college
calculus credit and will get their registration fee back.
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.
I am here for you! If you need any assistance with this summer assignment, please
email Ms. Price at carol.price@zacharyschools.org. 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.
I LOOK FORWARD TO SEEING YOU IN AUGUST!
ENJOY YOUR SUMMER!!!
ALGEBRA REVIEW
Without a calculator, simplify each expression.
1.
ln 1
2.
5.
9-3/2
7.
tan
ln e
3.
6.
2
3
8.
cos
eln 8
3
5
e-0.24x = 22
e3 ln x
x3/2(x + x5/2 – x2)
7
4
Solve the equation to the nearest thousandth.
10.
4.
9.
Sin-1 (sin
3
4
)
LIMITS REVIEW
Evaluate each limit.
11.
lim
x→3
12.
lim
h→0
13.
lim
x→0
14.
lim
2𝑥 2 − 3𝑥−9
𝑥−3
(𝑥+ℎ)2 − 𝑥 2
→0
15.
lim
x→0
16.
lim
x→-∞
ℎ
1−cos 𝑥
2𝑥
sin 6
sin 4
𝑠𝑖𝑛2 𝑥
4𝑥 2
2𝑥 2 − 3
𝑥− 5
18. Sketch a function whose limit as x
approaches -1 is 3, but f(-1) = -1.
17.
lim
x→∞
3𝑥 2 − 7
√𝑥 2 + 2
19. Sketch a function whose limit as x
approaches 2 exists, but f(2) is undefined.
CONTINUITY REVIEW
Identify the vertical asymptotes, horizontal asymptotes, and/or holes.
2− 𝑥
20.
f(x) =
21.
22.
2
f(x) = 2𝑥 − 8𝑥−64
𝑥 2 − 𝑥−2
𝑥 2 −16
3
f(x) = 𝑥 − 𝑥
𝑥 3 −4𝑥
23. Find the values of a and b if f(x) has a
horizontal asymptote at y = -2 and a
vertical asymptote at x = -1.
f(x) =
𝒂𝒙 + 𝟐
𝟒𝒙−𝒃
24. Is the function continuous at x = 0?
f(x) =
sin 𝑥
𝑥
2
; when x ≠ 0
; when x = 0
25. Find the value of k that makes the function continuous.
f(x) = x2 – 2 ; if x ≤ 3
3x + k ; if x > 3
DERIVATIVES REVIEW
Find the derivative of each function.
26.
f(x) = ln |x2 - 4|
27.
f(x) = etan (2x)
28.
f(x) = 4 sin3 ( ½ x)
29.
f(x) = x e5x
30.
f(x) = cos-1 x
31.
Write the equation of the normal line at (-1, 2) if x3 – 2xy – y2 + 3y = 5.
32.
Determine where f(x) = ex – x is decreasing.
33.
Find and label the critical points if f(x) =
34.
Find the points of inflection if f(x) = x4 – 4x3 + 1.
35.
Determine where f(x) = 2 sin x is concave down for [0, 2π).
4𝑥
𝑥2+ 1
.
INTEGRALS REVIEW
Evaluate each integral.
36.
∫
𝟒
𝟑
𝒙𝟐
dx
6𝑥
38.
∫
40.
∫ 𝑥(𝑥 − 4)7 dx
𝑥2− 1
dx
3
37.
∫ √1 − 2𝑥 dx
39.
∫ 2𝑒 4𝑥 dx