Download AP Calculus - Rocky Hill School

AP Calculus Review Problems 2016.
The following topics are considered prerequisites to AP calculus. The following work will be collected
on the first day of class, Wednesday September 3rd. It will be returned the following day. On the first
four days of class that week, the material will be reviewed and there will be a test on this material on
Wednesday September 10th.
Lines
1.
For (1,4) and (12,2)
a. Find the slope of the line.
b. Find the equation of the line in point slope form.
c. Find the equation of the line in standard form.
d. Find the equation of the line perpendicular to the line in standard form that contains (7, 5).
Quadratics
Graph f(x) = −.5𝑥 ! − 2𝑥 + 5 without a calculator.
a. Identify the y intercept and the vertex.
b. Give the roots in simplest radical form.
c. Describe the concavity.
d. Identify where the function is increasing and decreasing.
3. Factor the following:
a. 𝑥 ! + 4𝑥 − 21
b. 3𝑥 ! − 5𝑥 − 2
2.
Polynomials
4.
Graph f(x) = 𝑥 − 1 ! 𝑥 + 4 𝑥 ! without a calculator
a. Identify where the function is increasing and decreasing (approximately is ok, no calculator)
b. Identify where the function is concave up and concave down. (again approximately is ok, no
calculator)
Exponents and exponential functions
5. Rewrite the following using rational exponents.
!
a. !
b.
c.
6.
!
𝑥!
!!
!
!
Give an example of a decaying exponential function.
a. Graph the function.
b. Identify the y intercept.
7. Give an example of an exponential growth function.
a. Graph the function.
b. Identify the y intercept.
c. Identify the domain and range.
Logarithmic Functions
8. Graph ln (x-3) without a calculator.
a. Give the domain and range.
b. Give the x and y intercepts if any.
Radical functions.
9. Graph f(x) = 4 − 2 + x without a calculator.
a. What is the domain and range of this function?
b. Over which intervals is the function decreasing, increasing, concave up or concave
down?
Rational Functions
!!
10. Graph !!! without a calculator.
a. What is the domain and range of the function?
b. What horizontal or vertical asymptotes are there, if there are any.
!!!
11. Graph ! ! !!!!!
a. What is the domain and range of the function?
b. What horizontal or vertical asymptotes are there, if there are any.
Functions.
12. Consider f(x) = 5 + 9 − x
a. What is f(3)?
b. What is f(2k)
c. What is f(x-8)
13. f(g(x)) = 5 + 9 − x . Suggest a possible f(x) and g(x).
Trigonometry
14. The circle below is divided into 12 equal sections. For each angle give the measure in radians
starting at 0 and give the sine, cosine and tangent values for each angle. The values need to be
exact so do not use a calculator.
0
15. Graph sin(x)
a. Find the domain and range.
b. Find all zeros between 0 and 2π
16. Graph cos(x)
a. Find the domain and range.
b. Find all zeros between 0 and 2π
17. Graph tan(x)
a. Find the domain and range.
b. Find all zeros between 0 and 2π
18. Graph sec(x)
a. Find the domain and range.
b. Find all local maximums and minimums between 0 and 2π.
19. Find sin(𝑡𝑎𝑛!! (𝑥 + 1))