AP Calc AB
Precalc Refresh Packet
Name: __________________
“Contrary to common belief, the calculus is not the height of the so-called, higher mathematics. It is, in
fact, only the beginning.” -Morris Kline
There are no calculators allowed on this packet. You should be able to do everything without a
calculator. You MUST show all work to receive CREDIT!
Part 1: Complete the following family of functions table:
Function
Graph
Domain
Range
(Bounded ?)
Identity Function
f(x) = x
Square Function
f(x) = x2
Cube Function
f(x) = x3
Reciprocal Function
f(x) = 1/x
Square Root Function
f(x) = x
Exponential Function
f(x) = ex
Natural Logarithm
Function
f(x) = ln x
Sine Function
f(x) = sin x
Cosine Function
f(x) = cos x
Absolute Value
Function
f(x) = |x|
Greatest Integer
Function
f(x) = [x]
Logistic Function
f(x) =
1
1  ex
Asymptotes
Even,Odd,
Neither
AP Calc AB
Precalc Refresh Packet
Name: __________________
Part 2: Algebra Review
Show all work – No credit will be given for answers missing appropriate work. No calculators.
Simplify the rational expression. State any restrictions on the variables domain.
1.
𝑞 2 +11𝑞+24
𝑞 2 −5𝑞−24
2.
𝑛4 −11𝑛2 +20
𝑛4 −7𝑛2 +10
Multiply or divide. State any restrictions on the variables domain.
3.
𝑧2
𝑧+1
∙
𝑧 3 +3𝑧+2
𝑧 2 +3𝑧
4.
𝐶+1
𝐶−5
∙
𝑐−2
𝑐 2 −7𝑐+10
Simplify the complex fraction.
5.
1
2
−
𝑎+2 𝑎−2
2
1
+ 𝑎−2
𝑎+2
6.
3
2
−
4𝑦 𝑦
1
3
+
𝑦 2𝑦
Solve each equation or inequality for x over the set of real numbers
7.
2x  7
2x

x 1
x4
8.
3x  5
0
( x  1)( x 4  7)
9.
10.
x2  9  x  1
2 x  3  14
11. x 2  2 x  8  0
Write the following equations described.
12. Write the equations of a line that is parallel to y = 2x + 3 and passes through the point (6,2).
13. Write the equation of a line that is perpendicular to y=-3/2x -3 and passes through the point (6,7).
AP Calc AB
Precalc Refresh Packet
Name: __________________
Simplify the following radicals.
3  4 5k 2
4
14. 4 5
16.
3
10
3
15. 32
4
3k 3
3
17. 1  5
PART III: Precalculus Review
You are expected to know the Unit Circle and all unit circle values.
Use your knowledge of the unit circle to evaluate each of the following. Leave your answers in radical
form.
Given the function below, find the amplitude, period, and phase shift (if any):
Amplitude
Period
shift (if any)
1 

sin  2 x  
2 
3
2 
19. f ( x)  2  sin  x 
3 
18. f ( x) 
Phase
______________
______________
_____________
______________
______________
______________
Use your knowledge of the unit circle to evaluate each of the following. Leave all answers in simplest
radical form.
1  1 
cos
 
20.
2
 2
21. sin  2 


1
Solve each trigonometric equation for 0  x  2 .
17. sin x 
19. cos
3
2
x
2

2
2
18. tan 2 x  1
20. 2sin 2 x  sin x  1  0
22.
tan 1 (1)
AP Calc AB
Precalc Refresh Packet
Name: __________________
Solve each exponential or logarithmic equation.
x 1
x
23. 8  16
26.
log3 ( x  7)  log3 (2 x  1)
3
4
24. 81  x
1
log x  2
9
25.
27. e2x − 2ex + 3 = 0
Expand each of the following.
28.
log 3 5x 2
ln
29.
5x
y2
Know all pertinent Trigonometric Identities. For example, the Pythagorean Identities.
Know basic vector definitions and properties.