Download HPC Sem II Exam Review

Pre Calculus (H)
Semester II Exam Review
Name:____________________________________
Class Hour: ________ Date: ________________
Chapter 12: Probability
Important Formulas / Notes to Remember:
1) How many ways can a committee of four students be formed from a pool of seven students?
2) How many different batting orders of nine players can a baseball coach make from a roster of 12 players?
3) A license plate consists of 2 letters, excluding O and I, followed by a 4 digit number that cannot have 0 in
the lead position. How many plates are possible if repeats are allowed?
4) There are 12 red marbles and 5 blue marbles in a bag. What is the probability of pulling out 4 red marbles
and 2 blue marbles?
Chapter 5: Trigonometric Functions and Graphs
Important Formulas / Notes to Remember:
5) If the point  5,12 lies on the terminal side of the angle  , find the exact value of all six trigonometric
functions.
6) If tan  
8
and cos   0 , find the exact value of csc .
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7) If cos  
 6
, and tan   0 , find sin 2 .
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8) Graph the function y  2sin x  3
Amplitude:
Vertical Shift:
Phase Shift:
Period:


9) Graph the function y  cos  x    2
4

Amplitude:
Vertical Shift:
Phase Shift:
Period:
10) Graph the function y  3csc x
Amplitude:
Vertical Shift:
Phase Shift:
Period:
11) Graph the function y  sec  3x   
Amplitude:
Vertical Shift:
Phase Shift:
Period:
12) Graph the function y  2 tan
1
x 1
4
Amplitude:
Vertical Shift:
Phase Shift:
Period:
13) Graph the function y  cot x  1
Amplitude:
Vertical Shift:
Phase Shift:
Period:
Chapter 7: Solving Right and Non Right Triangles
Important Formulas / Notes to Remember:
14) Solve for the missing sides and angles of a right triangle if a  5, and b  3 .
15) Solve for the missing sides and angles of a triangle if A  40 , B  20 , and a  2 .
16) Solve for the missing sides and angles of a triangle if C  40 , a  5, and b  8 .
17) Solve for the missing sides and angles of a triangle if a  5, b  8, and c  9
Chapter 6: Inverse Trigonometric Functions and Identities
Important Formulas / Notes to Remember:
18) Give the exact value of the expression
  5  
sin 1  sin   
  6 
20) Given cot   2 and sec  0, find sin  2  .
21) Given sin   
1
and tan   0, find cos  2  .
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19) Give the exact value of the expression
3

cos  2sin 1 
5

22) Verify the identity
1  cot  1  cot    csc2   2cot 2 
24) Verify the identity
1  tan 2 
 1  2cos 2 
1  tan 2 
23) Verify the identity
sin x  cos x sin x  cos x

 sec x csc x
cos x
sin x
25) Verify the identity
cos 
1

cos   sin  1  tan 
26) Find the exact solutions to the equation on the interval 0, 2  .
sin 2 x  cos 2 x  0
27) Find the exact solutions to the equation on the interval 0, 2  .
2 cos 2   5cos   3  0
28) Find the exact solutions to the equation on the interval 0, 2  .
cos 2  6sin 2   4
29) Find the exact solutions to the equation on the interval 0, 2  .
tan x  2sin x
Chapter 8: Polar Coordinates
Important Formulas / Notes to Remember:
30) What are the rectangular coordinates for a point
 3 
that has polar coordinates  4,  ?
 2 
31) What are the rectangular coordinates for a point
3 

that has polar coordinates  2,  ?
4 

32) What are the polar coordinates for a point
33) What are the polar coordinates for a point
that has rectangular coordinates  3,0 ?
34) Plot and label the following points on the graph provided.
 2 
A  3,

 3 
3 

B  4,

2 



that has rectangular coordinates 4 3, 4 ?
Chapter 13: Limits and Derivatives
Important Formulas / Notes to Remember:
35) Find the limit, if it exists
36) Find the limit, if it exists
x3  27
lim
x 3 x  3
lim(3 x  7)
x 1
37) Find the limit, if it exists
38) Find the limit, if it exists
 3 1  cos x  
lim 

x 0
x


39) Given the function
 cos  tan  
lim 

 0



 x 2  3x

 x  3 if x > 3 


f(x)=  2
if x = 3 ,
x6


if x < 3 

 x  1
Find the limit, if it exists, lim f ( x )
x 3
40) Find the limit, if it exists lim f ( x )
x2
x 2  3x
and explain whether there is a hole or an asymptote.
x2  9
b) Find the limit as x approaches each point of discontinuity.
41)
a) Find any discontinuities of f ( x) 
42)
a) Determine where the function is discontinuous (if anywhere)
b) Determine where the function does not have a limit (if anywhere)
c) Find any x-values at which the function is not differentiable (if anywhere) and explain why.
x  2

f ( x)   1
 x 2
43)
x  2
x<2
What is the definition of the derivative?
Use the definition of the derivative to find the derivative for f ( x)  x 2  3x  1
Chapter 14: Derivatives
Important Formulas / Notes to Remember:
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44) Find the derivative f ( x)  4 x5  7 x 2  2
45) Find the derivative y 
46) Find the derivative f ( x)  4 csc x  2sec x
47) Find the derivative g ( x)  4 x5 cos x
48) Find the derivative y 
6x  5
x2  1
4x 
2 3
49) Find the derivative y  3 x  2
50) Find the derivative f ( x)  csc  x 3 
51) Find the derivative f ( x)  5 x  3x  4 
52) Find any x-values for which f ( x)  2 x 2  4 x has a horizontal tangent.
53) Find the slope of the tangent line to f ( x)  x 4  3x 2 at the point 1, 4  .
54) Find the equation of the tangent line to y  x3  x at the point (1, 2) .
55) Find the equation of the tangent line to the graph of x3  y3  2 xy at the point 1,1 .
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