Pre-Calculus : Semester 1 Final Study Guide
[ DOK1, 2]
B) Find the key features of the following rational functions, then sketch:
CC1 – DOK1, 2
‘
CC3 DOK2,3 - Solve the equations (no calculator):
CC3 Trig Functions – Mock Quiz
Scale: NY
1
2
3
4
Fill in the chart below:
a ) sec135o 
5

3
 5 
c) cos 

6


7
d ) cot

4
b) sin
 2
2
f ) tan   1
e) cos  
g )  4 cos   2 2  0
CC3 Trig Functions – Mock Quiz
Scale: NY
1
2
3
4
Fill in the chart below:
a ) sec135o 
5

3
 5 
c) cos 

6


7
d ) cot

4
b) sin
 2
2
f ) tan   1
e) cos  
g )  4 cos   2 2  0
CC3 Trig Functions – Mock Quiz
Scale: NY
1
2
3
4
Fill in the chart below:
a ) sec135o 
5

3
 5 
c) cos 

 6 
7
d ) cot

4
b) sin
 2
2
f ) tan   1
e) cos  
g )  4 cos   2 2  0
PLEASE NOTE: This CC3 Mock Exam covers only DOK1 and DOK2 problems
Solutions:
Unit Circle + Special Triangles + Trig Functions
Mock Test: Concept Category 1: Analyzing Mathematical Models
DOK1] Recall & Reproduction For the function
not exist, explain why.
whose graph is given, state the value of each quantity, if it exists. If it does
DOK2] Routine
A ) Find the equation of the line tangent(AROC) to the function
when
.
B) For the function
defined below, state the value of each quantity, if it exists. If it does not exist, explain why.
i.
ii.
iii.
iv.
C) Algebraically analyze the function shown below to find the key features, then use the key features to sketch the graph.
D) Find the IROC for y 
x3
E) Sketch the graph of an example of a function
,
that satisfies all of the given conditions:
,
,
F) WRITE DOWN all of the key terms and formulas you need to know for CC1
DOK3 Problem
E)
IROC Formula
AROC Formula
f ( x )  f (a )
xa
where a  given number
Tangent Line Slope at a
lim
xa
f ( x )  f (a )
xa
Mock Final CC2
DOK1, 2]
Solve: 2(5  3x1 )  2  98
Find the inverse of the function f ( x )  3 2 x  5  7
Solve: Log2 ( x  2)  Log2 ( x  1)  2
Solve: Log3 (2 x 2  4 x)  Log3 (3x  6)  3
DOK3]
Sketch f ( x )  2 x  3
Find : lim f ( x ) 
lim f ( x ) 
x
x
f ( 1) 
f (0) 
f (1) 
x
1
Sketch f ( x )     2
 3
Find : lim f ( x ) 
lim f ( x ) 
x 
x 
f ( 1) 
f (0) 
f (1) 
Use the limits described to sketch a graph, then create an exponential (or Log) equation for the sketch you have:
lim f ( x)  
x
lim f ( x)  5
f (0)  3
x
AND: Study all the application (word) problems from your quick checks and mastery checks !!!!
Mock Final CC2
DOK1, 2]
Solve: 2(5  3x1 )  2  98
Find the inverse of the function f ( x )  3 2 x  5  7
Solve: Log2 ( x  2)  Log2 ( x  1)  2
Solve: Log3 (2 x 2  4 x)  Log3 (3x  6)  3
DOK3]
Sketch f ( x )  2 x  3
1
 3
Find : lim f ( x ) 
x
lim f ( x ) 
x
f ( 1) 
f (0) 
f (1) 
x
Sketch f ( x )     2
Find : lim f ( x ) 
x 
lim f ( x ) 
x 
f ( 1) 
f (0) 
f (1) 
Use the limits described to sketch a graph, then create an exponential (or Log) equation for the sketch you have:
lim f ( x)  
x
lim f ( x)  5
x
f (0)  3
AND: Study all the application (word) problems from your quick checks and mastery checks !!!!
Extra Practice:
CC3 DOK3]
Verify (prove) the following statements:
a ) sin  sec   tan 
c)
b)
1  cos 
 csc   cot 
sin 
1
1

sin  cot  cos 
CC2 DOK3]
Sketch based on the description then create an exponential or Log equation based on the sketch:
a ) lim f ( x)  
x
b) lim f ( x)  
x
lim f ( x)  1
x
lim f ( x)  3
x
f (0)  5
f (0)  1
CC1 DOK3]
lim f ( x )  
x
f (3)  NS
lim f ( x )  4
x
f (0)  0.2
f ( 1)  1
lim f ( x )  
x4
lim f ( x )  
x2
lim f ( x )  
x4
lim f ( x )  
x2
Extra Practice
CC1] Find the limits:
a ) lim
x 0
1 x 1
x
b) lim
x c
c2  x  c
c
c) Find the slope then the equation of the tangent line (AROC): f ( x ) 
d) Create a sketch:
lim f ( x)  2
x
lim f ( x)  1.6
x
lim f ( x)  
x2
3
x3
x2
lim f ( x)  
lim f ( x)  1.2
x2
x3
f (3)  NS
b) Solve: 12  4(7)2 x5
CC2] a) Find the inverse: f ( x )  3 x  3  10
c) Solve
0  3e x  12e x  5
d) Solve Log4 (4 x 2  3)  Log4 ( x  2)  2
CC3] No Calculator (Unit Circle)
a) cot
4

3
b)Solve: 3  2 csc   7
Extra Practice
CC1] Find the limits:
a ) lim
x 0
1 x 1
x
b) lim
x c
c2  x  c
c
c) Find the slope then the equation of the tangent line (AROC): f ( x ) 
d) Create a sketch:
lim f ( x)  2
x
lim f ( x)  1.6
x
lim f ( x)  
x2
3
x3
lim f ( x)  
x2
b) Solve: 12  4(7)2 x5
c) Solve
d) Solve Log4 (4 x 2  3)  Log4 ( x  2)  2
a) cot
lim f ( x)  1.2
x3
f (3)  NS
CC2] a) Find the inverse: f ( x )  3 x  3  10
CC3] No Calculator (Unit Circle)
x2
4

3
b)Solve: 3  2 csc   7
0  3e x  12e x  5