Pre-Calc Semester Exam
Name ______________________________
PRACTICE!
Non-Calculator Part
1.
x
Simplify y
2
y 2 z 3
3

x 4 z 3
2

3
2. Evaluate:
.
log 5
1
6
125
1
2
y 13 z 3
x16
i 9 3  2i 
3. Simplify 3  i
x 1
4. Find the domain of
(3,  )
 3  11i
10
5. State the transformations on the graph
y  log x to form y  3 log2 x  4  5 .
x 2  3x  2
0
2
6. Solve the inequality x  5 x  4
.
Vertical reflection over x-axis
Vertical stretch of 3
1
Horizontal shrink of 2
Right 2
Up 5
[-2, -1] U (1, 4)
7. Find all asymptotes and intercepts of
x 2  2x  3
f x  
5 x .
x-int:
x = 3 or x = -1
(3, 0) and (-1, 0)
y-int:
3x  9
3
5
1
g ( x)  2
f
(
x
)

x

3
x 2.
8. If
and
State and simplify g  f and find its
domain in interval notation.
g ( f ( x)) 
1
x 1
Domain: [3,  )
End behavior asymptote is y = x + 3
Vertical asymptote: x = 5
9. Evaluate
sin
29
6
10. Describe the end behavior of
f ( x)  10 x  20  2 x 3 using limits.
Pre-Calc Semester Exam
Name ______________________________
PRACTICE!
lim f ( x)  
1
2
11. Solve the equation for the given
interval:
3
 x  2
tan x   3 for 2
.
x
lim f ( x)  
x 
x 
12. Find two complex number roots for the
2
equation x  13  6 x .
x  3  2i
5
3
13. Find the sec and csc if
and cos   0 .
cot   
4
3


1
14. Evaluate: sin cos 3x 
1  9x 2
sec  
csc  
5
4
5
3
15. Graph f x   5 cos(3x   ) between
  x   .
1
16. Evaluate: tan  1
Check the graph on your calculator and
make sure you graphed    x   . Set x

scl = .
6
Calculator Part
5 
17. Solve the inequality
Express in interval notation.
3 
 2 ,9 


3  2x
2
3
.
x

4
18. Find the slope intercept form of the
equation of the line where f 2  3 and
f 1  4 .
y = -7x + 11
Pre-Calc Semester Exam
Name ______________________________
PRACTICE!
19. The winning times in the women’s
100-meter freestyle event at the Summer
Olympic Games since 1952 are shown in
the table at the right. Let x = 0 represent
1950, x = 1 represent 1951 and so forth.
a. Make a scatter plot on your calculator
and decide what type of regression would
be the best fit for the points. State your
answer.
Natural log regression
b. Calculate the regression and state your
equation.
y  69.97 – 4.06 ln x
Year
1952
1956
1960
1964
1968
1972
1976
1980
1984
1988
1992
1996
2000
2004
Time
66.8
62.0
61.2
59.5
60.0
58.59
55.65
54.79
55.92
54.93
54.64
54.50
53.83
53.84
c. Use your equation to make a prediction
for the winning time in 2012.
53.21 sec
20. Picaro’s packaging Plant wishes to
3
design boxes with a volume of 80 in or
less. Squares are to be cut from the corners
of a 8-in by 15-in rectangular piece of
cardboard so that the remaining flaps fold
up to form an open box. What are the
possible sizes of squares to be cut from the
cardboard?
21. Graph the piecewise function below.
 x  4 for x  0

f x     1
 x  2 for x  0
3
(0, 1.05] U [2.35, 4)
22. Suppose the number of elk after t years
in a state park is modeled by the function
1001
Pt  
1  90e 0.2t
a. What was the initial population of elk
present?
11
b. When will the number of elk be 600?
Pre-Calc Semester Exam
Name ______________________________
PRACTICE!
24.51 years
c. What is the maximum number of elk
possible in the forest?
1001
2
23. Write the equation y  2 x  4  7 x
in vertex form, describe the
2
transformations to the graph of y  x ,
then sketch a graph.
24. Find a degree 3 polynomial passing
through (-1, 24) and that has zeros -2, 1, and
5.
f(x) = 2x3 – 8x2 – 14x + 20
7
17
y  2( x  ) 2 
4
8
Vertical reflection over x-axis
Vertical stretch of 2
7
Left 4
17
Up 8
3
2
25. Find all zeros of x  6 x  7 x  4 . Show
all work.
(4, 0) and ( 1 2 , 0)
26. The angle of elevation of the top of
the TV antenna mounted on top of the
Eiffel Tower in Paris is measured to be
80º1’12” at a point 185 ft from the base
of the tower. How tall is the tower plus
27. Solve the equation. Identify any
extraneous solutions.
x
5
25

 2
x  2 x 3 x  x 6
Pre-Calc Semester Exam
Name ______________________________
PRACTICE!
TV antenna?
x = -5 is the solution. x = 3 is extraneous
x  1051.33 ft
28. Roberta took out a $100,000
mortgage for a new home at 9.25%
APR. What is her monthly payment if it
is to be over a 25 year term? What is the
total amount she paid in over the 25
years?
29. Eliminate the parameter so that the relation
defined by the parametric equations is written
for y defined as a function in terms of x, then
simplify. Also find the endpoints of the
relation for  2  t  3 .
x  t 1
R  $856.39
y  x 2  4x  3
$256,917 paid in over the life of the
loan.
30. Write an exponential equation
where f(0) = 2 and f(3) = 1.
 1
y  2 3 
 2
x
31. Solve. Identify any extraneous solutions.
logx  2  logx  5  2 log 3 .
 3  85
2
x  3.11 is the solution, x  6.11 is extraneous.
33. Find a polynomial with real number
coefficients that has 2  4i as a zero.
f ( x)  x 2  4 x  20
2 x  3x  6 x  5 x  6  0
3
Endpoints: (-1, 8) and (4, 3)
x
32. Solve the inequality graphically.
Express your answer in interval
notation.
4
y  t 2  2t
2
(1.5, 2)