Pre-Calculus Honors PRACTICE Final Exam
YOU MAY USE A CALCULATOR ON THIS PART OF THIS EXAM.
Section I: Functions, Tables, and Equations
For each table of values below,
a. (1 point each) Identify which type of function each table represents.. The
possible types of functions are:
Linear
Exponential
Quadratic
Logarithmic
Square root
Sinusoidal
Power
Polynomial
b. (2 points each) Write an equation for the function you identified. You may
use any type of formula for that type of function.
1.
X
f (x )
1
4
2
6
3
9
a.
2.
X
g (x )
b.
0
---
0.5
-1
1
0
a.
3.
X
h(x)
a.
4
13.5
2
1
b.
0
4
2
6
3
8.5
4
12
b.
4.
X
j (x)
0
3
1
1
2
-1
a.
5.
x
k (x)
b.
0
2
2
5
3
6.5
a.
6.
x
l (x)
x
𝑚(𝑥)
a.
4
8
b.
-4
0
-3
1
0
2
a.
7.
3
1
5
3
b.
-2
0
-1
4
0
0
1
0
b.
Section II: Word Problems
(Various point values) For each word problem, read the explanation carefully
and answer each question. All answers should be rounded to two decimal places.
1. Belle, one of Mr. Minnich’s stars of track and field, throws an 8.8 lb shot put
during a meet. When the shot put leaves her hand, its height is given by the
quadratic function h(t )  16t 2  14t  6 and its horizontal distance is given by
linear function d (t )  22t .
a. (2 points) At what value of t does the shot put hit the ground? (HINT:
height = 0)
b. (2 points) What is the value of d (t ) when the shot put hits the ground?
c. (1 point) The shot put competition is scored based on how far the shot put
travels. How far does Belle throw the shot put?
d. (2 points) Sketch a graph of both h(t ) and d (t ) below, from 0  t  shot
hits the ground. Make sure to label your scale and axes.
2. An absent-minded museum curator hangs a painting in full sunlight, and it begins
to lose its color intensity, thanks to solar bleaching. The color intensity as a
function of time, I  f  t  , is given in the table below.
t, days
I  f t 
5
83.8
10
78.9
15
74.2
20
69.9
25
65.8
a. (1 point) Decide whether this function is linear or exponential.
b. (2 points) Write a formula for f  t  .
c. (2 points) What was the original color intensity of the painting?
d. (2 points) What is the “half-life” of the painting’s color intensity? In other
words, when will it reach half of its original intensity?
e. (2 points) When the painting’s color intensity reaches 30, the artist will
sue.
i. Write a formula for t  f 1 ( I ) , time as a function of color
intensity
ii. Evaluate with I = 30 to find when the artist will sue the museum.
3. The Singapore Flyer is the world’s largest Ferris wheel. Its wheel has a diameter
of 150m, and it is built on top of a 15m building, from which it is boarded. It
holds 28 cars, and each full rotation takes 36 minutes.
a. (2 points) If you begin riding at the 3 o’clock position, write a formula for
your height above the ground (in meters) as a function of time (in
minutes).
b. At what time(s) is your height 120 m?
4.
A
c
2
59°
B
4
(3 points) Find all the missing sides and angles of this triangle.
a. A:
b. B:
c. c:
5. A coastal town is surrounded by a seawall that can protect against waves up to 6
meters high. Two different storm systems have created waves that meet in the
harbor of this town. One storm produces waves that can be described by the
equation
by
and the second storm’s waves are described
. As the waves reach the harbor, they merge into a
single wave that can be described by a sine function.
a. (1 point) Will the seawall be high enough to protect against the combined
wave’s maximum height?
b. (2 points) Write a single sine function for the combined wave,
YOU MAY NOT USE A CALCULATOR ON THIS PART OF THIS EXAM.
Section I: Functions: Input, Output, Solving, Evaluating, Domain, and Range
1. (1 point each) Based on the graph of h  x  , answer the following questions.
a. How do you know that h(x) is a function?
b. What is h  0  ?
c. What is h  a  ?
d. Solve h  x   1 for x .
e. Solve h( x)  0 for x.
f. Is there a value of x for which h  x   h  x  1 ? If so, what is it?
g. Is there a value of x for which h  x   h  x   1 ? If so, what is it?
2. (2 points each) Find the domain and range of each of the following functions:
a.
f ( x)  x 2  2
Domain:
Range:
b. g ( x)  9  x 2
Domain:
c. h( x) 
Range:
1
4 x
Domain:
Range:
d.
j ( x)  3e x  1
Domain:
Range:
e. k ( x)  log( x  5)
Domain:
f.
Range:
l ( x)  sin( 2 x)
Domain:
Range:
3. (2 points each) Solve each equation for all exact value(s) of t . If t is an angle,
solve in radians for 0  t  2 . If t is a nonreal number, use i.
3
1
a.  t   2
5
4
b. 2t 2  14t  20
c.
4t 5  3
d. t 3  2t 2  2t  0
e. 22.6  2e t
f.
et  4  3e 2t
g.
t  7  log 3t  6  0
 
h. 4 sin  t   1  1
3 
i.
cos 2 t  1  
1
2
j.
sin( 2t )
 3
sin t
Section II: Word Problems
For each of these problems, carefully consider the information you have been
given and think about the answer.
6. (1 point each) Let x be the number of months that a shot-put thrower has
practiced her sport. Let f  x  be the resulting distance (in feet) she can throw the
shot-put. We will assume that this distance is a function of only x and ignore
other possible factors. For each of the following expressions, write its meaning in
non-mathematical terms.
c.
f  3
d.
f (20)  35
e.
f
1
(25)
11)
Suppose p  x   2 x4 12 x3  44 x  30
a)
What are all of the possible rational roots of p  x  ?
b)
What are the zeros of p  x  ?
c)
What is the factored form of p  x  ?
d)
Graph p  x  below.
f)
Based on the graph, is the function p  x  invertible?
Section IV: Trigonometry
1. (2 points) Simplify the following trigonometric identity:
2 sin 2 
tan 