Name: _____________________________
Pre-Calculus Honors | Chapter 1 Test
To receive credit, you must show all of your work. You may use an extra piece of paper if you
would like. Write as legibly as you can, keeping in mind that I can only grade what I am able to
read.
1. State the domain of each function. Write your answers using correct interval notation.
a. f (x) = 5x 2 -17x +1
b. y = x + 4
c. g(x) =
x +17
2x - 4
2. Find the average rate of change for the function f (x) = -2x 2 - 3x +12 over the interval
[ -5, 3] .
3. A function g(x) is an absolute value function that has been shifted 2 units to the right and 3
units down. Provide the equation for g(x) and draw its graph on the provided coordinate plane.
4. Given two functions f (x) = x 2 + 2x + 8 and g(x) = x - 5 , evaluate the following:
a. f (g(3))
b. g( f (3))
5. Given two functions f (x) = x + 3 and g(x) = 4x 2 -12x + 9 , fully simplify the following:
a. ( f + g)(x)
b. (g - f )(x)
y
y
6. Simplify ( )(x) if y(x) = 4x 2 -1 and z(x) = 2x +1. Then, provide the domain of ( )(x) .
z
z
7. Find the inverse function or relation for the following functions.
a.
f (x) = 5x +
2
3
b. g(x) = 2x 2 - 3
8. The function h(x) is graphed below. Provide the domain and range for h(x)
9. The function f (x) = -2x 5 + 4x 3 is graphed below. Using the equation and the graph, provide
and clearly label the following information:
a.
b.
c.
d.
e.
f.
Domain and Range of the function
y-intercept (label as a point (x, y))
x-intercept(s) (label as points (x, y))
Symmetry (prove evenness/oddness algebraically)
Extrema (label the points (x, y))
End behavior (in limit notation)
Name _________________________
Mr. Palermo
12/11/13
Honors Pre-Calculus
Chapter 3 Test
Directions: Sketch and analyze the graph of each function. Describe its domain, range,
intercepts, asymptotes, end behavior, and where the function is increasing or decreasing.
1. h(x)  2x 1 1

2. g(x)  log 3 (x  2)

Directions: Answer the following question.
3. Demographics In 2000, the number of people in the United States was 281,421,906. The
U.S. population is estimated to be growing at 0.88% annually.
a. Let t be the number of years since 2000. Write a function that models the annual
growth in population in the United States.
b. Predict the population in 2020 and 2030. Assume a steady rate of increase.
Directions: Evaluate the following expression.
1
2log 3 27  4 log 3
4.
3

Directions: Expand each expression.
log 2 [(2x) 3 (x 1)]
5.

6.

log 2
(x 1) 3
3
x 5
Directions: Condense each expression.
7.
2  log 7 6  2log 7 x
8.
log 3 8  log 3 x  2log 3 (x  4)


Name _________________________
Mr. Palermo
1/15/14
Honors Pre-Calculus
Honors Pre-Calculus
Mid-Chapter 4 Test
Lesson 4.1: Right Triangle Trigonometry
Directions: Solve each triangle (find all missing side lengths and all angle measures). Round
side lengths to the nearest tenth and angle measures to the nearest degree.
1.
2.
Directions: Answer the following word problems.
3. TRIATHLONS Suppose a competitor in the swimming portion of a triathlon is swimming
along the course shown. Find the distance the competitor must swim in order to reach the shore.
4. AIRPLANES A ground crew worker who is 6 feet tall is directing a plane on a runway. If the
worker sights the plane at an angle of elevation of 32º, what is the horizontal distance from the
worker to the plane?
5. MOUNT RUSHMORE The faces of the presidents at Mount Rushmore are 60 feet tall. A
visitor sees the top of Washington’s head at a 48º angle of elevation and his chin at a 44.76º
angle of elevation. Find the height of Mount Rushmore.
Lesson 4-2: Degrees and Radians
Directions: Write each degree measure in radians as a multiple of  and each radian measure in
degrees.
6.
5
a. 30º
b.
2

Directions: Identify all angles that are coterminal with the given angle. Then find and draw one
positive and one negative angle coterminal with the given angle.
7.

a. 120º
b.
3

Directions: Find the length of the intercepted arc with the given central angle measure in a circle
with the given radius. Round to the nearest tenth.
8. 45º, r = 5 miles
Directions: Find the rotation in revolutions per minute given the angular speed.
9.   104 radians/minute

Lesson 4-3: Trigonometric Functions on the Unit Circle
Directions: The given point lies on the terminal side of an angle  in standard position. Find the
values of the six trigonometric functions of .
10. (-2, -1)
Directions: Find the exact value of the following expression.
5
11. sin
6

Directions: Find the exact values of the five remaining trigonometric functions of .
5
12. sin   , cot > 0
7

Name ________________________
Mr. Palermo
4/4/14
Honors Pre-Calculus
Chapter 5 Test:
Trigonometric Identities and Equations
Part I: Multiple Choice (4 points each)
For the following, circle the correct answer.
1. Which statement is NOT true?
B. tan(-q ) =
A. tan(-q ) = - tanq
C. tan(-q ) =
sin(-q )
cos(-q )
1
cot(-q )
D. tan(-q ) = 1+ sec(-q )
2. Which method for solving trigonometric equations would be best for sin x = cos x +1?
A. Factoring
B. Multiplying by the conjugate
C. Squaring both sides
D. Using a multiple-angle identity
3. Which of the following is NOT a Half-Angle Identity for tangent?
q
1- cosq
 1  cos 
A. tan = ±
B. tan 
2
sin 
2
1+ cosq
q
sinq
q
sinq
C. tan =
D. tan =
2 1 - cosq
2 1+ cosq

4. Which of the following is equivalent to
cos x(cot 2 x +1)
?
csc x
A. tan x
C. sec x
B. cot x
D. csc x
5. If cos x = -0.45 , what is sin(x A. -0.55
B. -0.45
p
2
)
C. 0.45
D. 0.55
Part II: Short Answer (8 points each)
For the following, write out all of your work and circle the correct answer. If you do not
write out your work, you will receive no credit.
Directions: Find all solutions of each equation on the interval [0,2]
1. 2 sin  1  0

2. sec 2  
4
3

Directions: Solve each equation for all values of .
3. tan 2   tan   0

4.

1
sec  1

1
sec  1
2
Directions: Find the exact value of each trigonometric expression.
  
5. cos 
 12 

6. sin 75

Directions: Simplify each expression.

3

3
 sin sin
7. cos cos
8
8
8
8

8.
tan135  tan15
1 tan135tan15

Directions: Find the values of sin2, cos2, and tan2 for the given value and interval.
3

9. tan   3, ,2 
 2


1
10. cos  ,(0,90)
5

Name ________________________
Mr. Palermo
4/16/14
Honors Pre-Calculus
Multivariable Linear Systems & Matrices
Directions: Write the augmented matrix for each system of linear equations. (5 pts each)
3x  4 y  7z  8
4 x  2y  z  5
5x  2y  14
2x  z  8
1.
2. 2x  3y  z  6
3.
3x  y  7
5x  2y  z  4
y  2z  4



Directions: Write each system of equations in triangular form using Gaussian
elimination. Then solve the system. (10 pts. each)
4.
1 1 12 


3 2 32 

5.

2 3 1 23


3 1 4 5 

1 5 1 19 

Directions: Solve each system of equations using Gauss-Jordan elimination. (10 pts. each)
6.
4 x  2y  6
x  3y  11

7.
2x  5y  z  6
3x  2y  4z  1
5x  y  2z  6

8.
4 x  2y  z  5
2x  z  8
y  2z  4

Directions: Find AB and BA, if possible. (10 pts. each)
9.
3 0
 3 5
A  
, B  

1 2
2 0

10.
2 4 
1 6 0
A  
, B  

1 3 
3 2 1 

Directions: Find the determinant of each matrix. (5 pts. for #11, 10 pts. for #12)
11.
6 5
B  

2 2

12.

2
3 4 


A   3 6 5 

2 8 1 

Name ________________________
5/6/14
Mr. Palermo
Honors Pre-Calculus
Conic Sections Quiz:
Parabolas & Ellipses
Part I: Graphing (10 points each)
Directions: Graph the following parabolas and ellipses. For each parabola, identify the
vertex, focus, axis of symmetry, and directrix. For each ellipse, identify the center,
vertices, co-vertices, and foci.
1
2
1.  x 1  y  6
12

2. x 2 17  8y  39

3.
x  42 y  2
2
81

16
1

4. x 2  9y 2  4 x  90y  228  0

Part II: Making Equations (10 points each)
Directions: Write an equation in standard form for the following conic sections with each
set of characteristics.
5. A parabola with a Focus at (1,5) and a Vertex at (1,3).
6. A parabola with a Focus at (1,4), Opens down, and Contains (-3,1).
7. An ellipse with Vertices at (9, -3) & (-3, -1) and Foci at (7, -3) & (-1, -3).
8. An ellipse with Vertices at (8,5) & (8,-9) and the length of the Minor Axis = 6.