San Diego State University Unit 3 Math Exam Practice

Please help with this practice exam of 18 questions. Please make sure all work is shown for all problems, and in clear handwriting (or typed, whichever you prefer).

Please make sure all work is being shown!

Unit 3 Exam
Name:________________________________________________________
Make sure to show all necessary work per problem to show understanding as described in our zoom classes and
video lessons in order to receive full credit.
1) Determine whether each statement is TRUE or FALSE. If it is TRUE, show support as to why it is TRUE.
If it FALSE, fix the error that makes the statement FALSE.
a) _________ The system below is considered consistent dependent.
4𝑥 − 8𝑦 = 12
2𝑥 − 4𝑦 = 20
b) _________ The maximum of the graph of 𝑦 = −3(𝑥 + 11)2 − 4 is −11.
c) _________ The simplified form of 5𝑖 3 (3 − 4𝑖) − (6 − 2𝑖) is −26 − 13𝑖.
d) _______ The graph of 𝑦 = 3𝑥 2 − 6𝑥 + 2 has a discriminant of 12 which means the graph passes through
the 𝑥 −axis twice.
e) _______ The rational function 𝑦 =
43−5𝑥
𝑥−7
−5
can be rewritten as 𝑦 = 𝑥−7 + 8.
2) Solving a system by substitution or elimination. Show all necessary work clearly and if you obtain one
answer, state your answer as an ordered triple.
5𝑥 − 𝑦 + 3𝑧 = 4
3𝑥 + 2𝑦 − 6𝑧 = −34
7𝑥 − 3𝑦 + 2𝑧 = −14
3) Solve the system by graphing.
{
𝑦 = 𝑥2 − 2
3𝑦 − 6𝑥 = 3
−25
4) Given the rational function 𝑓(𝑥) = 𝑥−2 + 1, answer the following questions
a) List the domain and range of the function.
b) Identify the asymptotes:
Domain:______________________________
Vertical Asymptote: __________________________
Range:________________________________
Horizontal Asymptote: ________________________
c) Show substitution work to label six points on the graph, including the
turning points.
𝑥
𝑦
d) Describe the end behavior of 𝑓(𝑥)
As 𝑥 → ∞, 𝑦 → _________ and as 𝑥 → −∞, 𝑦 → _________
5) Divide each polynomial
a)
4𝑥 5 −7𝑥 3+𝑥 2 −4𝑥+2
b)
2𝑥 2 −3𝑥−6
5𝑥 4 −4𝑥 3+3𝑥 2−2𝑥+1
𝑥−1
6) Fill in the blanks to properly set up each start for partial fraction decomposition. Do not complete the
problems, just the set up.
5𝑥+1
a) (𝑥−2)(𝑥 2+5) =
4𝑥 2 −2𝑥+11
b) 𝑥 2(3𝑥 2+7𝑥−1)2 =
+
+
+
+
7) Solve the system algebraically (using substitution or elimination).
{
(𝑥 − 2)2 + (𝑦 + 3)2 = 4
𝑥−𝑦 =3
8) Graph the plane −6𝑥 + 5𝑦 + 10𝑧 = 30 by plotting the intercepts.
z
x
y
9) Complete the partial fraction decomposition using systems of equations to solve.
5 − 38𝑥
8𝑥 2 + 2𝑥 − 1
10) Given the parabola 𝑦 = 4𝑥 2 − 32𝑥 + 39
a) Find the vertex
b) Find the x-intercepts
c) Graph and label the axis of symmetry.
12) Describe transformation from 𝑓(𝑥) = 𝑥 2 to
8
𝑔(𝑥) = − 5 (𝑥 − 1)2 + 8
11) Plot the ordered triples below on the graph
labeling them by their corresponding letters.
z
The graph is translated ____________ _____ units.
A(3,2, −4)
The graph is translated ____________ _____ units.
B(−4, −3,1)
The graph is opens ____________ since a is ______.
x
y
The graph has a vertical _______________ since a is
_______.
13) Write the equation of a parabola with a zero 9 − 2𝑖 in standard form given that the quadratic passes
through (5, 80).
b) How many times will the parabola cross through the 𝑥 −axis? Explain your reasoning.
14) Given the function ℎ(𝑥) = 5𝑥 4 + 27𝑥 3 − 93𝑥 2 + 85𝑥 − 24
a) What are the maximum number of turning points? ________
b) If −8 and 1 are two of the zeros of the polynomial, then find the fully factored form of ℎ(𝑥).
c) List all of the zeros of the function.
15) a) Rewrite the quadratic 𝑦 = −9𝑥 2 + 108𝑥 − 4 in standard form.
b) Identify the vertex:__________
c) Identify the axis of symmetry: _________
d) Does the graph have a maximum or minimum? Find it.
16) Given the function 𝑔(𝑥) = −(𝑥 − 1)2 (𝑥 + 2)(𝑥 − 3)
a) What is the degree of the polynomial? _____
b) List the zeros and their multiplicities.
𝑥
c) Describe the end behavior:
As 𝑥 → ∞, 𝑦 → _________
As 𝑥 → −∞, 𝑦 → _________
d) Graph the polynomial below labeling points in
between the zeros.
𝑦
17) Set up each word problem WITHOUT solving. Make sure to define the variables you are solving for!
a) Big 5 is a sporting goods store that sells footballs, basketballs, and volleyballs. A football costs $35, a
basketball costs $25, and a volleyball costs $15. On a given day, the store sold 5 times as many footballs as
volleyballs. They brought in a total of $3750 that day, and the money made from the basketballs alone was 4
times the money made from the volleyballs. How many footballs were sold?
b) Stella wants to create a rectangular garden in her backyard using 74 feet of fencing. She already has a
cement wall on one side where the garden will be located, meaning that she only needs three sides of fencing.
If she wants the area of the garden to be 672 square feet, then set up a system to solve for the missing
dimensions she needs for the garden.
18) Given the ration function, find the x and y intercepts without graphing.
𝑦=
3𝑥 3 +20𝑥2 −7𝑥
𝑥 2 −𝑥−6