Algebra 2
Review – Open Response – Final Exam
Name _______________________________________________
Do your work on a separate sheet of paper.
1) Olivia opened a compounded continuously account. She invested $7000 at an interest rate of 6%. How much
money is in her account after 8 years?
2) Eric invested $2000 into a compounded continuously account that had an interest rate of 4%. He currently has
$2442.80 in his account. How many years has the money been invested?
3a) Solve the system of equation and graph.
y  x2  9
y  2 x  6
3b) Verify the solution(s) solving the system
of equations algebraically.
4) Multiple Choice. Using Algebra, which point is a solution(s) of the system of equations for the equations below.
y = 13 (x – 2)2 - 3
y=
6) Solve.
3
4
x+3
a. (5, 0)
b. (0, 3)
c. (8, 9)
d. (2, -3)
150 = 4(1.2)x
7) Caroline is saving for a new $600 phone. She is starting with $75 in her account and plans to save 18% of the
previous month’s balance each month.
a) Complete the table.
b) Write an equation that represents the total money
Month
Total Saved
she saved as a function of time in months.
0
$75
c) How many months will it take her to save enough
1
$88.50
money to get her phone?
2
$104.43
3
4
5
8) Using the remainder theorem, what is the value of the function when I I divided 3x3 – 4x2 + 2x – 1 by (x + 1)?
9) Divide x3 + 3x2 – 6x – 7 by x + 4.
a) Is x + 4 a factor?
b) What is the value of f(-4)?
10) Solve. Check for extraneous solutions.
20  5 x  5 x  0
11) Solve. Check for extraneous solutions.
y 7 y 8

y 8 y 3
12) Given the following system of constraints and graph, find the value of x and y that maximizes the objective
function.
13) Superbats Inc. manufactures two different types of wood baseball bats, the Homer-Hitter and the Big Timber. The
Homer Hitter takes 8 hours to turn on the lathe and 2 hours to finish. The Big-Timber takes 5 hours to turn on the lathe
and 5 hours to finish. The total time available for trimming and lathing is 80 hours. The total time for finishing is 50
hours.
a) If 8x + 5y ≤ 80 represents one of the constraints, what do x and y represent?
b) Write an inequality to represent the time finishing the bat.
c) Graph the inequalities assuming x ≥ 0 and y ≥ 0.
d) What are the coordinates of the feasible region’s vertices?
e) The company makes $17 profit on the Homer-Hitter bat and $29 on the
Big- Timber bat. Write an objective function to maximize the profit.
f) Find the number of bats the company needs to make to maximize its
profit.
14) Find the maximum of each function and then decide which function has the largest maximum.
A)
f ( x)  7 ( x  1)  7
B)
15) Find the maximum of each function and then decide which function has the largest maximum.
A)
16) Factor completely.
B)
2x2 – 9x – 35
f ( x)  2( x  5) 2  6
17) Factor Completely. 3x3 + 3x2 – 60x
18) Add, simplify, and state all the restrictions.
7
2

x6 x2
19) Add, simplify, and state all the restrictions.
4
2

x  25 x  5
2
20) Given the equations:
a) Identify the zeros
b) Sketch the graph including zeros, end-behavior, and approximate max/min values.
f(x) = -(x + 3)(x + 1)(x – 1)
f(x) = (x – 2)(x + 1)(x + 3)