Algebra 2 Honors
First Semester Final Exam Review
Finals Review Day 2
Numbers Game
1. Solve: 4  2x  10
2. Find the domain of the function: f ( x ) 
x 2
x 5
3. Determine matrix X if AX = B
 1 2
14
A
B 

3 3
3
4. A farmer has 300ft of fencing that he wants to use to build a pen for his cow next to
an existing barn.
X
Y
a. Write the area function, A(x), representing the area of the pen.
b. What is the maximum area the farmer can create.
5. Graph the following quadratic equation:
y  2x 2  4x  3
6. Find the inverse of the following function, sketch the inverse, and state its domain:
f ( x)  x  6
7. Simplify i 13
8. Simplify (5 – 2x)3
9. Find all the zeroes for the function: p(x) = x4 – 6x3 +14x2 – 14x + 5
10. A chemical storeroom has an 80% alcohol solution and a 30% alcohol
solution. How many milliliters of each should be used to obtain 50 milliliters
of 60 % solution?
11. You are on a boat that travels 6 miles per hour upstream and 10 miles per hour downstream.
You are on the boat five hours but cannot remember when the boat went halfway and turned
around. Find the time it took the boat to go upstream and how far you traveled upstream.
12. Clear Eyes Problem – Assume that the length of time it takes a person to wake
up and start functioning in the morning varies linearly with the temperature
of the room in which he or she is sleeping. At 81°F, it takes 17 minutes to start
functioning. At 63 °F, it takes 47 minutes.
a) Define the variables, write the ordered pairs, and find the particular
equation of this function expressing time in terms of temperature.
b) Predict the time it takes to start functioning at 45 °F.
c) What temperature would cause you to take 20 minutes to start functioning?
d) Find the intercepts and tell what they mean in the real world
13. Hand glider Problem – Icann Flie loves to hand glide at a nearby beach. When
he jumps off the escarpment he dives downward toward the water until the
wind catches his hand glider, the he flies upward. Assume that his distance in
feet from the water varies quadratically with the time since he started his flight.
The escarpment is 105 feet above the water. After 5 seconds, he is 30 feet above
the water. Five seconds later, he is 21 feet above the water.
a. Define the variables, write the ordered pairs, and find the particular equation
of this function expressing distance above the water in terms of seconds in flight.
b. How high is he at 15 seconds?
c. What is his lowest point and when does it occur?
d. When will his reach a height of 200 feet?
14. A company produces Italian sausages and bratwursts at plants in Green
Bay and Sheboygan. The hourly production rates at each plant are given in
the table. How many hours should each plant be operated to exactly fill an
order for 62,250 Italian sausages and 76,500 bratwurst?
Plant
Italian Sausage
Bratwurst
Green Bay
800
800
Sheboygan
500
1000
15. Find the standard form of the equation for the quadratic function whose graph is shown.
16. A more challenging D = rt Problem 
A student group flies to Cancun for spring break, a distance of 1,200 miles.
The plane used for both trips has an average cruising speed of 300 miles per
hour in still air. The trip down is with the prevailing winds and takes 1½ hours
less than the trip back, against the same strength wind. What is the wind speed?