Algebra 2
Algebra 2 Name__________________________________
Review, Unit 13 KEY Per______ Teacher_______________________
Find the least common denominator.
1. [pic] and [pic]. 2. [pic] and [pic] 1.(x-3)(x+3)(x-2)
2. 15x2(x-8)
Perform the indicated operation and simplify.
3. [pic] 4. [pic] 3.___[pic]___________
4.__[pic]_________
5. [pic] 6. [pic] 5.__[pic]_____
6.__[pic]______
Solve each equation. Check for extraneous solutions.
7. [pic] 8. [pic] 7._x=5______________
8._x=-3,x=-5__________
9. [pic] 10. [pic] 9._x=0______________
X=-2 Extra Sol
10._x=-5,x=2__________
11. [pic] 11._x=0______________
X = 7
12. The current in a river is 6 miles per hour. In her motorboat Marissa 12. ___42 mph_______
can travel 12 miles upstream or 16 miles downstream in the same amount
of time. What is the speed of her motorboat in still water?
13. Adam, Bethany, and Carlos own a painting company. To 13. ___1.6 Days________
paint a particular house alone, Adam estimates that it would take him
4 days, Bethany estimates 5 days, and Carlos 6 days. If these estimates
are accurate, how long should it take the three of them to paint the house
if they work together?
14. Kiana has made 9 of 19 free throws so far this season. Her goal is to make 14. ____6_________
60% of her free throws. If Kiana makes her next x free throws in a row, the
function f(x) = [pic] represents Kiana’s new ratio of free throws made.
How many successful free throws in a row will raise Kiana’s
percent made to 60%?
15. The lens equation [pic] + [pic] = [pic] relates the distance p of an object from a 15. ___20 cm_______
lens, the distance q of the image of the object from the lens, and the focal
length f of the lens. What is the distance of an object from a lens if the image
of the object is 5 centimeters from the lens and the focal length of the lens is
4 centimeters?
16. Serena can be described as being 8 inches shorter than her sister 16. __56 in_______
Malia, or as being 12.5% shorter than Malia. In other words, [pic] = [pic] ,
where H is Serena’s height in inches. How tall is Serena?
17. The distance between John F. Kennedy International Airport and
Los Angeles International Airport is about 2500 miles. Let S be
the airspeed of a jet. The wind speed is 100 miles per hour.
Because of the wind, it takes longer to fly one way than the other.
a. Write an equation for S if it takes 2 hours and 5 minutes longer 17a.__________________
to fly between New York and Los Angeles against the wind versus
flying with the wind.
2500 - 2500 = 2 1
S-100 S+100 12
b. Solve the equation you wrote in part a for S. 17b._500 mph___
c. Write an equation and find how much longer it would take to 17c.__________________
fly against the wind between New York and Los Angeles if the wind 2500 - 2500 = X
speed increases to 150 miles per hour and the airspeed of the jet is 525 525-150 525 +150
miles per hour. X = 2.96 hrs
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