maths 099 final exam
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Math099-Review-1.pdf
Math 099 Final Exam Review for Math& 141 Page 1 of 7
Due on Wdenesday, 20th September. Name: ____________________________________________
SIMPLIFY THE FOLLOWING EXPRESSIONS. Show all appropriate work!
1. (16𝑝6) 3
2 1. _________________ (2)
2. √32𝑎6𝑏5 3
2. _________________ (3)
3. 18𝑑−3𝑡2
−54𝑑4𝑡−5 (write the answer using positive exponents only) 3. _________________ (3)
4. 2𝑥2+𝑥−3
𝑥2+2𝑥−3 4. _________________ (3)
5. 𝑥2−4
8𝑥+20 ÷
𝑥+2
12 5. _________________ (3)
6. 𝑥−1
𝑥 −
2𝑥+1
𝑥+2 6. _________________ (3)
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Show all appropriate work!
7. Simplify: √20𝑥 + 6√45𝑥 − 4√5𝑥 7. _________________ (3)
8. Rewrite log5(𝑃) = 𝑁 into exponential form. 8. _________________ (2)
9. Factor Completely: 9𝑚2 − 3𝑚𝑝 − 6𝑝2
9. _________________ (4)
SOLVE AS INDICATED.
10. √2𝑥 + 7 = 𝑥 − 4 10. ________________ (4)
11. 3𝑥 2 = 10𝑥 + 2 (write the answer in simplified radical form) 11. _________________ (4)
12. log7(3𝑥 + 1) = 2 12. ________________ (3)
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SOLVE AS INDICATED. Show all appropriate work!
13. 1
𝑥−4 −
5
𝑥+2 =
2
𝑥2−2𝑥−8 13. ________________ (4)
14. 3 ∙ 5𝑥 = 51 14. ________________ (4) (round to hundredth place)
15. Solve for 𝒙: 𝐴 = 𝐵𝑥 2 + 4 (both 𝐴 and 𝐵 are positive numbers) 15. ________________ (3)
16. The graph of 𝐹(𝑥) is shown below. Use the graph to answer the parts a) to d) below.
a. For what value(s) of 𝑥 does 𝐹(𝑥) = 4?
𝑥 = ____________________ (2) (list all solutions, separated by commas)
b. 𝐹(2) = _______________________________ (2)
c. Give the domain of 𝐹(𝑥) = _________________ (2)
x
y
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d. Give the range of 𝐹(𝑥) = ________________ (2)
Show all appropriate work!
17. Average U.S. personal income increased approximately linearly from $14,420 in 1990 to $27,589 in
2008. Estimate the average personal income in 2010. Round your answer to two decimal places.
17. ________________ (4)
18. The intensity of light produced by a light source varies inversely as the square of the distance from the
source. If the intensity of light 3 feet from a light source is 750 foot-candles (foot-candles is the unit of
intensity of light), find the intensity of light produced 5 feet from the same source.
18. ________________ (4)
19. You have 800 feet of fencing to enclose a rectangular field. However, one side of the field lies along a
canal and requires no fencing. Let 𝑥 be the length of the side parallel to the canal.
a. Express the width of the rectangle in terms of 𝑥.
19a. _______________ (1)
b. Write area of the rectangle as a function of 𝑥.
19b. _______________ (1)
c. What is the maximum area you can enclose with 800 feet of fencing?
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19c. _______________ (2)
Show all appropriate work!
20. The value of Tammy’s car is depreciating since she bought the car. The value (in dollars) of her car at
any time t (in years) is given by: 𝑉 = 22,500 ∙ 10−𝑡 12⁄ .
a. What was the price of Tammy’s new car? 20a. _______________ (1)
b. When will the value of the car be $10,000? Round your answer to the nearest whole year.
20b. _______________ (4)
21. Find the equation of a line in slope-intercept form which is perpendicular to the line 2
5 𝑥 + 2𝑦 = 10
and passes through the point (−1,2).
21. _______________ (4)
22. The Authur Ashe Stadium tennis court is center court for the U.S. Open tennis tournament. The
dimensions of the court are 78 ft by 36 ft, with an uniform border of width x feet around the outside
for additional play area. If the outer perimeter of the entire play area is 292 ft, determine the value of
x.
x
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22. ________________ (4)
Show all appropriate work!
23. Ashley and Hanna each make an ice-cream sundae. Ashley gets 2 scoops of Cherry ice-cream and 1
scoop of Mint Chocolate Chunk ice-cream for a total of 43 g of fat. Hanna has 1 scoop of Cherry and 2
scoops of Mint Chocolate Chunk for a total of 47 g of fat. How many grams of fat does 1 scoop of each
type of ice-cream have?
Cherry: ___________
(4)
Mint Chocolate: ____________
24. Given ℎ(𝑥) = 2𝑥 2 + 1
a. Find ℎ(−3). 24a. _______________ (2)
b. Find all x so that ℎ(𝑥) = 99
24b. _______________ (3)
c. Evaluate ℎ(𝑐 − 3) and simplify the result.
24c. _______________ (3)
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Show all appropriate work!
25. Consider the function 𝑓(𝑥) = √𝑥4+4
𝑥+2
Use your calculator to sketch a neat graph of the function in the given grid. (3)
26. Ryan wants to put a rope between two trees in his backyard. He has measured his property, and made
the sketch shown below, where all the lengths listed are in meters. Find the shortest distance x
between the trees as shown in the diagram below. Round your answer to the nearest hundredth.
x
y
Tree
15
25 25
20
Tree
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26. _______________ (4) (round to two decimal places)
