Name:____________________________________________ Period:___________
College Algebra: Ch.10.5-10.8 Test
A
For every problem, supporting work/reasoning must be shown in order to receive credit
for your answer.
1. Solve for x. |
a.
b.
c.
d.
e.
𝑥
3
1
| = −2
𝑥
2 or -1
1 or -1
3 or -3
0.5 or -0.5
None of the above.
1._______(+2)
2. Find the equation of the line perpendicular to 2x – 3y = -1 and contains the point
(-4,2)
3
a. 𝑦 = 𝑥 + 8
2
2._______(+2)
2
b. 𝑦 = − 𝑥 − 5
c.
𝑦=
2
3
1
3
𝑥+2
d. 𝑦 = 𝑥 − 1
2
e. None of the above.
3. Find the difference quotient,
a. 4x + 3 – h
b. 2x + 3 – h
c. 4x – 3 + h
d. 2x – 3 + h
e. None of the above.
𝑓(𝑥+ℎ)−𝑓(𝑥)
ℎ
, ℎ ≠ 0, for 𝑓(𝑥) = 𝑥 2 − 3𝑥 − 2.
4. Find the average rate of change of 𝑓(𝑥) = 𝑥 3 − 2𝑥 + 1 from -3 to -2.
a. 21
b. 14
c. 17
d. 12
e. None of the above.
5. Solve the system.
a.
b.
c.
d.
e.
2𝑥 + 3𝑦 = 6
𝑥 − 𝑦 = 0.5
(2, 1)
(1.5, 1)
(.5, -1)
(2,2)
None of the above.
3._______(+2)
4._______(+2)
5._______(+2)
Solve each system of nonlinear equations algebraically.
6.
xy = 20
x + y = −9
6.__________________________(+5)
7.
𝑥 2 + 𝑦 2 = 61
𝑥−𝑦 =1
7.__________________________(+5)
8.
2𝑥 2 + 𝑦 2 = 17
3𝑥 2 − 2𝑦 2 = −6
8.__________________________(+5)
9.
𝑥 2 − 𝑥𝑦 − 2𝑦 2 = 0
𝑥𝑦 + 𝑥 + 6 = 0
9.__________________________(+5)
Write the partial fraction decomposition for each rational expression.(+5 each)
10.
2𝑥 2 −𝑥−9
𝑥 3 −𝑥
10._________________________(+5)
2𝑥 2 −13𝑥+16
11. (𝑥+2)(𝑥+1)2
11._________________________(+5)
12.
𝑥 2 −111
𝑥 4 − 𝑥 2 −72
12._________________________(+5)
13. Maximize 𝑧 = 2𝑥 + 3𝑦 subject to 𝑥 ≥ 0, 𝑦 ≥ 0, 𝑥 + 𝑦 ≥ 3, 𝑥 + 𝑦 ≤ 9, 𝑎𝑛𝑑 𝑥 + 3𝑦 ≥ 6.
13._________________________(+5)
14. A doctor has told a patient to take vitamin pills. The patient needs at least 24 units of
vitamin A, at least 8 units of vitamin C, and at least 81 units of vitamin D. The red vitamin
pills cost $0.20 each and contain 7 units of A, 1 unit of C, and 7 units of D. The blue
vitamin pills cost $0.40 each and contain 3 units of A, 1 unit of C, and 12 units of D. How
many pills should the patient take each day to minimize costs?
14.________________________(+10)