Tennessee State University
College of Engineering, Technology, Computer and Mathematical Sciences
Department of Mathematical Sciences
College Algebra
Final Exam Review Package – Short Form A
√
1. Let f (x) = x and g(x) = x + 1. Find the composition function (f ◦ g)(x).
√
(a) (f ◦ g)(x) = x + 1
√
(b) (f ◦ g)(x) = 4 x
√
(c) (f ◦ g)(x) = x + 1
8. Find the real solutions of
√
x2 + 144 = x + 6
(a) x = 144
(c) x = 9
(b) x = 0
(d) x = −18
9. Find the graph of the equation 2x + y = 4
(d) (f ◦ g)(x) = x + 2
2. Find the domain of the rational function
x2
y=
.
x−7
(a) (−∞, 1) ∪ (1, ∞)
(b) (−∞, 8) ∪ (8, ∞)
(c) (−∞, 6) ∪ (6, ∞)
(a)
(d) (−∞, 7) ∪ (7, ∞)
3. Find the slope of the line 2x + 15y = 29.
2
15
2
(b) m =
29
(a) m =
2
15
15
(d) m =
2
(c) m = −
4. Solve the inequality |x + 3| > 10. Express the solution set in interval notation
(a) (−13, −7)
(b) (−∞, −13)∪(7, ∞)
(b)
(c) (7, 13)
(d) (−∞, 7) ∪ (13, ∞)
5. Tell whether the graphs of the lines y = 5x + 5 and
y = 5x − 1 are parallel, perpendicular, or neither.
(a) Perpendicular
(b) Parallel
(c) Neither parallel nor perpendicular
√
√
6. Simplify (4 + −16)(4 − −9) and express it in
the a + bi form.
(a) −4 + 4i
(b) −28 + 4i
(c)
(c) 28 − 4i
(d) 28 + 4i
7. A printer charges a fixed setup cost, plus $0.40
for every 40 copies. If 320 copies cost $43.20, how
much will it cost to print 1200 copies?
(a) $160
(c) $128
(b) $48.8
(d) $52
10. Use the quadratic formula to solve the equation
2x(x + 7) = −5
√
√
−7 ± 11
−7 ± 39
(a) x =
(c) x =
2
2
√
√
−7 ± 11
−7 ± 39
(b) x =
(d) x =
4
4
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Review Package · College Algebra – Short Form A
11. Find the vertex of the parabola y = 7(x − 9)2 + 8
(a) (81, 8)
(c) (9, 7)
(b) (9, 8)
(d) (8, 9)
12. Solve the proportion
Department of Mathematical Sciences
(c) (f + g)(x) = x + 1
x
(d) (f + g)(x) =
x−1
19. A farmer wants to partition a rectangular feed
storage area in a corner of his barn.
The
barn walls form two sides of the stall, and the
farmer has 58 feet of partition for the remaining two sides. If a = 58 in the picture below
x
2
=
21
x+1
(a) x1 = 7 and x2 = 6
(b) x1 = 7 and x2 = −6
(c) x1 = −7 and x2 = 6
(d) No solutions
31
. Find f (5).
+ 28
31
31
(a) f (5) =
(c) f (5) =
53
56
31
(b) f (5) =
51
13. Let f (x) =
x2
What dimensions will maximize the area of the
partition?
14. Find the distance between the point P (4, 6) and
Q(6, 5)
√
√
(a) 12
(c) 17
√
√
(b) 8
(d) 5
(b) x = 3
(d) No solution
x+2
(c) f −1 (x) =
7
17. Given that P varies jointly with r and s. If P = 7
when r = 3 and s = 6, find P when r = 9 and
s = 24.
(c) P = 3
(b) P = 24
(d) P = 84
18. Let f (x) = x2 + x and g(x) = x2 − 1.
(f + g)(x)
(d) 29ft by 29ft
(a) (−∞, 3) ∪ (3, ∞)
(b) (0, ∞)
(c) (−∞, 0) ∪ (0, ∞)
(c) x = −3
(a) P = 9
(b) 23.2ft by 34.8ft
domain of f −1 (x)
16. Find the inverse of f (x) = 2x + 7
x−7
(a) f −1 (x) =
2
x
−
2
(b) f −1 (x) =
7
(c) 11.6ft by 46.4ft
20. Find the range of f (x) =
15. Find the value of x if logx (27) = 3
(a) x = 27
(a) 14.5ft by 43.5ft
4x
. Hint: Find the
x−3
(d) (−∞, 4) ∪ (4, ∞)
(e) (−∞, ∞)
21. Simplify i−30
(a) 1
(c) i
(b) −1
(d) −i
22. Find the graph of the function g(x) = (x − 1)3 .
Find
(a) (f + g)(x) = x4 + x3 − x2 − x
(b) (f + g)(x) = 2x2 + x − 1
Page 2 of 3
(a)
Review Package · College Algebra – Short Form A
Department of Mathematical Sciences
(a) x = −2 and x = 1
(b) x = −2 and x = 4
(c) x = 3 and x = 4
(d) x = 1 and x = 5
(b)
28. Solve the equation log(9x − 6) = log(4x + 24)
(a) x = 6
(c) x = 9
(b) x = 4
(d) x = 5
29. Find the vertex of the parabola y = x2 − 8x + 16
(c)
(a) (0, 4)
(c) (−8, 0)
(b) (4, 0)
(d) (16, 0)
30. Find where the function f (x) = 16 − x2 is increasing.
(a) (0, ∞)
23. If a and h are real numbers and f (x) = x2 − x + 2,
find f (a) + f (h).
(a)
(b)
(c)
(d)
f (a) + f (h) = a2 + h2 + a + h
f (a) + f (h) = a2 + h2 − a − h − 4
f (a) + f (h) = a2 + h2 − a − h
f (a) + f (h) = a2 + h2 + a + h + 4
(b) It is always constant
(c) y = 5
(b) y = x
(d) x = −3
(a) 45 logc (x) + 9 logc (y)
(b) 5 logc (x) + 45 logc (y)
(c) 5 logc (x) + 9 logc (y)
(d) 5 logc (x) + 5 logc (y)
32. Solve for x the equation f =
(a) x = f − kq
25. Solve the equation |2x + 1| = 3
(a)
(b)
(c)
(d)
(b) x = k − f q
x = 1 and x = 2
x=1
x = −2 and x = 1
x = −2 and x = −1
k−x
.
q
(c) x = f q − k
(d) x = kq − f
33. Solve the equation x(x − 5) − 23 = (x − 1)2
(a) x = −3
(b) x = −17
8
1
1
26. Solve the equation
− =
x + 30 5
x + 30
(c) x = 0
(a) x = 2
(b) x = −3
(d) (−∞, 0)
31. Assume that x, y and c are positive numbers. Use
the properties of logarithms to write the expression logc (x5 y 9 ) in terms of the logarithms of x and
y.
24. Find the line that passes through the points P (5, 5)
and Q(−3, −3).
(a) y = 5x
(c) It is always decreasing
(c) x = −8
(d) x = −1
34. The ratio of women to men in a mathematics class
is 5 to 8. How many women are in the class if there
are 48 men?
(d) x = 5
27. Solve the equation x2 − 2x − 8 = 0 by completing
the square.
Page 3 of 3
(a) 48
(c) 8
(b) 30
(d) 5