MATH 21
1. Simplify
FINAL EXAM
4x2 + 8x
.
x3 + 8
a)
4x + 8
x2 + 8
b)
4x
x2 − 2x + 4
SAMPLE C
3
14
a
+
= 2
.
a+2
a+4
a + 6a + 8
6. Solve
a) a = −8, a = 1
b) a = 1
c) a = 1, a = −
7
2
c)
4x
(x + 2)2
d) a = 0
d)
x2 + 2x
x3 + 2
7. Simplify (2−2 4−1 )−1 .
2. Perform the indicated operation
a)
b)
14y
7xy
÷ 2
.
x2 − 4x + 4
x −4
x(x + 2)
2(x − 2)
2(x2
a)
1
16
b)
1
32
c) 8
x
− 4)(x2 − 4x + 4)
d) 16
x
c) −
2
8. Write
x+2
d)
x−2
1√
90 in simplest radical form.
3
1√
10
9
1√
b)
10
3
√
10
c)
√
d)
30
a)
3. Simplify
3
1
+ .
x2 + x
x
a)
4
x(x + 1)
b)
4
x(x + 2)
c)
x+4
x(x + 1)
d)
3x + 4
x(x + 1)
4. Simplify
3
+ 34
8
5
7
− 12
8
9. Write
p
49x5 y 4 in simplest radical form.
a) 7x2 y 2
√
b) 7x2 y 2 x
√
c) 7y 2 x5
p
d) 7 x5 y 4
.
a) 18
√
√
√
10. Simplify −2 25x − 4 36x + 7 64x.
b) 27
c) 1
d)
5. Solve
7
3
=
.
x+4
x−8
a) x =
√
x
√
b) 22 x
√
√
√
c) −10 5x − 24 6x + 56 8x
√
d) −26 x
a)
27
29
22
5
b) x = 17
c) x = −13
d) x = 11
1
MATH 21
FINAL EXAM
√
11. Rationalize the denominator and simplify √
SAMPLE C
16. Find the product of the roots of the quadratic equation 2x2 −4x+7 =
0.
2x
√ .
2x + 5y
√
2x + 10xy
2
4x − 25y 2
√
2x − 10xy
b)
2
4x + 25y 2
√
2x − 10xy
c)
2x − 5y
√
10xy
d)
5y
a)
a)
b) −
a) −
b) −
c)
3
2
c) −10
d) 2
17. Solve
12. Evaluate (−
7
2
8 −1
) 3.
27
3
10
+ = 1.
x+6
x
√
3±3 7
a) {
}
2
3
2
b) {
2
3
c) {9}
2
i
3
−17
}
3
d) {−2, 9}
3
d) − i
2
18. Solve the inequality 4x2 − x − 14 ≤ 0.
13. How many solutions does the equation
√
a) [−2,
−x − 6 = x have?
7
]
4
b) (−∞, 2]
a) 0
b) 1 only
7
c) [− , 2]
4
c) 2
d) [2, ∞)
d) There are an infinite number of solutions.
19. Solve the inequality
14. Write (−5 + 3i)2 in standard form.
2x − 1
≥ −1.
x+2
1
a) (−2, − ]
3
a) 16 − 15i
b) 16 − 30i
1
b) (−∞, −2) ∪ [− , ∞)
3
c) −34 − 30i
c) (−2, ∞)
d) 34 − 15i
1
d) (−∞, −2] ∪ [ , ∞)
3
15. Solve (x + 3)(2x + 1) = −3.
20. The graph of y = (x + 2)2 + 1 is the basic parabola moved
a) {−6, −2}
a) 2 units to the left and 1 unit down.
1
b) {−3, − }
2
b) 2 units to the right and 1 unit down.
c) {−3,
c) 2 units to the left and 1 unit up.
1
}
2
d) 2 units to the right and 1 unit up.
3
d) {−2, − }
2
2
MATH 21
FINAL EXAM
21. Find the vertex of the parabola y = 3x2 + 6x + 1.
SAMPLE C
27. Find the equations of the asymptotes of the hyperbola 4x2 − 16x −
y 2 + 4 = 0.
a) (1, −2)
a) y = 2x, y = −2x
b) (1, 2)
b) y = 2x − 2, y = −2x + 2
c) (−1, −2)
c) y = 2x − 4, y = −2x + 4
d) (−1, 2)
d) y = x − 2, y = −x + 2
22. Find the center and the length of the radius of the circle x2 + y 2 −
16x + 6y + 71 = 0.
a) center (8, −3); radius
√
28. Find the value of x in the solution of the system
2
x − 3y = 25
−3x + 2y = −26
.
a) 3
b) center (8, −3); radius 2
√
c) center (−8, 3); radius 2
b) 4
c) 5
d) center (−8, 3); radius 2
d) 6
23. Write the equation of the circle with center (6, −8) and radius 10.
1
1
 3 x − 2 y = −3

29. Find the value of x in the solution of the system 

1
2
x+ y =4
3
4

a) x2 + y 2 + 12x − 16y = 0
b) x2 + y 2 − 12x + 16y = 0
c) x2 + y 2 + 12x − 16y + 90 = 0
a) 3
d) x2 + y 2 − 12x + 16y + 90 = 0
b) −3



.

c) 6
24. Find the length of the minor axis and the length of the major axis
of the ellipse 16x2 + 9y 2 = 144.
d) −6
30. Jane bought 2 packages of cookies and 1 bag of potato chips for a
total of $9.25. Later she bought 3 more packages of cookies and
2 additional bags of potato chips for $15.50. Find the price of a
package of cookies.
a) minor = 6; major = 8
b) minor = 3; major = 4
c) minor = 9; major = 16
d) minor = 4; major = 9
a) $2.5
b) $3
25. Find the center of the ellipse 4x2 + y 2 + 4y − 12 = 0.
c) $3.25
d) $3.5
a) (2, −1)
b) (2, 1)
c) (0, 2)
FINAL EXAM- SAMPLE C
d) (0, −2)
1. B
26. Find the intercepts of the hyperbola y 2 − 9x2 = 36.
2. A
a) (6, 0), (−6, 0)
3. C
b) (0, 6), (0, −6)
4. B
c) (2, 0), (−2, 0)
5. B
d) (0, 2), (0, −2)
6. A
7. D
3
MATH 21
FINAL EXAM
8. C
9. B
10. B
11. C
12. A
13. B
14. B
15. D
16. A
17. D
18. C
19. B
20. C
21. C
22. A
23. B
24. A
25. D
26. B
27. C
28. B
29. A
30. B
4
SAMPLE C