Download Practice Final.tst - Columbia Basin College

Math 95/98
Practice Final
Name___________________________________
Date_______________________________________
Subtract. Simplify, if possible.
10x
4
5)
x2 - 16 4 - x
Find all numbers for which the rational expression is not
defined.
x2 - 64
1)
x2 + 6x - 16
A) x = 8 and x = -8
B) x = -8 and x = 2
C) x = 0
D) x = 8 and x = -2
E) None of the above.
A)
6x - 16
x2 - 16
B)
10x - 4
x2 - 16
C)
14x + 16
x2 - 16
D)
14x - 16
x2 - 16
Solve.
2) -3(4y - 3) < -15y + 15
A) (2, ∞)
B) (-∞, 2]
C) [2, ∞)
D) (-∞, 2)
E) None of the above.
E) None of the above.
Add. Simplify, if possible.
4
7
6)
+
2
2
y - 3y + 2 y - 1
Perform the indicated operation.
3) (8x - 3 2)2
A) 64x2 + 36
B) 64x2 - 48x 2 + 36
C) 64x2 + 18
D) 64x2 - 48x 2 + 18
E) None of the above.
Solve. Give exact solutions.
4) (x - 1)2 +14= -2
A) 1 ± 4
B) ±4i
C) 4i
D) ±5i
E) None of the above.
A)
11 y - 10
(y - 1)(y - 2)
B)
56 y - 10
(y - 1)(y + 1)(y - 2)
C)
10 y - 11
(y - 1)(y + 1)(y - 2)
D)
11 y - 10
(y - 1)(y + 1)(y - 2)
E) None of the above.
Find the domain of f|(x).
7) f(x) = 3 - 4x
A) x x >
3
4
B) x x <
3
4
C) x x ≥ D) x x ≤
3
4
3
4
E) None of the above.
1
Solve the problem.
8) Tom Quig traveled 300 miles east of St. Louis.
For most of the trip he averaged 70 mph, but
for one period of time he was slowed to 10
mph due to a major accident. If the total time
of travel was 6 hours, how many miles did he
drive at the reduced speed?
A) 20 miles
B) 15 miles
C) 40 miles
D) 30 miles
E) None of the above.
Solve and graph.
11) 2x + 9 ≥ -1 and 7x - 4 ≥ -32
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
A) [-4, ∞)
-7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
B) (-∞, -5] ∪ [-4, ∞)
-7 -6 -5 -4 -3 -2 -1 0
C) [-5,-4]
Solve.
9) John and Tony start from GraysLake at the
same time and head for a town 10 miles away.
John walks twice as fast as Tony and arrives 3
hours before Tony. Find how fast each walks.
3
6
A) Tony's speed = m/h and John's =
5
5
-7 -6 -5 -4 -3 -2 -1 0
D) [-5, ∞)
-7 -6 -5 -4 -3 -2 -1 0
E) None of the above.
m/h.
B) Tony's speed =
Solve the problem.
12) The Epson Stylus can print Helen's class project in
18 minutes. The Hp Deskjet can print the project in
30 minutes. If the two printers work together, how
long would they take to print out the project?
A) 90 minutes
B) 8 minutes
4
C)
of a minute
45
5
10
m/h and John's =
3
3
m/h.
C) Tony's speed = 3 m/h and John's = 6 m/h.
D) Cannot be determined with information
given
E) None of the above.
For the function represented in the graph,
10) Find the range.
3
D) 11
y
1
minutes
4
E) None of the above.
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
Solve and graph.
13) 9x - 6 < 3x or -4x ≤ -12
6 x
-2
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-3
A) (-∞, 1) ∪ [3, ∞)
-4
-5
-6
-7 -6 -5 -4 -3 -2 -1 0
-7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
B) (1, 3)
A) {y∣ - 6 ≤ y ≤ 0}
B) {y∣ - 6 ≤ y ≤ 2}
C) {y∣ - 5 ≤ y ≤ 4}
D) All real numbers.
E) None of the above.
-7 -6 -5 -4 -3 -2 -1 0
C) [1, 3]
-7 -6 -5 -4 -3 -2 -1 0
D) ∅
E) None of the above.
2
Solve.
Rationalize the denominator.
3+ x
18)
3- x
14) -9x2 = 5x + 5
-5 ± i 155
A)
-18
B)
-5 ± i 155
18
C)
-5 ± 205
-18
D)
-5 ± 205
18
A) 59 + 22i
B) -24i 2 - 22i + 35
C) 12 - 40i
D) 11 - 62i
E) None of the above.
Solve the problem.
20) Ellen wishes to mix candy worth $1.22 per pound
with candy worth $2.30 per pound to form 20
pounds of a mixture worth $1.49 per pound. How
many pounds of the more expensive candy should
she use?
A) 17 pounds
B) 5 pounds
C) 10 pounds
D) 15 pounds
E) None of the above.
8
40
x+
3
3
D) y =
5
40
x+
3
3
9+x
9-x
Multiply. Write in a + bi form.
19) (5 - 6i)(7 + 4i)
Find an equation of the line containing the given pair of
points.
16) (5, 0) and (2, 8)
5
40
A) y = - x +
3
3
8
40
x+
3
3
B)
E) None of the above.
Add or subtract. Then simplify by collecting like radical
terms, if possible. Assume that no radicands were formed
by raising negative numbers to even powers.
15) 20 - 8 80 - 4 125
A) 26 5
B) -50 5
C) -80 5
D) 50 5
E) None of the above.
C) y =
9-x
9-6 x+x
C) -1
9+6 x+x
D)
9-x
E) None of the above.
B) y = -
A)
Solve. Provide answers in interval notation.
2x + 3
21)
≤0
x-3
E) None of the above.
A) -∞, Solve.
17) 2x + 3y = -1
-10x - 15y = 5
A) (-3, -2)
B) (-2, -3)
C) No solution
D) Infinite number of solutions
E) None of the above.
B) -3,
C) -
3
∪ [3, ∞)
2
3
2
3
,3
2
D) (-∞, -3) ∪
3
,∞
2
E) None of the above.
3
Simplify.
Rationalize the denominator and simplify.
3
3x
25)
3
4y
3
1
+
5x 5
22)
3
1
+
4 4x
3
A)
4
A)
5
B)
B)
5
C)
4
D)
C)
25
16
D)
x6 y10z3
A) xy
B) x
2y
48xy2
4y
Express in terms of i.
26) -108
A) 6 3
B) 6i 3
C) -6 3
D) -6i 3
E) None of the above.
y4 z3
6 4
y z3
C) xyz
6xy2
E) None of the above.
Simplify. Leave radical with given index.
6
192xy2
4y
3
E) None of the above.
23)
4y
3
16
25
48xy
6 4
y
6
D) xy y4 z3
E) None of the above.
Divide and simplify to the form a + bi.
-7i
27)
9 - 10i
Determine the slope and the y-intercept.
24) 3x - 4y + 8 = 0
3
A) Slope - , y-intercept (0, -2)
4
A) -
70
63
i
181 181
4
B) Slope - , y-intercept (0, 2)
3
B) -
70 63
i
+
19 19
4
C) Slope , y-intercept (0, -2)
3
C)
70 63
i
+
19 19
D)
70
63
i
181 181
3
D) Slope , y-intercept (0, 2)
4
E) None of the above.
E) None of the above.
4
Find the requested composition of functions.
2
28) Given f(x) =
and g(x) = x - 3,
x2
Find the vertex.
32) f (x) = -2x2 + 12x - 19
A) (3, 1)
B) (3, -1)
C) (-3, -37)
D) (3, 53)
E) None of the above.
find (g∘f)(x).
2
A)
(x - 3)
x2
B)
C)
D)
2
x2 - 3
Solve for x.
33) x = x + 6
A) -6
B) 0
C) -2
D) No solution
E) None of the above.
2
(x - 3)2
-1
x2
E) None of the above.
Determine the slope, if it is not defined state so.
34) x = 3
1
A) m =
3
Solve the absolute value inequality. Write the solution set
using interval notation.
29) x - 4 + 2 < 4
A) 2, 6
B) -∞, - 6 ∪ - 2, ∞
C) -∞, 2 ∪ 6, ∞
D) - 6, - 2
E) None of the above.
B) m = 3
C) m = 0
D) Slope is not defined.
E) None of the above.
Solve.
35) A man rode a bicycle for 12 miles and then
hiked an additional 8 miles. The total time for
the trip was 5 hours. If his rate when he was
riding a bicycle was 10 miles per hour faster
than his rate walking, what was each rate?
A) Bike: 11.5 mph
Hike: 1.5 mph
B) Bike: 13 mph
Hike: 3 mph
C) Bike: 14.5 mph
Hike: 4.5 mph
D) Bike: 12 mph
Hike: 2 mph
E) None of the above.
Divide and, if possible, simplify.
x2 + 10x + 21
x2 - 9
30)
÷
x+7
7x - 21
A)
1
7
B)
7x - 21
x-3
C) 7
(x + 3)2
D)
7
E) None of the above.
Solve.
Find the inverse of f (x). If f (x) is not one-to-one, state so.
36) f (x) = 6x - 3
x
A) f -1(x) = + 3
6
31) A ladder is resting against a wall. The top of
the ladder touches the wall at a height of 12 ft.
Find the length of the ladder if the length is 4 ft
more than its distance from the wall.
A) 12 ft
B) 16 ft
C) 20 ft
D) 24 ft
E) None of the above.
B) f -1(x) =
1
6x - 3
C) f -1(x) =
x+3
6
D) Not a one-to-one function
E) None of the above.
5
D)
Solve the formula for the indicated letter. Assume that all
variables represent nonnegative numbers.
1
37) S = gt2 for t
2
y
4
2
A) t = 2gS
2S
B) t =
g
-4
-2
C) t = 2 gs
g
D) t =
2S
E) None of the above.
Find a linear function.
39) A student who studies for 30 hours for a
standardized exam can get a score of 620. A
student who studies for 70 hours can get a score of
740 on the exam.
Find a linear function, that fits this data and
expresses the exam score, S (t), as a function of
time, t.
A) S (t) = 3t - 1520
B) S (t) = 3t + 530
C) S (t) = -3t + 710
D) S (t) = 3t - 20
E) None of the above.
Graph the system of inequalities.
38) x + y ≤ 3
y≥x
A)
4
y
2
(3/2, 3/2)
-2
2
4 x
-2
-4
Find the function value.
40) Find f (- 2) when f (x) = -x2 - 5x .
A) 14
B) -6
C) -14
D) 0
E) None of the above.
B)
y
4
2
-4
(3/2, 3/2)
-2
2
4 x
Solve.
-2
41) log 4
-4
C)
4
-2
2
1
=x
16
A)
1
64
B)
1
4
y
C) 2
D) -2
E) None of the above.
2
-4
2
4 x
(3/2, -3/2)
-4
E) None of the above.
-4
-2
4 x
(-3/2, -3/2)
-2
-4
6
Solve the problem. If necessary, round to the nearest tenth.
42) If your tablet is stated to have a 10" screen, then the
diagonal of the rectangular screen actually
measures 10 inches long. If the length of the screen
is 2 inches longer than the width. What is the
measure of the length of the screen?
A) 10 in
B) -8 in
C) 6 in
D) 8 in
E) None of the above.
Solve for x.
47) log a x = 9
a
A) 1
B) 9
C) a 9
D) 9loga a
E) None of the above.
Graph the function.
48) f(x) = ln(x + 5)
y
Find the logarithm.
1
43) log8
512
10
5
A) -3
B) -64
C) 64
D) 3
E) None of the above.
-10
-5
5
10
x
-5
Express in terms of logarithms of a single variable or a
number.
44) loga 4x6 yz3
-10
A)
y
A) 4 + loga y + loga z 3
10
B) 18 loga 4xyz
C) loga 4 - 6 loga x - loga y - 3 loga z
D) loga 4 + 6 loga x + loga y + 3 loga z
E) None of the above.
5
-10
-5
Express as a single logarithm.
45) (log a x - log a y ) + 2 log a z
A) log a
B) log
C) log
a
10
x
5
10
x
-5
2xz
y
-10
B)
x z2
y
y
10
x
a
5
z2 y
5
D) log a x z 2 y
E) None of the above.
-10
Rewrite without rational exponents, and simplify.
3/2
46) (9y4 )
A) 27y3/2
-5
-5
-10
B) 9y6
C) 27y6
D) 2711
E) None of the above.
7
Use a calculator and the change-of-base formula to find
the logarithm to four decimal places.
50) log5.7 2.1
C)
y
10
A) 0.4263
B) 2.3458
C) 0.3684
D) 0.3222
E) None of the above.
5
-10
-5
5
10
x
-5
Simplify the radical completely.
51)
3 48
x6
-10
D)
y
A)
10
5
B)
-10
-5
5
10
x
C)
-10
y
8
6
4
2
2
6
x2
4
3
x3
2
x
Solve the equation.
52) 5 x - 1 = 21 (Round to the nearest
thousandth.)
A) 3.900
B) 3.892
C) 1.892
D) 2.892
E) None of the above.
Determine the domain of the given graph.
49) Find the domain.
-10 -8 -6 -4 -2
-2
3
8
E) None of the above.
E) None of the above.
10
2
x2
-5
D)
3
6
4
6
8
x
53) ln(4x - 3) = ln 3 - ln (x - 1)
1
A) 1,
4
-4
-6
-8
B) 0,
-10
A) {x | x is a real number.}
B) {x -5 ≤ x < 5 }
C) {x | -7< x ≤ 7 }
D) {x -5 < x ≤ 5 }
E) None of the above.
C)
7
4
7
4
D) ∅
E) None of the above.
8
C)
Solve. Provide answers in interval notation.
54) x2 - 8x + 7 > 0
y
6
A) (1, 7)
B) (7, ∞)
C) (-∞, 1)
D) (-∞, 1) ∪ (7, ∞)
E) None of the above.
4
2
-6
-4
-2
2
6x
4
-2
Find the domain of the given function.
x+3
55) f (x) =
x-2
-4
-6
D)
A) {x | x is a real number.}
B) {x ∣ x is a real number and x ≠ 2}
C) {x ∣ x is a real number and x ≠ - 3}
D) {x ∣ x is a real number and x ≠ 0}
E) None of the above.
y
6
4
2
-6
Solve the absolute value inequality. Write the solution set
using interval notation.
56) 2 x - 1 ≥ 9
A) - ∞, - 4 ∪ 5,∞
B) - 4, 5
C) - 4, 5
D) - ∞, - 4 ∪ 5, ∞
E) None of the above.
-4
58) When solving the given equation by completing the
square, what number should be added to both
sides to form a perfect square trinomial?
4z2 + 12z +5 = 0
A) 144
3
B)
2
C)
2
D) 36
E) None of the above.
4
6x
Solve the problem.
59) Andy has 31 coins made up of quarters and
half dollars, and their total value is $11.25.
How many quarters does he have?
A) 16 quarters
B) 17 quarters
C) 22 quarters
D) 14 quarters
E) None of the above.
-4
-6
B)
6
y
4
2
-4
9
4
4
2
-2
6 x
E) None of the above.
y
-2
4
-6
-2
-6
2
-4
A)
-6
-2
-2
Graph the function.
57) f (x) =2 x + 1
6
-4
2
4
6x
-2
-4
-6
9
Solve for x.
60)
5
2
1
=
x+3 x+2
2
A) -1, 2
B) -3, -2
C) -2, 1
D) No Solution.
E) None of the above.
10
Answer Key
Testname: PRACTICE FINAL
1) B
2) D
3) D
4) E
5) C
6) D
7) D
8) A
9) B
10) B
11) A
12) D
13) A
14) B
15) B
16) B
17) D
18) D
19) E
20) B
21) C
22) A
23) D
24) D
25) C
26) B
27) D
28) E
29) A
30) C
31) C
32) B
33) E
34) D
35) D
36) C
37) B
38) B
39) B
40) E
41) D
42) D
43) A
44) D
45) B
46) C
47) B
48) C
49) B
50) A
51) E
52) D
53) C
54) D
11
Answer Key
Testname: PRACTICE FINAL
55) B
56) D
57) E
58) C
59) B
60) A
12