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I have a packet that is extra credit and I need it for my grade. it is college algebra and multiple choice
EXTRA CREDIT
DUE: Day of the Final Exam
Name___________________________________
ANSWERS must be on DATALINK Form 1200, Reorder #26760-RR.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the vertex of the graph of the function.
1) f(x) = 3×2 + 24x + 50
A) (-4, 2)
1)
B) (-1, 5)
C) (2, -4)
D) (5, -1)
Divide using synthetic division, and write a summary statement in fraction form.
2×4 – x3 – 15×2 + 3x
2)
x+3
A) 2×3 – 7×2 + 6x -15 +
C) 2×3 + 5×2 + 3 +
– 45
x+3
2)
B) 2×3 – 7×2 + 6x -15 +
9
x+3
D) 2×3 – 5×2 + 3 +
45
x+3
-9
x+3
Write the product in standard form.
3) (5 + 2i)(5 – 2i)
3)
C) 25 + 4i2
D) 25 – 4i2
Write the sum or difference in the standard form a + bi.
4) 8i + (-2 – i)
A) -2 + 9i
B) 2 – 7i
C) 2 – 9i
D) -2 + 7i
Find the product of the complex number and its conjugate.
5) 1 – 7i
A) 8
B) -48
C) -6
D) 50
A) 21
B) 29
4)
5)
State the domain of the rational function.
x-5
6) f(x) =
x2 – 9
6)
A) (- ∞, – 3) ∪ (- 3, 3) ∪ (3, ∞)
C) (- ∞, 5) ∪ (5, ∞)
B) (- ∞, 3) ∪ (3, ∞)
D) (- ∞, -3) ∪ (-3, ∞)
Solve the problem.
7) A(x) = -.015x 3 + 1.05x gives the alcohol level in an average person’s blood x hrs after drinking 8 oz
of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be
drunk after 2 hours?
A) Yes
B) No
Write the expression in the form bi, where b is a real number.
8) -36
A) 6i
B) i 6
8)
C) ±6
1
7)
D) -6i
Divide f(x) by d(x), and write a summary statement in the form indicated.
9) f x = x3 + 3; d x = x + 4 (Write answer in fractional form)
9)
A)
fx
– 61
= x2 + 4x + 16 +
x+4
x+4
B)
fx
– 64
= x2 – 4x + 16 +
x+4
x+4
C)
fx
– 61
= x2 – 4x + 16 +
x+4
x+4
D)
fx
– 64
= x2 + 4x + 16 +
x+4
x+4
Find the vertex of the graph of the function.
10) f(x) = 3(x – 7)2 + 10
A) (- 7, 10)
10)
B) (7, 10)
C) ( 7, 10)
D) (-7, 10)
Solve the problem.
11) Suppose you contribute to a fund that earns 6.5% annual interest. What should your quarterly
payment be if you want to accumulate $160,000 in 13 years?
A) $15,851.01
B) $2377.65
C) $2972.06
D) $1981.38
12) How long will it take for prices in the economy to double at a 13% annual inflation rate? (Round to
the nearest year.)
A) 5 yr
B) 6 yr
C) 9 yr
D) 23 yr
Use the change of base rule to find the logarithm to four decimal places.
13) log 8 0.989
A) 8.0890
B) -0.0048
11)
12)
13)
C) -0.0053
D) -187.9985
Rewrite the expression as a sum or difference or multiple of logarithms.
6 x
14) log7
y
14)
1
log7 x ÷ log7 y
2
A) log7 (6 x) – log7 y
B) log7 6 ∙
1
C) log7 6 + log7 x – log7 y
2
D) log7 y – log7 6 –
1
log7 x
2
Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
2
1
15) loga x + loga y
15)
5
9
A) loga (xy2/45)
B)
2
loga xy
45
C) loga (y2/45)
D) loga (x2/5 y1/9 )
Solve the equation.
-64
16) ex – 16 =
ex
A) 0.903, 0.903
16)
B) 8, 8
C) -1
Choose the graph which matches the function.
2
D) 2.079, 2.079
17) f(x) = 3e- x
17)
y
5
4
3
2
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5
x
-2
-3
-4
-5
A)
B)
y
y
5
5
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5
x
-5 -4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
C)
1
2
3
4
5
x
1
2
3
4
5
x
D)
y
y
5
5
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5
x
-5 -4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
Find the determinant of the given matrix.
18)
9-8 9
0 4 2
0 0-3
A) -108
B) -124
18)
C) 108
3
D) 92
Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
19) x + 4y = -5
4x – y = 14
-3x + 4y = -1
A) (-1, -1)
B) (7, -3)
C) (3, -2)
D) No solution
Solve the system graphically.
20) y = ln(3x – 2)
x2 + 3y2 = 7
A) ≈(0.74, -1.47) and ≈(1.73, 1.16)
C) ≈(0.77, 1.46) and ≈(-0.59, -1.49)
20)
B) ≈(1.73, -1.16) and ≈(0.74, 1.47)
D) ≈(5.25, 2.62)
Determine which function matches the graph. Do this without using your grapher.
21)
20
18
16
14
12
10
8
6
4
2
-6 -5 -4 -3 -2 -1-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
21)
y
1
2
A: y = x – 3 +
1
1
+
x-3 x+1
B: y = x – 3 –
1
1
+
x-3 x+1
C: y = 2 +
1
1
x-3 x+1
D: y = 2 –
1
1
+
x-3 x+1
A) A
19)
3
4
5
6 x
B) B
C) D
D) C
Solve the problem.
22) The total number of cars sold at a used car lot for the years 1996 and 1997 was 1044. From 1996 to
1997 the number of cars sold declined by 158. How many cars were sold in 1997?
A) 437
B) 453
C) 443
D) 449
4
22)
Solve the system algebraically.
23) y = x3 – x2
23)
y = 4×2
A) (0, 0) and (3, 36)
C) (0, 0) and (5, 125)
B) (5, 100)
D) (0, 0) and (5, 100)
Decompose into partial fractions.
9×2 – 117x + 6
24)
(x2 + 3x – 2)(x – 9)
24)
A)
12x
3
+
2
x
9
x + 3x – 2
B)
12x
3
x – 9 x2 + 3x – 2
C)
12x
3
2
x
9
x + 3x – 2
D)
3x
12
2
x
-9
x + 3x – 2
Find the vertex, focus, directrix, and focal width of the parabola.
25) (x – 3)2 = 16(y – 6)
A)
B)
C)
D)
25)
Vertex: (6, 3); Focus: (10, 3); Directrix: x = -1; Focal width: 4
Vertex: (3, 6); Focus: (3, 10); Directrix: y = 2; Focal width: 16
Vertex: (-3, -6); Focus: (-3, 10); Directirx: y = -22; Focal width: 16
Vertex: (6, 3); Focus: (22, 3); Directrix: x = -13; Focal width: 16
Find a polynomial of lowest degree with only real coefficients and having the given zeros.
26) 8, -14, and 3 + 8i
A) f(x) = x4 – 75×2 + 1110x – 8176
B) f(x) = x4 – 11×3 + 64×2 – 555x + 8176
C) f(x) = x4 – 11×3 – 64×2 + 555x – 8176
26)
D) f(x) = x4 – 277.5×2 + 1110x – 8176
Use Descartes’ Rule of Signs to determine the possible number of positive real zeros and the possible number of negative
real zeros for the function.
27) -9×4 + 3×3 – 7×2 + 7x – 9 = 0
27)
A) Positive (4, 2, 0), negative (4, 2, 0)
C) Positive (2, 0), negative (2, 0)
B) Positive (4, 2, 0), negative (0)
D) Positive (2, 0), negative (4, 2, 0)
Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
28) f(x) = x4 – 6×3 + 7×2 – 6x + 6
A) i, -i, 3 + 3, 3 – 3
C) i, -i, -3 + 3, -3 – 3
B) i, -i, 3 + 2 3, 3 – 2 3
D) i, -i, 1 + 3, 1 – 3
Give the equation of the oblique asymptote, if any.
x2 – 9x + 3
29) f(x) =
x+9
A) x = y + 9
28)
29)
B) None
C) y = x – 18
5
D) y = x + 12
If f is one-to-one, find an equation for its inverse.
30) f(x) = 8×2 – 9, x ≥ 0
A) f-1 (x) =
30)
8
, x ≠ -9
x+3
C) Not a one-to-one function
B) f-1 (x) =
8
x+3
D) f-1 (x) =
x+9
, x ≥ -9
8
Graph the parabola.
31) (x – 1)2 = 2(y – 2)
31)
y
10
-10
10
x
-10
A)
B)
y
y
10
10
-10
10
x
-10
-10
10
x
10
x
-10
C)
D)
y
y
10
-10
10
10
x
-10
-10
-10
6
Find an equation in standard form for the ellipse that satisfies the given conditions.
32) An ellipse with foci at (-3, 7) and (-3, 1); major axis length of 10
(y – 4)2 (x – 3)2
(x – 4)2 (y – 3)2
A)
B)
+
=1
+
=1
25
16
25
16
C)
(y – 4)2 (x + 3)2
+
=1
25
16
D)
32)
(x – 4)2 (y – 3)2
+
=1
16
25
Find an equation in standard form for the hyperbola that satisfies the given conditions.
33) Center (1, -3), focus (6, -3), vertex (5, -3)
(x – 1)2 (y + 3)2
(x – 1)2 (y + 3)2
A)
B)
=1
=1
16
25
9
16
C)
(x + 1)2 (y + 3)2
=1
16
9
D)
33)
(x – 1)2 (y + 3)2
=1
16
9
Expand the binomial.
34) (3x + 4y) 4
34)
A) 81×4 + 432×3 y – 864×2 y2 + 768xy3 – 256y4
B) 81×4 + 432×3 y + 864×2 y2 + 768xy3 + 256y4
C) 81×4 + 6912×3 y + 5184×2 y2 + 768xy3 + 256y4
D) 81×4 + 6912×3 y – 5184×2 y2 + 768xy3 – 256y4
Find an explicit rule for the nth term of the arithmetic sequence.
35) -13, -19, -25, -31, …
A) a n = -13 × (-6)(n-1)
B) a n = -13 + (-6)(n+1)
C) a n = -13 + (-6)(n-1)
35)
D) a n = -13 – (-6)(n+1)
36) a 9 = 45, a10 = 6
36)
A) a n = 357 + 39(n + 1)
B) a n = 357 + 39(n – 1)
C) a n = 357 – 39(n + 1)
D) a n = 357 – 39(n – 1)
Find an explicit rule for the nth term of the sequence.
37) The second and fifth terms of a geometric sequence are -24 and 1536, respectively.
A) a n = 6 ∙ 4 n
B) a n = 6 ∙ 4 n-1
C) a n = 6 ∙ (-4)n-1
D) a n = 6 ∙ (-4)n+1
Write the series using summation notation.
38) 9 – 27 + 81 – 243 + …
A)
∞
∑
n=0
9 ∙ 3 n+1
B)
∞
∑
9(-3)n
C)
n=0
∞
∑
n=0
Find the sum of the arithmetic series.
39) 247 + 245 + 243 + 241 + … + 229
A) 227
B) 2461
9 ∙ 3n
D)
∞
∑
37)
38)
9(-3)n+1
n=0
39)
C) 2580
7
D) 2380
Find the sum of the geometric series.
4 16 64 256 1024
40) +
+
+
+
3
3
3
3
3
1360
3
A)
40)
B)
1364
15
C)
Find the sum of the first n terms of the sequence.
41) 5 + 2 – 1 – 4 + … ; n = 11
253
A) B) – 110
2
Find the sum.
42)
n
∑
1364
3
D)
272
3
41)
275
D) 2
C) – 138
42)
(k2 + 30)
k=1
A)
n(n+1)(2n+1) + 6n
6
B)
n(n+1)(2n+1)
6
C)
n(n+1)(2n+1) + 180
6
D)
n(n+1)(2n+1) + 180n
6
Write a linear factorization of the function. (Factor the given function completely.)
43) f(x) = x3 + 2×2 + 2x – 5
A) f(x) = (x + 1)(2x + 3 + 7i)(2x + 3 – 7i)
C) f(x) = (x – 1)(x + 3 + 11i)(x + 3 – 11i)
B) f(x) = (x + 1)(2x + 3 + 11i)(2x + 3 D) f(x) = (x – 1)(2x + 3 + 11i)(2x + 3 –
43)
11i)
11i)
Find all rational zeros and factor f(x).
44) f(x) = x3 – 6×2 + 3x + 10
44)
A) 2, 5, -1; f(x) = (x – 2)(x – 5)(x + 1)
C) -3, -6, 1; f(x) = (x + 3)(x + 6)(x – 1)
B) 3, 6, -1; f(x) = (x – 3)(x – 6)(x +1)
D) -2, -5, 1; f(x) = (x + 2)(x + 5)(x – 1)
Determine which of the rational functions given below has the following feature(s).
45) There is a “hole” in its graph at x = 4
4x – 1
(x – 4)(x + 9)
A) f(x) =
B) f(x) =
x+9
(x + 5)(x – 4)
C) f(x) =
x+9
x-4
46) x-intercepts: -5 and -1, y-intercepts:
D) f(x) =
x+4
(x + 9)(x + 4)
5
, vertical asymptote: x = 4, horizontal asymptote: y = 1
16
A) f(x) =
(x + 5)(x + 1)
(x – 4)2
B) f(x) =
(x – 5)(x – 1)
(x + 4)2
C) f(x) =
(x + 5)(x + 1)
(x – 4)
D) f(x) =
(x – 5)(x – 1)
(x + 4)
8
45)
46)
Solve the problem.
47) As one approaches a certain sound source, the sound intensity in arbitrary units increases
according to the following function of time:
2(x – 4)2 + 2(x – 4) – 9
F(x) = .
2(x – 4) + 40
47)
Starting at x = 0, when the source of sound is first sensed, how much time elapses until maximum
sound intensity is felt? Round the result to the nearest hundredth.
A) 35.38 sec.
B) 19.69 sec.
C) 3.38 sec.
D) 0.24 sec.
Find the domain and range of the inverse of the given function.
3
48) f(x) = 3x – 2
A) Domain: [2, ∞); range: [0, ∞)
B) Domain: all real numbers; range: [0, ∞)
C) Domain and range: all real numbers
D) Domain: [0, ∞); range: all real numbers
Solve the equation.
1 3x + 6
49)
= 9 x- 5
3
A) –
1
4
49)
B)
16
3
C)
4
5
D) –
1
5
1 x+4
50) ex – 1 =
e5
A) –
19
6
48)
50)
B)
5
6
C) –
21
4
D) –
5
4
Solve the problem.
51) In September 1998 the population of the country of West Goma in millions was modeled by
f(x) = 17.4e0.0014x. At the same time the population of East Goma in millions was modeled by
51)
g(x) = 14.9e0.0185x. In both formulas x is the number of years since September 1998. Assuming
these trends continue, estimate the year when the population of West Goma will equal the
population of East Goma.
A) 1989
B) 2007
C) 2006
D) 9
Solve the equation.
4
52) x = log4 16
A) 8
52)
B)
1
2
C) –
9
1
2
D) 2
Write the expression as a sum, difference, or product of logarithms. Assume that all variables represent positive real
numbers.
53) logb
3
x8
y7 z 9
53)
A) 8logbx – 7logby – 9logbz
C)
1
logbx8 – logby7 – logbz 9
3
B)
8
7
logbx ÷ ( logby ∙ 3logbz)
3
3
D)
8
7
logbx – logby – 3logbz
3
3
Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
1
1
1
54) log2 (x4 )+ log2(x4 ) – log2 x
54)
2
4
6
A) log2 (x17/6 )
B)
7
log2 (x8 )
6
C) log2 (x9/2)
D) log2 (x7 )
Given log 10 2 = 0.3010 and log 10 3 = 0.4771, find the logarithm without using a calculator.
9
55) log 10
8
A) 0.8293
B) 0.1992
C) 0.0512
D) 2.0333
Solve the problem.
56) How long will it take a sample of radioactive substance to decay to half of its original amount, if it
decays according to the function A(t) = 800e-.207t, where t is the time in years? Round your answer
to the nearest hundredth year.
A) 3.35 years
B) 32.29 years
C) 35.64 years
55)
56)
D) 165.60 years
57) An artifact is discovered at a certain site. If it has 52% of the carbon-14 it originally contained, what
is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of 0.0125%
annually.)
A) 5231 years
B) 2272 years
C) 3840 years
D) 4160 years
57)
58) Coffee is best enjoyed at a temperature of 115° F. A restaurant owner wants to discover the
temperature T at which he should serve his coffee so that it will have cooled to this ideal
temperature in 4 minutes. He discovers that a cup of coffee served at 199° F cools to 181° F in one
minute when his restaurant is at 74° F. If he maintains the restaurant temperature at 74° F, at what
temperature should he serve the coffee to meet his goal?
A) 170° F
B) 150° F
C) 199° F
D) 145° F
58)
Solve the system.
5 1
31
59) + = x y
72
59)
5 1
49
– =x y
72
A) {(8, -9)}
B) {(-9, 8)}
C) {(9, -8)}
10
D) {(5, 5)}
Find the partial fraction decomposition for the rational expression.
7×2 – 67x + 14
60)
(x2 + 2x – 7)(x – 7)
A)
C)
2x
-9
x-7
B)
9x
-2
+
x – 7 x2 + 2x – 7
D)
x2 + 2x – 7
+
60)
9x
x2 + 2x – 7
9x
x2 + 2x – 7
+
2
x-7
+
-2
x-7
Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
61) x2 + 3xy + y2 = 4
x2 – 3xy – y2 = 4
A) {(2, 0), (-2, 0)}
C) {(2, 0), (-2, 0), (2, -6), (-2, 6)}
62)
B) {(0, 2), (0, -2), (2, -6), (-2, 6)}
D) {(2, -6), (-2, 6)}
xy = 7
2
2y – x2 = 7
62)
1
, (7, 1)
2
A)
-14, –
B)
2i 7, -i 7 , – 2i 7, i 7 ,
i 14
i 14, , 7, 7
2
C)
D)
61)
i 14, –
7,
i 14
i 14
, -i 14,
,
2
2
7 , –
7,
7, –
7 , –
Find the indicated matrix.
63) Let A = 1 3 and B = 0 4 . Find 4A + B.
25
-1 6
A)
B)
4 16
4 16
1 11
7 26
7
7, –
7
63)
C)
D)
4 28
4 44
4 7
7 11
Solve the problem.
0 -1 0
-1 1 0
0 1 -1 and B = 0 -1 0 , find AB and BA.
1 1 0
-1 0 -1
A)
B)
0 -1 0
0 -1 0
AB = 0 -1 0 ; BA = 0 -1 0
AB =
-1 0 0
-1 0 0
C)
D)
0 -1 0
0 0 1
AB = -1 0 0 ; BA = 0 1 -1
AB =
0 -2 0
0 -2 1
64) Given A =
11
64)
0 2 -1
0 1 0
;
BA
=
0 -1 1
-1 -2 0
0 0 -1
0 -2 0
0 1 0
0 2 -1
-1 -2 0 ; BA = 0 -1 1
0 -2 0
0 0 -1
Find the inverse, if it exists, for the matrix.
65) 1 -4
-3 -4
A)
B)
1
1
1
1
4
4
16 4
–
3
1
16 16
0 2 2
66) -4 0 7
0 2 0
A)
7
8
–
–
3
16
65)
C)
D)
3
1
16 16
1
4
1
1
4
4
1
4
1
4
1
3
16
16
66)
B)
1
4
7
8
1
2
0
1
2
1
2
0
0
7
8
0
1
2
–
1
4
0
0
–
7
8
1
2
–
1
2
D) The inverse does not exist.
C)
7
8
1
4
7
8
0
0
1
2
1
2
0
–
1
2
12
6 -2
67) 6 -1
12 -3
0 -4
A)
5 -2
-2 -1
3 -3
10 0
67)
B)
1
0
0 –
1
3
1
6
0
1 0 –
5
9
1
6
0
0
1 –
2
9
1
12
0
0
0
0
0
1
2
1
5
-1
-2
–
1
3
1
3
–
1
4
1
10
–
–
1
2
-1
–
1
3
0
D) The inverse does not exist.
C)
1
6
1
2
1
6
-1
1
12
–
1
3
0
–
1
4
1
1
2
5
–
1
2
-1
1
1
3
3
1
10
0
Solve the problem.
68) A basketball fieldhouse seats 15,000. Courtside seats sell for $10, endzone for $7, and balcony for $
4. Total revenue for a sell-out is $84,000. If half the courtside and balcony and all the endzone seats
are sold, the total revenue is $49,000. How many of each type of seat are there in the fieldhouse?
A) 3,200 courtside; 1,800 endzone; 10,000 balcony
B) 3,000 courtside; 2,000 endzone; 10,000 balcony
C) 4,000 courtside; 3,000 endzone; 8,000 balcony
D) 2,000 courtside; 5,000 endzone; 8,000 balcony
Perform the operation or operations when possible.
9x + 8y
-4x – 6y
8k – 7z – -4k – 4z
69)
-8w + 7v
-4w + 9v
4m – 6n
8m – 8n
A)
B)
5x + 2y
5x + 14y
4k – 11z
4k – 3z
-12w + 16v
-12w – 2v
12m – 14n
12m + 2n
68)
69)
C)
D)
13x + 14y
12k – 3z
-4w – 2v
-4m + 2n
13
13x + 2y
12k – 11z
-4w + 16v
-4m – 14n
Solve the problem.
70) A bookstore is having a sale. All books included in the sale have a colored sticker on them to
indicate the sale price. There are green stickers, red stickers, and orange stickers. Bob, Sue, and Fred
each make purchases of books that are on sale. Each row of the table gives information about the
numbers of book purchases and the total cost of the purchase (before taxes).
Person Green Red Orange Total Cost
Bob
1
2
2
$30.44
Sue
1
3
2
$37.31
Fred
1
2
3
$36.31
Use this information to set up a matrix equation of the form AX = B, which can be solved to
determine the price for each type of sale book. Solve this matrix equation to find the price of a book
with a red sticker.
122
5 -2 -2
Use the fact that for A = 1 3 2 , A-1 = -1 1 0 .
123
-1 0 1
A) $6.87
B) $6.50
C) $6.99
D) $6.79
14
70)
