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Math 96 - Final Exam Sample Packet A
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve.1) Find the volume of the circular cylinder below whose diameter is 12 m and height is 8 m.
12 m
8 m
A) 288π m3 B) 108π m3 C) 648π m3 D) 54π m3
1)
2) The sum of two numbers is -2. Three times the first number equals 4 times the second number.Find the two numbers.
A) 87
and 67
B) -2 and 12 C) -8 and -6 D) - 87
and - 67
2)
3) A boat moves 5 kilometers upstream in the same amount of time it moves 20 kilometersdownstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in stillwater.
A) 6 23
km/hr B) 9 km/hr C) 3 km/hr D) 15 km/hr
3)
4)34x - 2 =
3x + 6
A) 2 B) 83
C) 43
D) 45
4)
5) The amount of water in a leaky bucket is given by the linear function f(t) = 125 - 7t, where f(t) isin ounces and t is in minutes. Find the amount of water in the bucket after 4 minutes.A) 28 oz B) 118 oz C) 153 oz D) 97 oz
5)
6) x4 + 36 = 37x2
A) -1, 1, -6, 6 B) 1, 36 C) -i, i, -6i, 6i D) -1, 1, -6i, 6i6)
7) 4x + 6 - 3 = 0
A) 34
B) 43
C) 12 D) ∅
7)
Appendix A - 1
Graph the piecewise defined function.8)
f(x) = -4 if x ≤ -1-2 + x if x > -1
A)
x-4 -2 2 4 6
y
4
2
-2
-4
x-4 -2 2 4 6
y
4
2
-2
-4
B)
x-4 -2 2 4 6
y
4
2
-2
-4
x-4 -2 2 4 6
y
4
2
-2
-4
C)
x-4 -2 2 4 6
y
4
2
-2
-4
x-4 -2 2 4 6
y
4
2
-2
-4
D)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
8)
Solve the equation.
9) (4x + 2)2 = 36A) 10, -10 B) 0, 1 C) 1, 2 D) 1, -2
9)
Find the vertex of the graph of the quadratic function.
10) f(x) = -7x2 - 14x - 5A) (1, -26) B) (-1, 2) C) (-2, -19) D) (2, -61)
10)
Solve for x.11) log
3/5 x = 2
A) 925
B) 23/5 C) 95
D) 35
11)
Appendix A - 2
Graph the function. Find the vertex.
12) f(x) = -5x2
A) vertex: (0, 0)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B) vertex: (0, 0)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C) vertex: (0, 0)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D) vertex: (0, -5)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
12)
Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor thetrinomial.
13) x2 + 13x + _______
A) x2 + 13x + 19
= x + 13
2B) x2 + 1
3x + 36 = (x +6)2
C) x2 + 13x + 136
= x + 16
2D) x2 + 1
3x + 16
= x + 13
2
13)
Appendix A - 3
Graph the exponential function.
14) f(x) = 4x + 1
A)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
14)
Find the power of i.
15) i15
A) 1 B) -i C) i D) -115)
Solve the equation.
16) x2 + 2x - 35 = 0A) -7, 1 B) 7, -5 C) 7, 5 D) -7, 5
16)
17) 11x
= 6 - 1x
A) 116
B) 2 C) 1 D) 35
17)
18) 1x + 6
+ 2x + 3
= -3
x2 + 9x + 18
A) -6 B) 0 C) 3 D) no solution
18)
Appendix A - 4
19) 4( 3x - 5 )
= 256
A) 128 B) 3 C) 164
D) -3
19)
20) log9 (x + 2) - log
9 x = 2
A) 140
B) 40 C) 9 D) 281
20)
Solve the proportion.
21) 4y - 6
= 5y + 6
A) 54 B) 12 C) - 54 D) - 43
21)
Graph the function.22) f(x) = -|x + 2| + 6
x-10 10
y
10
-10
x-10 10
y
10
-10
A)
x-10 10
y
10
-10
x-10 10
y
10
-10
B)
x-10 10
y
10
-10
x-10 10
y
10
-10
22)
Appendix A - 5
C)
x-10 10
y
10
-10
x-10 10
y
10
-10
D)
x-10 10
y
10
-10
x-10 10
y
10
-10
23) f(x) = x - 4A)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
23)
Rationalize the denominator and simplify.
24) 3 - 43 + 4
A) -7 - 2 12 B) 7 + 2 12 C) 2 12 - 7 D) 7 - 2 12
24)
Appendix A - 6
Write the series with summation notation.25) 14 + 20 + 26 + 32
A)4
i = 1
(6i + 2)∑ B)4
i = 1
(6i + 8)∑ C)4
i = 1
(i + 13)∑ D)4
i = 1
14i∑
25)
Use the quadratic formula to solve the equation.
26) 4x2 + 1 = 3x
A) -3 - i 78
, -3 + i 78
B) -3 - i 78
, 3 + i 78
C) 3 - i 78
, -3 + i 78
D) 3 - i 78
, 3 + i 78
26)
Evaluate.27)
7 0 06 3 96 2 8A) -42 B) 294 C) 47 D) 42
27)
Write the first five terms of the sequence whose general term is given.
28) an = n2 - nA) 2, 6, 12, 20, 30 B) 1, 4, 9, 16, 25 C) 0, 2, 6, 12, 20 D) 0, 3, 8, 15, 24
28)
Find an equation of the line.29) Through (-2, 4); perpendicular to y = 2x - 2
A) y= -2x + 3 B) y = 2x + 3 C) y = 12x + 3 D) y= - 1
2x + 3
29)
Write the function in the form y = a(x - h)2 + k.
30) f(x) = -2x2 + 4x - 9
A) y = -2(x + 1)2 - 15 B) y = -2(x + 2)2 - 25
C) y = -2(x - 1)2 - 7 D) y = -2(x - 2)2 - 13
30)
Appendix A - 7
!
Math 96 - Final Exam Sample Packet B
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation.1) log
5 (x + 2) - log
5 x = 2
A) 12 B) 225 C) 5 D) 112
1)
2) x2 + 9x - 36 = 0A) 12, -3 B) -12, 3 C) -12, 1 D) 12, 3
2)
3) 1x + 7
+ 4x + 5
= -2x2 + 12x + 35
A) 5 B) no solution C) 0 D) -7
3)
4) 273x - 5
= 95x
A) 115 B) - 115 C) 15 D) - 15
4)
Solve the proportion.
5) 3y + 2
= 2y - 2
A) 4 B) 45 C) 10 D) - 10
5)
Solve.6) 3x - 2 - 2 = 0
A) 23 B) 2 C) 4 D) ∅
6)
7) One number is four more than a second number. Two times the first number is 12 more than fourtimes the second number. Find the two numbers.A) - 10 and - 14 B) 2 and - 2 C) 1 and - 3 D) 3 and - 1
7)
8) How many real solutions are possible for a system of equations whose graphs are a parabola anda hyperbola?A) 1, 2, 3, or 4 real solutions B) 0, 1, 2, or 3 real solutionsC) 1, 2, or 3 real solutions D) 0, 1, 2, 3, or 4 real solutions
8)
Appendix B - 1
9) Find the volume of the circular cylinder below. Leave your answer in terms of π.
10 m
17 m
A) 220π m3 B) 2420π m3 C) 110π m3 D) 425π m3
9)
10) x4 - 7x2 - 144 = 0A) -4, 4, -3, 3 B) -16, 16, -9i, 9i C) -3, 3, -4i, 4i D) -4, 4, -3i, 3i
10)
11) A painter can finish painting a house in 6 hours. Her assistant takes 8 hours to finish the samejob. How long would it take for them to complete the job if they were working together?
A) 5 hr B) 3 37
hr C) 7 hr D) 724
hr
11)
12) A boat moves 5 kilometers upstream in the same amount of time it moves 18 kilometersdownstream. If the rate of the current is 8 kilometers per hour, find the rate of the boat in stillwater.
A) 6 1213
km/hr B) 3 113
km/hr C) 14 213
km/hr D) 8 km/hr
12)
13) An arrow is fired into the air with an initial velocity of 160 feet per second. The height in feet ofthe arrow t seconds after it was shot into the air is given by the function h(t) = -16t2 + 160t. Findthe maximum height of the arrow.A) 720 ft B) 80 ft C) 1200 ft D) 400 ft
13)
Evaluate the expression.
14) 5
i=2(2i - 2)∑
A) 12 B) 18 C) 16 D) 20
14)
Solve the nonlinear system of equations for real solutions.
15) 4x2 - 2y2 = 6-x2 + y2 = 1A) ( 5, 2), ( 5, -2), (- 5, 2), (- 5, -2) B) (2, 5), (2, - 5)C) (2, 5), (2, - 5), (-2, 5), (-2, - 5) D) (2, 5), (-2, - 5)
15)
Write in terms of i.16) -1600
A) ±40 B) -40i C) i 40 D) 40i16)
Appendix B - 2
Graph the function.17) y = log
2x
A)
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
B)
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
C)
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
D)
x-6 -4 -2 2 4 6
y
4
2
-2
-4
x-6 -4 -2 2 4 6
y
4
2
-2
-4
17)
Appendix B - 3
18) f(x) = -|x| - 5
A)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
18)
Solve the equation. Give an exact solution.
19) e(x + 6)
= 3
A) -3 B) e3 C) ln 3 - 6 D) e3 - 6
19)
Find the value of the logarithmic expression.
20) log5
1125
A) 3 B) -3 C) - 125
D) 13
20)
Find the indicated term of the sequence.21) The eighth term of the arithmetic sequence whose first term is -3 and whose common difference
is -3A) -27 B) 18 C) -24 D) 21
21)
Appendix B - 4
Sketch the graph of the quadratic function. Give the vertex and axis of symmetry.
22) f(x) = 15(x - 3)2 - 1
A) vertex (1, -3); axis x = 1
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B) vertex (-1, 3); axis x = -1
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C) vertex (3, -1); axis x = 3
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D) vertex (-3, -1); axis x = -3
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
22)
Write an equation of the circle with the given center and radius.23) (1, 2); 5
A) (x + 3)2 + (y - 9)2 = 5 B) (x + 1)2 + (y + 2)2 = 5
C) (x - 1)2 + (y - 2)2 = 5 D) (x + 2)2 + (y + 1)2 = 25
23)
Use the Pythagorean theorem to find the unknown side of the right triangle.24)
6
5A) 11 B) 31 C) 41 D) 31
24)
Appendix B - 5
Find the power of i.
25) i13
A) -1 B) i C) 1 D) -i25)
Solve the equation for x. Give an exact solution.26) ln 3x = 4
A) e3
4B) e
43 C) e
4
3D) 12
26)
Simplify the radical expression. Assume that all variables represent positive real numbers.
27) 50k7q8
A) 5k7q8 2k B) 5k3q4 2 C) 5k3q4 2k D) 5q4 2k727)
Solve the equation for the indicated variable.
28) P = A1 + rt
for t
A) t = P - 1Ar
B) t = A - PPr
C) t = P - Ar D) t = P - A1 + r
28)
Find the inverse of the one-to-one function.
29) f(x) =3x - 7
A) f-1(x) = x + 7 B) f-1(x) = x3 + 49 C) f-1(x) = x3 + 7 D) f-1(x) = 1
x3 + 7
29)
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
30) 5x + 6
A) - 30 - 5 xx - 36
B) - 30 + 5 xx - 36
C) - 30 + 5 x
x2 - 36D) - 30 - 5 x
x + 36
30)
Appendix B - 6
Math 96 - Final Exam Sample Packet C
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Given the matrix in echelon form, find the solution for the system.1)
1 1 4 20 1 -2 60 0 1 -3A) (2, 6, -3) B) (14, 0, -3) C) (-3, 0, 14) D) (2, 12, -3)
1)
Complete the indicated row operation.2) Replace R2 in -5 8 1
-3 0 6 with -4R1 + R2.
A) -5 8 1 -8 8 7
B) -5 8 1 17 -32 2
C) 17 -32 2 -3 0 6
D) -5 8 1
-23 32 10
2)
Find the sum of the terms of the infinite geometric sequence.
3) 2, - 23, 29, ...
A) 43
B) 2 C) - 23
D) 32
3)
Graph the function.4) f(x) = -3x2
A)
x-4 -2 2 4
y
4
2
-2
-4
x-4 -2 2 4
y
4
2
-2
-4
B)
x-4 -2 2 4
y
4
2
-2
-4
x-4 -2 2 4
y
4
2
-2
-4
C)
x-4 -2 2 4
y
4
2
-2
-4
x-4 -2 2 4
y
4
2
-2
-4
D)
x-4 -2 2 4
y4
2
-2
-4
x-4 -2 2 4
y4
2
-2
-4
4)
Appendix C - 1
5) f(x) = -|x| - 4
A)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
5)
Appendix C - 2
6) y = log4x
A)
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
B)
x-6 -4 -2 2 4 6
y
4
2
-2
-4
x-6 -4 -2 2 4 6
y
4
2
-2
-4
C)
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
D)
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y6
4
2
-2
-4
-6
6)
Solve the equation.7) x2 + 6x + 5 = 0
A) -1, -5 B) 2, -1 C) 10, -5 D) 1, 5
7)
Solve.8) A boat moves 7 kilometers upstream in the same amount of time it moves 15 kilometersdownstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in stillwater.
A) 13 18
km/hr B) 7 78
km/hr C) 9 km/hr D) 24 34
km/hr
8)
9) An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet ofthe arrow t seconds after it was shot into the air is given by the function h(t) = -16t2 + 96t. Findthe maximum height of the arrow.A) 240 ft B) 144 ft C) 432 ft D) 48 ft
9)
10) How many real solutions are possible for a system of equations whose graphs are an ellipse anda circle?A) 0, 1, 2, or 3 real solutions B) 0, 1, 2, 3, or 4 real solutionsC) 1, 2, or 3 real solutions D) 1, 2, 3, or 4 real solutions
10)
Appendix C - 3
11) One number is four more than a second number. Two times the first number is 6 more than fourtimes the second number.A) - 7 and - 11 B) 6 and 2 C) 5 and 1 D) 4 and 0
11)
12) x4 - 21x2 - 100 = 0A) -5, 5, -2i, 2i B) -2, 2, -5i, 5i C) -5, 5, -2, 2 D) -25, 25, -4i, 4i
12)
13) 5x - 4 - 4 = 0
A) 4 B) 16 C) 125
D) ∅
13)
Use the Pythagorean theorem to find the unknown side of the right triangle.14)
5
3
A) 4 B) 2 7 C) 22 D) 22
14)
Find the distance between the pair of points.15) (7, -7) and (3, -5)
A) 12 3 units B) 6 units C) 2 5 units D) 12 units15)
Solve the equation.16) log
5 (x + 2) - log
5 x = 2
A) 112
B) 5 C) 225
D) 12
16)
17) 274x - 3
= 92x
A) 98
B) 89
C) - 98
D) - 89
17)
18) 1x + 7
+ 3x + 4
= -3x2 + 11x + 28
A) 4 B) 0 C) -7 D) no solution
18)
Appendix C - 4
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
19) 4x + 7
A) - 28 + 4 x
x2 - 49B) - 28 + 4 x
x - 49C) - 28 - 4 x
x + 49D) - 28 - 4 x
x - 49
19)
Use the quadratic formula to solve the equation.
20) 2x2 + 12x = - 7
A) -12 - 222
, -12 + 222
B) -6 - 22
, -6 + 22
C) -6 - 224
, -6 + 224
D) -6 - 222
, -6 + 222
20)
Find the indicated term of the sequence.21) The eighth term of the arithmetic sequence whose first term is 6 and whose common difference is
-4A) -26 B) 34 C) 38 D) -22
21)
Find the indicated term for the sequence whose general term is given.
22) an = (-1)n
n + 4; a
18
A) - 911
B) 172
C) - 122
D) 122
22)
Appendix C - 5
Graph the piecewise defined function.23)
f(x) = -x + 4 if x < 03x - 4 if x ≥ 0
A)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
B)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
C)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
D)
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
x-6 -4 -2 2 4 6
y
6
4
2
-2
-4
-6
23)
Appendix C - 6
Sketch the graph of the equation. Find its vertex.
24) x = y2 + 2
A) vertex (0, 2)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
B) vertex (2, 0)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
C) vertex (0, -2)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
D) vertex (-2, 0)
x-10 -5 5 10
y10
5
-5
-10
x-10 -5 5 10
y10
5
-5
-10
24)
Write as a logarithmic equation.
25) 4-2
= 116
A) log4116
= -2 B) log4
-2 = 116
C) log-2
116
= 4 D) log1/16
4 = -2
25)
For the given functions f and g, find the composition.
26) f(x) = x3 + 2x; g(x) = 3x Find (g ∘ f)(x).
A) 27x3 + 6x B) 3x3 + 2x C) 3x3 + 6x D) 27x2 + 6x
26)
Appendix C - 7
Find the surface area of the figure.27)
2 m
6 m
4 m
A) 88 m2 B) 48 m2 C) 96 m2 D) 44 m2
27)
Solve the equation. Give an exact solution.
28) e(x + 6)
= 3
A) -3 B) ln 3 - 6 C) e3 - 6 D) e-328)
Use the given right triangle to find the trigonometric function.29) sin A
A) 35
B) 54
C) 45
D) 34
29)
Solve the equation for x. Give an exact solution.30) ln 11x = -2
A) e11
-2B) e
-2
11C) e
- 211 D) -22
30)
Appendix C - 8
1
Final Exam Sample Packet Answer Keys Form A Form B Form C
1. A D B 2. D B B 3. D B D 4. B D A 5. D C D 6. A B B 7. A B A 8. A D D 9. D D B 10. B D B 11. A B C 12. C C A 13. C D A 14. C D D 15. B C C 16. D D A 17. B D A 18. D B D 19. B C B 20. A B D 21. A C D 22. A C D 23. C C A 24. C B B 25. B B A 26. D C C 27. D C A 28. C B B 29. D C C 30. C B B