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 2
0 1 -2 6
0 0 1 -3
A) (2, 6, -3)
B) (14, 0, -3)
C) (-3, 0, 14)
Complete the indicated row operation.
2) Replace R 2 in -5 8 1 with -4R 1 + R 2.
-3 0 6
A)
-5 8 1
-8 8 7
C)
17 -32 2
-3
0 6
1)
D) (2, 12, -3)
2)
B)
-5
8 1
17 -32 2
D)
-5
-23
8 1
32 10
Find the sum of the terms of the infinite geometric sequence.
2 2
3) 2, - , , ...
3 9
A)
4
3
B) 2
3)
C) -
2
3
D)
3
2
Graph the function.
4) f(x) = -3x2
A)
4)
B)
y
y
4
4
2
2
-4
-2
2
4
-4
x
-2
2
4
x
-2
-2
-4
-4
C)
D)
y
y
4
4
2
2
-4
-2
2
4
-4
x
-2
2
-2
-2
-4
-4
1
4
x
5) f(x) = -|x| - 4
5)
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
2
6) y = log
4
x
6)
A)
B)
y
y
6
4
4
2
2
-6
-4
-2
2
4
6 x
-6
-4
-2
2
-2
4
6 x
-2
-4
-4
-6
C)
D)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6 x
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
4
6
x
Solve the equation.
7) x2 + 6x + 5 = 0
A) -1, -5
7)
B)
2, -1
C) 10, -5
D) 1, 5
Solve.
8) A boat moves 7 kilometers upstream in the same amount of time it moves 15 kilometers
downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in still
water.
1
7
3
A) 13 km/hr
B) 7 km/hr
C) 9 km/hr
D) 24 km/hr
8
8
4
8)
9) An arrow is fired into the air with an initial velocity of 96 feet per second. The height in feet of
the arrow t seconds after it was shot into the air is given by the function h(t) = -16t2 + 96t. Find
9)
the maximum height of the arrow.
A) 240 ft
B) 144 ft
C) 432 ft
D) 48 ft
10) How many real solutions are possible for a system of equations whose graphs are an ellipse and
a circle?
A) 0, 1, 2, or 3 real solutions
B) 0, 1, 2, 3, or 4 real solutions
C) 1, 2, or 3 real solutions
D) 1, 2, 3, or 4 real solutions
3
10)
11) One number is four more than a second number. Two times the first number is 6 more than four
times the second number.
A) - 7 and - 11
B) 6 and 2
C) 5 and 1
D) 4 and 0
11)
12) x4 - 21x2 - 100 = 0
A) -5, 5, -2i, 2i
12)
13)
B) -2, 2, -5i, 5i
C) -5, 5, -2, 2
B) 16
12
C)
5
D) -25, 25, -4i, 4i
5x - 4 - 4 = 0
A) 4
13)
D) ∅
Use the Pythagorean theorem to find the unknown side of the right triangle.
14)
14)
5
3
A) 4
B) 2
7
C) 22
Find the distance between the pair of points.
15) (7, -7) and (3, -5)
A) 12 3 units
B) 6 units
Solve the equation.
16) log (x + 2) - log x = 2
5
5
1
A)
12
4x - 3
17) 27
A)
18)
D)
22
15)
C) 2
5 units
D) 12 units
16)
B) 5
C)
2
25
D) 12
2x
=9
9
8
17)
B)
8
9
C) -
9
8
D) -
8
9
1 + 3 =
-3
x + 7 x + 4 x2 + 11x + 28
A) 4
18)
B) 0
C) -7
4
D) no solution
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
4
19)
x +7
A)
- 28 + 4 x
x2 - 49
B)
- 28 + 4 x
x - 49
C)
- 28 - 4 x
x + 49
D)
- 28 - 4 x
x - 49
Use the quadratic formula to solve the equation.
20) 2x2 + 12x = - 7
22 , -12 +
2
20)
-12 2
C)
-6 - 22 , -6 + 22
4
4
22
A)
19)
2 , -6 +
2
2
B)
-6 2
D)
-6 - 22 , -6 + 22
2
2
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
-4
A) -26
B) 34
C) 38
D) -22
21)
Find the indicated term for the sequence whose general term is given.
n
22) an = (-1) ; a
18
n +4
A) -
9
11
22)
B)
1
72
C) -
5
1
22
D)
1
22
Graph the piecewise defined function.
23)
-x + 4 if x < 0
f(x) =
3x - 4 if x ≥ 0
23)
A)
B)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
-2
-2
-4
-4
-6
-6
C)
2
4
6
x
2
4
6
x
D)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
-2
-2
-4
-4
-6
-6
6
Sketch the graph of the equation. Find its vertex.
24) x = y 2 + 2
24)
A) vertex (0, 2)
B) vertex (2, 0)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C) vertex (0, -2)
10 x
5
10 x
D) vertex (-2, 0)
y
-10
5
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Write as a logarithmic equation.
-2
25) 4 = 1
16
A) log
C) log
25)
1 = -2
B) log
1 =4
D) log
4 16
-2 16
4
-2 = 1
16
1/16
4 = -2
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
26)
B) 3x3 + 2x
C) 3x3 + 6x
7
D) 27x2 + 6x
Find the surface area of the figure.
27)
27)
2m
6m
4m
A) 88 m2
B) 48 m2
C) 96 m2
D) 44 m2
Solve the equation. Give an exact solution.
28) e
(x + 6)
=3
A) -3
28)
3
B) ln 3 - 6
C) e - 6
D) e
-3
Use the given right triangle to find the trigonometric function.
29) sin A
A)
3
5
B)
5
4
C)
29)
4
5
D)
3
4
Solve the equation for x. Give an exact solution.
30) ln 11x = -2
11
A)
e
-2
30)
-2
B)
e
11
C) e
8
- 2
11
D) -22
Answer Key
Testname: MATH 96 - PACKET C
1) B
2) B
3) D
4) A
5) D
6) B
7) A
8) D
9) B
10) B
11) C
12) A
13) A
14) D
15) C
16) A
17) A
18) D
19) B
20) D
21) D
22) D
23) A
24) B
25) A
26) C
27) A
28) B
29) C
30) B
9