Download Review - Final Exam Math 2412

Review - Final Exam Math 2412
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Suppose that a ball is rolling down a ramp. The distance traveled by the ball is given by the function s(t), where t is the
time, in seconds, after the ball is released, and s(t) is measured in feet. For the given function, find the ball's average
velocity from t1 to t2 .
1) s(t) = 9t2 ; t1 = 4 to t2 = 5
A) 81 ft/sec
1)
B) 9 ft/sec
C) 225 ft/sec
D) 162 ft/sec
Sin t and cos t are given. Use identities to find the indicated value. Where necessary, rationalize denominators.
5
2
, cos t = . Find sec t.
2) sin t =
2)
3
3
A)
5
2
B)
2 5
5
C)
3
2
D)
3 5
5
Find the exact value of the indicated trigonometric function of .
21
, 180°< < 270°
Find cos .
3) tan =
20
A)
-20 41
41
B) -
20
29
3)
C) -20
D)
21 41
41
Use a sketch to find the exact value of the expression.
6
4) cos tan-1
5
A)
61
5
B)
4)
5 61
61
C)
5
61
D)
6
5
Use a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the
given inverse trigonometric function.
x2 + 25
)
5) sin(sec-1
5)
x
A) x 5
B)
x2 + 5
x2 + 5
C)
5 x2 + 25
x2 + 25
D)
x x2 + 5
x2 + 5
Complete the identity.
6)
(sin x + cos x)2
=?
1 + 2 sin x cos x
A) 1 - sin x
7) 1 -
6)
C) - sec2 x
B) 1
D) 0
cos2 x
=?
1 + sin x
A) sin x
7)
B) cot x
C) tan x
1
D) 0
Use the given information to find the exact value of the expression.
4
2
8) sin = , lies in quadrant II, and cos = , lies in quadrant I
5
5
A)
8 + 3 21
25
=
5
,
12
A) -
119
169
9) tan
B)
8 - 3 21
25
lies in quadrant III
B)
C)
Find cos ( - ).
6 - 4 21
25
D)
8)
-6 + 4 21
25
Find sin 2 .
9)
120
169
C)
119
169
D) -
120
169
Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than
1.
10) cos3 x
10)
A)
3
1
cos x + cos 3x + cos 2x
4
4
B)
3
1
cos x - cos 3x - cos 2x
4
4
C)
3
1
cos x + cos 3x
4
4
D)
3
1
cos x - cos 3x
4
4
Find all solutions of the equation.
11) 9 cos x + 6 2 = 7 cos x+ 5 2
A) x =
4
C) x =
4
+ n or x =
+ 2n or x =
11)
+n
4
4
B) x =
+ 2n
D) x =
4
4
+ n or x =
+ 2n or x =
4
4
+n
+ 2n
Solve the equation on the interval [0, 2 ).
3
12) cos 2x =
2
A)
C)
,
6
12)
11
6
B)
3
2
D)
12
,
11 13 23
,
,
12 12 12
2
13) sec2 x - 2 = tan2 x
A)
B)
4
14) sin x +
A)
13)
11
6
2
,
- sin x -
4
11
6
C)
3
6
D) no solution
=1
B)
14)
2
,
C)
3
2
D)
4
,
3
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
15) A = 26°, B = 51°, c = 27
A) C = 103°, a = 21.5, b = 12.1
B) C = 103°, a = 12.1, b = 21.5
C) C = 103°, a = 60, b = 33.9
D) C = 97°, a = 11.9, b = 21.1
15)
Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle,
two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures
to the nearest degree.
16) B = 41°, a = 4, b = 3
16)
A) A1 = 61°, C1 = 78°, c1 = 0.1;
B) A = 29°, C = 110°, c = 5.7
A2 = 119°, C2 = 20°, c2 = 0.1
C) no triangle
D) A1 = 61°, C1 = 78°, c1 = 4.5;
A2 = 119°, C2 = 20°, c2 = 1.6
Solve the problem.
17) Two tracking stations are on the equator 173 miles apart. A weather balloon is located on a bearing
of N36°E from the western station and on a bearing of N18°W from the eastern station. How far is
the balloon from the western station? Round to the nearest mile.
A) 203 miles
B) 173 miles
C) 212 miles
D) 164 miles
Find a. If necessary, round your answer to the nearest hundredth.
18)
57°
A) 0.73
17)
18)
21°
1.7
B) 2.43
C) 1.04
D) 3.98
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
19) a = 9, b = 13, c = 16
A) A = 36°, B = 52°, C = 92°
B) A = 32°, B = 54°, C = 94°
C) A = 34°, B = 54°, C = 92°
D) no triangle
Solve the problem.
20) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a
transit. Point C is 52 feet from point A and 74 feet from point B. The angle ACB is 51°. How far
apart are points A and B?
A) 114.1 feet
B) 103 feet
C) 75.9 feet
D) 57.8 feet
21) A painter needs to cover a triangular region 62 meters by 67 meters by 73 meters. A can of paint
covers 70 square meters. How many cans will be needed?
A) 318 cans
B) 3 cans
C) 14 cans
D) 28 cans
3
19)
20)
21)
Find another representation, (r, ), for the point under the given conditions.
22) 2,
2
, r < 0 and 0 <
A) -2, -
<2
3
2
22)
B) -2,
3
2
C) -2, -
1
2
D) -2,
Select the representation that does not change the location of the given point.
23) (5, 30°)
A) (-5, 390)°
B) (5, 210)°
C) (-5, 120)°
5
2
D) (5, 390)°
The rectangular coordinates of a point are given. Find polar coordinates of the point. Express in radians.
24) (0, - 3)
A) (- 3, 90°)
B) (- 3, 180°)
C) ( 3, 90°)
D) (- 3, 270°)
Convert the rectangular equation to a polar equation that expresses r in terms of .
25) 8x - 7y + 10 = 0
-10
A) r =
B) 8 cos - 7 sin = 10
(8 sin - 7 cos )
C) r =
(8 cos
-10
- 7 sin )
D) 8 cos
26) y2 = 3x
A) r2 (cos
- 7 sin
24)
25)
= -10
26)
+ sin ) = 3
C) r = 3 cot2 x
B) r = 3 cot x cscx
D) r = 9 cot x cscx
Convert the polar equation to a rectangular equation.
27) r = 6 cos + 4 sin
A) x2 + y2 = 4x + 6y
27)
B) x2 + y2 = 6x + 4y
D) x2 - y2 = 6x + 4y
C) 6x + 4y = 0
The graph of a polar equation is given. Select the polar equation for the graph.
28)
A) r = 4 cos
23)
B) r = 2 + sin
C) r = 4 sin
4
28)
D) r = 2 + cos
Solve the problem.
29) The wind is blowing at 10 knots. Sailboat racers look for a sailing angle to the 10-knot wind that
produces maximum sailing speed. This situation is now represented by the polar graph in the
figure shown below. Each point (r, ) on the graph gives the sailing speed, r, in knots, at an angle
to the 10-knot wind. What angle to the wind produces the maximum sailing speed? What is the
speed to the nearest knot, of the sailboat sailing at 60° angle to the wind?
A) 120°; 5 knots
B) 120°; 8 knots
C) 60°; 5 knots
D) 60°; 7 knots
Write the complex number in polar form. Express the argument in radians.
30) - 5 3 - 5i
4
4
4
4
+ i sin
+ i sin
A) 5 3 cos
B) 10 cos
3
3
3
3
C) 5 3 cos
13
6
+ i sin
13
6
D) 10 cos
30)
7
7
+ i sin
6
6
Write the complex number in rectangular form.
2
2
)
+ i sin
31) -5(cos
3
3
A)
5 5 3
i
+
2
2
B) -
29)
31)
5 -5 3
i
+
2
2
C) -
5 5 3
i
+
2
2
D)
5 -5 3
i
+
2
2
Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.
5
7
7
+ i sin
)
32) 2 2 (cos
32)
4
4
A) -64 2 + 64 2i
B) -128 + 128i
C) -
Find the specified vector or scalar.
33) u = 2i + 7j and v = 12i + 42j; Find v - u .
A) 5 53
B) 53
2+
2i
D) -64 + 64i
33)
C) 6 53
D) 5 54
Write the vector v in terms of i and j whose magnitude v and direction angle are given.
34) v = 7, = 225°
7 3
7
7
7 3
i- j
j
A) v = B) v = - i 2
2
2
2
C) v = -
7 2
7 2
ij
2
2
D) v =
5
7 2
7 2
i+
j
2
2
34)
Solve the problem.
35) The magnitude and direction of two forces acting on an object are 35 pounds, N45°E, and 55
pounds, S30°E, respectively. Find the magnitude, to the nearest hundredth of a pound, and the
direction angle, to the nearest tenth of a degree, of the resultant force.
A) F = 65.19; = -7.5°
B) F = 57.04; = -23.6°
C) F = 49.17; = -11.3°
D) F = 43.30; = 2.7°
Find the angle between the given vectors. Round to the nearest tenth of a degree.
36) u = -i + 4j, v = 2i - 5j
A) 59°
B) 82.2°
C) 1°
D) 172.2°
Solve the problem.
37) Find the work done by a force of 2 pounds acting in the direction of 41° to the horizontal in moving
an object 6 feet from (0, 0) to (6, 0).
A) 7.9 ft-lb
B) 18.1 ft-lb
C) 9.7 ft-lb
D) 9.1 ft-lb
Write the partial fraction decomposition of the rational expression.
6x2 - x - 17
38)
x3 - x
39)
40)
41)
A)
17
6
-5
+
+
x
x+1 x-1
B)
17
-5
-6
+
+
x
x+1 x-1
C)
17
5
-6
+
+
x
x+1 x-1
D)
17
5
-6
+
+
x
x+1 x-1
x+3
3
x - 2x2 + x
35)
36)
37)
38)
39)
A)
3
4
-3
+
+
x x - 1 (x - 1)2
B)
3
4
-3
+
+
x
x - 1 (x - 1)2
C)
3
7
-3
+
+
x x - 1 (x - 1)2
D)
3
4
-3
+
+
x x - 1 (x - 1)2
8x2 + 7x - 7
x3 + 3x2 + 2x + 6
40)
A)
4
4
+
x + 3 x2 + 2
B)
4
4
-5
+
+
x + 3 x + 2 (x + 2)2
C)
4
4x - 5
+
x + 3 x2 + 2
D)
4
4x - 5
+
x + 2 x2 + 3
-19x + 32
(x + 2)2 (x2 + 3)
41)
A)
6x + 4
-3x - 4
+
2
(x + 2)
x2 + 3
B)
3
6
-3x + 4
+
+
x + 2 (x + 2)2
x2 + 3
C)
3
10
-3
+
+
x + 2 (x + 2)2 x2 + 3
D)
3
10
-3x - 4
+
+
x + 2 (x + 2)2
x2 + 3
Graph the ellipse.
6
42)
(x - 1)2 (y + 1)2
+
=1
16
9
42)
A)
B)
C)
D)
Convert the equation to the standard form for an ellipse by completing the square on x and y.
43) 4x2 + 16y2 - 16x - 96y + 96 = 0
(x + 2)2 (y + 3)2
+
=1
A)
16
4
C)
(x - 3)2 (y - 2)2
+
=1
B)
16
4
(x - 2)2 (y - 3)2
+
=1
4
16
D)
7
(x - 2)2 (y - 3)2
+
=1
16
4
43)
Solve the problem.
44) The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width
of the roadway is 38 feet and the height of the arch over the center of the roadway is 11 feet. Two
trucks plan to use this road. They are both 8 feet wide. Truck 1 has an overall height of 10 feet and
Truck 2 has an overall height of 11 feet. Draw a rough sketch of the situation and determine which
of the trucks can pass under the bridge.
A) Neither Truck 1 nor Truck 2 can pass under the bridge.
B) Truck 1 can pass under the bridge, but Truck 2 cannot.
C) Both Truck 1 and Truck 2 can pass under the bridge.
D) Truck 2 can pass under the bridge, but Truck 1 cannot.
Find the standard form of the equation of the hyperbola satisfying the given conditions.
45) Center: (6, 5); Focus: (3, 5); Vertex: (5, 5)
(y - 6)2
(y - 5)2
=1
=1
A) (x - 5)2 B) (x - 6)2 8
8
C)
(x - 5)2
- (y - 6)2 = 1
8
D)
C)
(y - 2)2 (x - 2)2
=1
B)
4
25
(y - 2)2 (x - 2)2
=1
25
4
D)
8
45)
(x - 6)2
- (y - 5)2 = 1
8
Convert the equation to the standard form for a hyperbola by completing the square on x and y.
46) 4y2 - 25x2 - 16y + 100x - 184 = 0
(x + 2)2 (y + 2)2
=1
A)
4
25
44)
(y + 2)2 (x + 2)2
=1
25
4
46)
Use the center, vertices, and asymptotes to graph the hyperbola.
47) (y + 1)2 - (x - 1)2 = 5
A)
B)
C)
D)
Find the standard form of the equation of the parabola using the information given.
48) Focus: (-3, -1); Directrix: x = 7
A) (y + 1)2 = -20(x - 2)
B) (y - 2)2 = -20(x + 1)
C) (x - 2)2 = -20(y + 1)
D) (x + 1)2 = -20(y - 2)
9
47)
48)
Solve the problem.
49) An experimental model for a suspension bridge is built. In one section, cable runs from the top of
one tower down to the roadway, just touching it there, and up again to the top of a second tower.
The towers are both 6.25 inches tall and stand 50 inches apart. At some point along the road from
the lowest point of the cable, the cable is 1 inches above the roadway. Find the distance between
that point and the base of the nearest tower.
A) 15 in.
B) 15.2 in.
C) 9.8 in.
D) 10.2 in.
Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term.
50) x2 + 2xy + y2 - 8x + 8y = 0
2+
2
A) x =
2
x' -
22
2
y'; y =
B) x =
2
2
(x' - y'); y =
(x' + y')
2
2
C) x =
1
3
3
1
x' y'; y =
x' + y'
2
2
2
2
22
2
x' +
2+
2
2
49)
50)
y'
D) x = -y'; y = x'
Identify the equation without applying a rotation of axes.
51) 3x2 + 10xy + 2y2 - 3x - 2y - 3 = 0
A) parabola
B) ellipse
C) hyperbola
D) circle
51)
Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.
52) x = 2t - 1, y = t2 + 3; -4 t 4
52)
A) y =
1 2
x + 1; -6 x 4
2
C) y = -
B) y = x2 + 1; -2 x 2
1
x + 30; -6 x 4
2
D) y =
53) x = 9 sin t, y = 9 cos t; 0 t 2
A) y = a 2 - x2 = 81; - < x <
1 2 1
13
x + x+
; -9 x 7
4
2
4
53)
B) x2 + y2 = 81; -9 x 9
C) y2 - x2 = 81; - < x <
D) y = x2 - 9; -2 x 2
Identify the conic section that the polar equation represents. Describe the location of a directrix from the focus located at
the pole.
3
54) r =
54)
4 + 2 cos
A) ellipse; The directrix is
3
3
unit(s) to the right of the pole at x = .
2
2
B) ellipse; The directrix is
3
3
unit(s) to the left of the pole at x = - .
2
2
C) ellipse; The directrix is
3
3
unit(s) above the pole at y = .
2
2
D) ellipse; The directrix is
3
3
unit(s) below the pole at y = - .
2
2
10
Evaluate the factorial expression.
10!
55)
8! 2!
A) 1
56)
55)
B) 45
C) 0!
D) 10
n(n + 9 )!
(n + 10 )!
A)
1
n + 10
56)
B)
n
(n + 10)!
C)
Find the indicated sum.
7
i!
57)
(i - 1 )!
i=4
A) 7
n
n + 10
D)
n
10
57)
B) 22
C)
7
3
D) 14
Solve the problem.
58) A brick staircase has a total of 15 steps The bottom step requires 108 bricks. Each successive step
requires 5 fewer bricks than the prior one. How many bricks are required to build the staircase?
A) 1095 bricks
B) 2190 bricks
C) 2145 bricks
D) 1057.5 bricks
Solve the problem. Round to the nearest dollar if needed.
59) Lonnie deposits $125 each month into an account paying annual interest of 6.5% compounded
monthly. How much will his account have in it at the end of 11 years?
A) $24,135
B) $24,006
C) $23,852
D) $1921
Find the sum of the infinite geometric series, if it exists.
2
60) 50 + 10 + 2 + + . . .
5
A) 62
B)
59)
60)
125
2
C) -
Find the term indicated in the expansion.
61) (2x + 3)5 ; 5th term
A) 810x
58)
25
2
C) 540x2
B) 270x
D) does not exist
61)
D) 1215
Solve the problem.
62) A combination lock has 45 numbers on it. How many different 3-digit lock combinations are
possible if no digit can be repeated?
A) 14,190
B) 28,380
C) 85,140
D) 1980
11
62)
Solve the problem. Round to the nearest hundredth of a percent if needed.
63) A traffic engineer is counting the number of vehicles by type that turn into a residential area. The
table below shows the results of the counts during a four-hour period. What is the probability that
the next vehicle passing is an SUV?
Type of vehicle Number
Car
284
SUV
420
Van
73
Small truck
289
Large truck
229
Dump truck
24
Other
65
A) 20.52%
B) 30.88%
C) 30.35%
D) 31.84%
Find the probability.
64) A bag contains 5 red marbles, 4 blue marbles, and 1 green marble. What is the probability of
choosing a marble that is not blue when one marble is drawn from the bag?
3
5
2
A)
B) 6
C)
D)
5
3
5
65) A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or
a 6?
13
2
7
A) 7
B)
C)
D)
2
13
26
63)
64)
65)
The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit or
function value does not exist.
66) a. lim f(x)
66)
b. f(1)
x 1
A) a. lim f(x) = 2
x 1
B) a. lim f(x) = 1
x 1
b. f(1) = 2
C) a. lim f(x) = 1
x 1
b. f(1) = 0
D) a. lim f(x) does not exist
x 1
b. f(1) = 2
b. f(1) = 2
12
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties
can be applied.
x2 - 2x - 15
67) lim
67)
x+3
x -3
A) 0
B) does not exist
C) 5
D) -8
Determine for what numbers, if any, the given function is discontinuous.
3x + 3
68) f(x) =
x2 - 16
A) -4 and 4 and 1
B) None
C) 4
68)
D) -4 and 4
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties
can be applied.
(x + h)3 - x3
69) lim
69)
h
h 0
A) 0
B) 3x2
Find the derivative of f at x. That is, find f '(x).
70) f(x) = x2 - 8x + 11; x = 2
A) -8
B) -6
13
C) 3x2 + 3xh + h 2
D) does not exist
C) -4
D) 4
70)
Answer Key
Testname: REVIEW - FINAL EXAM FALL 2015 - VER A
1) A
18) C
2) C
19) C
3) B
20) D
4) B
21) D
5) C
22) B
6) B
23) D
7) A
24) A
8) D
25) C
9) B
26) B
Objective: (1.5) Find a Function's Average Rate of Change
Objective: (6.1) Additional Concepts
Objective: (4.2) Recognize and Use Fundamental
Identities
Objective: (6.2) Use the Law of Cosines to Solve Oblique
Triangles
Objective: (4.4) Use the Signs of the Trigonometric
Functions
Objective: (6.2) Solve Applied Problems Using the Law of
Cosines
Objective: (4.7) Find Exact Values of Composite Functions
with Inverse Trigonometric Functions
Objective: (6.2) Solve Applied Problems Using the Law of
Cosines
Objective: (4.7) Find Exact Values of Composite Functions
with Inverse Trigonometric Functions
Objective: (6.3) Find Multiple Sets of Polar Coordinates
for a Given Point
Objective: (5.1) Use the Fundamental Trigonometric
Identities to Verify Identities
Objective: (6.3) Find Multiple Sets of Polar Coordinates
for a Given Point
Objective: (5.1) Use the Fundamental Trigonometric
Identities to Verify Identities
Objective: (6.3) Convert a Point from Rectangular to Polar
Coordinates
Objective: (5.2) Use the Formula for the Cosine of the
Difference of Two Angles
Objective: (6.3) Convert an Equation from Rectangular to
Polar Coordinates
Objective: (5.3) Use The Double-Angle Formulas
Objective: (6.3) Convert an Equation from Rectangular to
Polar Coordinates
10) C
27) B
Objective: (5.3) Use the Power-Reducing Formulas
Objective: (6.3) Convert an Equation from Polar to
Rectangular Coordinates
11) C
Objective: (5.5) Find All Solutions of a Trigonometric
Equation
28) B
Objective: (6.4) Use Point Plotting to Graph Polar
Equations
12) B
Objective: (5.5) Solve Equations With Multiple Angles
29) A
13) D
Objective: (6.4) Solve Apps: Graphs of Polar Equations
Objective: (5.5) Solve Trigonometric Equations Quadratic
in Form
30) D
Objective: (6.5) Write Complex Numbers in Polar Form
14) C
31) D
Objective: (5.5) Use Identities to Solve Trigonometric
Equations
Objective: (6.5) Convert a Complex Number from Polar to
Rectangular Form
15) B
32) B
Objective: (6.1) Use the Law of Sines to Solve Oblique
Triangles
Objective: (6.5) Find Powers of Complex Numbers in
Polar Form
16) D
33) A
Objective: (6.1) Use the Law of Sines to Solve, if Possible,
the Triangle or Triangles in the Ambiguous
Case
Objective: (6.6) Perform Operations with Vectors in Terms
of i and j
34) C
17) A
Objective: (6.6) Write a Vector in Terms of Its Magnitude
and Direction
Objective: (6.1) Solve Applied Problems Using the Law of
Sines
14
Answer Key
Testname: REVIEW - FINAL EXAM FALL 2015 - VER A
35) B
54) A
Objective: (6.6) Solve Applied Problems Involving Vectors
Objective: (9.6) Define Conics in Terms of a Focus and a
Directrix
36) D
55) B
Objective: (6.7) Find the Angle Between Two Vectors
Objective: (10.1) Use Factorial Notation
37) D
56) C
Objective: (6.7) Compute Work
Objective: (10.1) Use Factorial Notation
38) B
57) B
Objective: (7.3) Decompose P/Q, Where Q Has Only
Distinct Linear Factors
Objective: (10.1) Use Summation Notation
39) D
58) A
40) C
59) B
Objective: (7.3) Decompose P/Q, Where Q Has Repeated
Linear Factors
Objective: (10.2) Use the Formula for the Sum of the First
n Terms of an Arithmetic Sequence
Objective: (7.3) Decompose P/Q, Where Q Has a
Nonrepeated Prime Quadratic Factor
Objective: (10.3) Find the Value of an Annuity
60) B
41) D
Objective: (10.3) Use the Formula for the Sum of an
Infinite Geometric Series
Objective: (7.3) Decompose P/Q, Where Q Has a
Nonrepeated Prime Quadratic Factor
61) A
42) C
Objective: (10.5) Find a Particular Term in a Binomial
Expansion
Objective: (9.1) Graph Ellipses Not Centered at the Origin
43) D
62) C
44) B
63) C
Objective: (9.1) Graph Ellipses Not Centered at the Origin
Objective: (10.6) Use the Permutations Formula
Objective: (9.1) Solve Applied Problems Involving
Ellipses
Objective: (10.7) Compute Empirical Probability
64) A
45) B
Objective: (10.7) Compute Theoretical Probability
Objective: (9.2) Write Equations of Hyperbolas in
Standard Form
65) C
Objective: (10.7) Find the Probability of One Event or a
Second Event Occurring
46) C
Objective: (9.2) Write Equations of Hyperbolas in
Standard Form
66) D
Objective: (11.1) Find One-Sided Limits and Use Them to
Determine If a Limit Exists
47) A
Objective: (9.2) Graph Hyperbolas Not Centered at the
Origin
67) D
Objective: (11.2) Find Limits of Fractional Expressions in
Which the Limit of the Denominator is Zero
48) A
Objective: (9.3) Write Equations of Parabolas in Standard
Form
68) D
Objective: (11.3) Determine For What Numbers a
Function is Discontinuous
49) A
Objective: (9.3) Solve Applied Problems Involving
Parabolas
69) B
Objective: (11.2) Find Limits of Fractional Expressions in
Which the Limit of the Denominator is Zero
50) B
Objective: (9.4) Use Rotation of Axes Formulas
70) C
51) C
Objective: (11.4) Find the Derivative of a Function
Objective: (9.4) Identify Conics Without Rotating Axes
52) D
Objective: (9.5) Eliminate the Parameter
53) B
Objective: (9.5) Eliminate the Parameter
15