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WorksheetsAlgebra II 2016 Final Review
Total questions: 35
Worksheet time: 9hrs 32mins
Name
Class
Date
1.
11.1 Parabolas
Find the equation given:
F (0, -4) and directrix of y=4
Find the equation given:
F (0, -4) and directrix of y=4
a)
y2=-16(x)
b)
x2=-16(y)
c)
x2=-4(y)
d)
x2=16(y)
2.
7.4 Double Angles
Find the exact values of sin 2θ, cos 2θ, and tan 2θ given cosθ= 3/5. 0˚<θ<90˚
Find the exact values of sin 2θ, cos 2θ, and tan 2θ given cosθ= 3/5. 0˚<θ<90˚
a)
Sin2θ=12/5, cos2θ=7/25, tan2θ=8/7
b)
Sin2θ=24/25, cos2θ=(-7/25), tan2θ=(-24/7)
c)
Sin2θ=25/24, cos2θ=7/25, tan2θ=3/7
d)
Sin2θ=24/5, cos2θ=25/7, tan2θ=7/24
3.
11.1 Parabolas
Find vertex, focus, directrix and graph the equation 20x=y2.
Find vertex, focus, directrix and graph the equation 20x=y2.
a)
Center(0,0) Focus(-5,0) D x=5
b)
Center(0,0) Focus(5, 0) D x=-5
c)
Center(0,0) Focus(0,5) D y=-5
d)
Center(20,0) Focus (0,5) D y=-5
4.
5.4 Log Equations: Solve the equation
a)
-8
b)
248
c)
-24
d)
4
5.
5.4 Log Equations
a)
11/2
b)
21
c)
13
d)
7
6.
9.2 Systems
Solve
2x+3y=2
x-2y=8
Solve
2x+3y=2
x-2y=8
a)
(4, -2)
b)
(-2, 4)
c)
(4, 2)
d)
(-4, -2)
7.
9.2 Systems
Write and solve an equation for the following:
An airline that flies from LA to Alberquerque with a stop in Phoenix charges $90 to Phoenix and $120 from LA to Alberquerque. 185 passengers total boarded in LA and fares totaled $21,000. How many got off in Phoenix?
Write and solve an equation for the following:
An airline that flies from LA to Alberquerque with a stop in Phoenix charges $90 to Phoenix and $120 from LA to Alberquerque. 185 passengers total boarded in LA and fares totaled $21,000. How many got off in Phoenix?
a)
145
b)
20
c)
40
d)
105
8.
9.2 Systems
The price of admission to a high school play was $3 for students and $4.50 for nonstudents. If 450 tickets were sold for a total of $1555.50, how many of each kind were purchased?
The price of admission to a high school play was $3 for students and $4.50 for nonstudents. If 450 tickets were sold for a total of $1555.50, how many of each kind were purchased?
a)
207 student, 243 nonstudent
b)
254 student, 137 nonstudent
c)
137 student, 313 nonstudent
d)
313 student, 137 non student
9.
7.6 Inverse Trig
Find the exact value of
sec[arctan (-3/5)]
Find the exact value of
sec[arctan (-3/5)]
a)
√34/5
b)
√35/5
c)
-√34/3
d)
5/√34
10.
7.3 Sum and Difference Formulas
Find the exact value of cos 75°.
Find the exact value of cos 75°.
a)
√2/4 - √6/4
b)
√6/4 - √2/4
c)
√4/4
d)
√5/4
11.
9.1 Systems
Solve
x²+y²=8
y-x=4
Solve
x²+y²=8
y-x=4
a)
(-2, 2)
b)
(-4, 0)
c)
No solution
d)
(2, -2)
12.
8.1 Law of Sines
Solve the triangle given
A=52.17
a=21.3
b=18.9
Solve the triangle given
A=52.17
a=21.3
b=18.9
a)
B=40.5 C=87.3 c=20.3
b)
B=87.3 C=44.5 c= 26.3
c)
B=26.3 C=87.3 c=44.5
d)
B=44.5 C=83.3 c=26.3
13.
6.5 Trig Graphs
Graph the function. Identify the period, amplitude and phase shift.
y=3cosx
Graph the function. Identify the period, amplitude and phase shift.
y=3cosx
a)
Period: 2 π Amp: 3 P.S: None
b)
Period: 2π/3 Amp: X P.S: 3
c)
Period: 3π/2 Amp: 4 P.S: X
d)
Period: π/2 Amp: 1 P.S: 1
14.
6.5 Trig Graphs
Graph the function. Identify the period, amplitude and phase shift.
y=3 sin(x+ π/6)
Graph the function. Identify the period, amplitude and phase shift.
y=3 sin(x+ π/6)
a)
Period: π/6
Amp: 3
P.S: 2π
Amp: 3
P.S: 2π
b)
Period: 2π/3
Amp: π/6
Period: π/3
Amp: π/6
Period: π/3
c)
Period: 2π
Amp: 3
P.S: π/6
Amp: 3
P.S: π/6
d)
Period: 2π
Amp: 3
P.S: -π/6
Amp: 3
P.S: -π/6
15.
10.1 Sequence Sums
a)
0
b)
15
c)
25
d)
23
16.
5.2 Exponential Functions
Suppose you invest $1000 in a savings account that earns 2% interest compounded semi-annually. You do not make any deposits or withdrawals. How much money will be in the account after 5 years?
Suppose you invest $1000 in a savings account that earns 2% interest compounded semi-annually. You do not make any deposits or withdrawals. How much money will be in the account after 5 years?
a)
$1072.14
b)
$2024
c)
$1104.62
d)
$1024
17.
9.2 Systems
6 grapefruit cost as much as a dozen oranges. A dozen grapefruit and two dozen oranges together are $12. How much does 1 grapefruit cost?
6 grapefruit cost as much as a dozen oranges. A dozen grapefruit and two dozen oranges together are $12. How much does 1 grapefruit cost?
a)
$0.25
b)
$0.50
c)
$0.75
d)
$1.00
18.
11.3 Hyperbolas
Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions: F(0,±4), V(0,±1)
Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions: F(0,±4), V(0,±1)
a)
y2/15−x2/1=1
b)
y2/1−x2/15=1
c)
y2/4−x2/1=1
d)
y2/1−x2/4=1
19.
9.2 Systems
Solve the system
4x + 3y = 13
20x + 15y = 65
Solve the system
4x + 3y = 13
20x + 15y = 65
a)
No solution
b)
(5, 3)
c)
(-3, 5)
d)
Infinitely Many Solutions
20.
6.2 Values of trig functions
Find the values of the six trig functions for theta if the hypotenuse is 5 and the opposite side is 2. (The answer choices are only for sin, cos, and tan).
Find the values of the six trig functions for theta if the hypotenuse is 5 and the opposite side is 2. (The answer choices are only for sin, cos, and tan).
a)
sinθ=2/√29
cosθ=5/√29
tanθ=2/5
cosθ=5/√29
tanθ=2/5
b)
sinθ=√29/2
cosθ=√29/5
tanθ=5/2
cosθ=√29/5
tanθ=5/2
c)
sinθ=5/2
cosθ=5/√21
tanθ=√21/2
cosθ=5/√21
tanθ=√21/2
d)
sinθ=2/5
cosθ=√21/5
tanθ=2/√21
cosθ=√21/5
tanθ=2/√21
21.
11.3 Hyperbolas
Find the vertices, foci, asymptotes, and sketch/label the graph.
x2 - 2y2 = 8
Find the vertices, foci, asymptotes, and sketch/label the graph.
x2 - 2y2 = 8
a)
V: (±√8,0) F:(±√12,0) A: y=±2/√8x
b)
V:(0, ±√8) F:(0, ±√12) A: y=±2/√8x
c)
V: (±8,0) F:(±12,0) A: y=±2/√8x
d)
V:(0, ±8) F:(0, ±12) A: y=±2/√8x
22.
5.1 Inverse Functions
Determine if the function is one-to-one algebraically.
f(x)=3x-7
Determine if the function is one-to-one algebraically.
f(x)=3x-7
a)
Yes, 1-1
b)
No, not 1-1
23.
5.1 Inverse Functions
Determine if the function is one-to-one algebraically.
f(x)=1/(x-2)
Determine if the function is one-to-one algebraically.
f(x)=1/(x-2)
a)
Yes, 1-1
b)
No, not 1-1
24.
6.1 Conversions
Convert the degree angle to radians
135°
Convert the degree angle to radians
135°
a)
3π/4
b)
135π/180
c)
135/180π
d)
3/4π
25.
6.1 Conversions
Find the exact degree measure of
5π/6
Find the exact degree measure of
5π/6
a)
π²/1,080
b)
5(30)°
c)
150°
d)
(900/6)°
26.
6.1 Conversions
Find the exact degree measure of the angle 7π/8.
Find the exact degree measure of the angle 7π/8.
a)
175.7
b)
2.7
c)
157.5
d)
170
27.
8.2 Law of Cosines
Solve triangle ABC.
a=2.0 b=3.0 c=4.0
Solve triangle ABC.
a=2.0 b=3.0 c=4.0
a)
α=4.67
β=79.2
γ=96.13
β=79.2
γ=96.13
b)
α=97.18
β=62.72
γ=20.10
β=62.72
γ=20.10
c)
α=177.37
β=.81
γ=1.82
β=.81
γ=1.82
d)
α=28.95
β=46.57
γ=104.48
β=46.57
γ=104.48
28.
11.2 Ellipses
Find the center, vertices, and foci of the ellipse. Know how to graph.
x2/9 + y2/4=1
Find the center, vertices, and foci of the ellipse. Know how to graph.
x2/9 + y2/4=1
a)
Center (0,0)
Foci(±√5, 0)
Vertices:(±3,0)
Foci(±√5, 0)
Vertices:(±3,0)
b)
Center (0,0)
Foci(±4, 0)
Vertices:(±9,0)
Foci(±4, 0)
Vertices:(±9,0)
c)
Know how to graph!
29.
9.6 Matrices
I cannot insert matrices into the questions, but make sure you know how to add, subtract, and multiply them. Also how to write the size.
I cannot insert matrices into the questions, but make sure you know how to add, subtract, and multiply them. Also how to write the size.
a)
I will make sure I know
b)
What's a matrix?
30.
10.3 Geometric Sequences
Find the common ratio. Then, write a rule for the nth term of the sequence.
6, 12, 24, 48, 96
Find the common ratio. Then, write a rule for the nth term of the sequence.
6, 12, 24, 48, 96
a)
r= 6
an= 12(6)n-1
an= 12(6)n-1
b)
r= 2
an= 6(2)n-1
an= 6(2)n-1
c)
r= 6
an= 2(6)1-n
an= 2(6)1-n
d)
r= 3
an= 6(3)n-1
an= 6(3)n-1
31.
6.2 Trig
You and your kitten go outside on a walk. Suddenly, 30 feet from the base of a tree your kitten decides to jump into the branches. You approximate the angle between the ground and the top of the tree to be 55°. How long of a ladder will the fire dept need to rescue kitty?
You and your kitten go outside on a walk. Suddenly, 30 feet from the base of a tree your kitten decides to jump into the branches. You approximate the angle between the ground and the top of the tree to be 55°. How long of a ladder will the fire dept need to rescue kitty?
a)
43 feet
b)
33 feet
c)
40 feet
d)
38 feet
32.
10.1 Sequences
Find the first five terms of the recursively defined infinite sequence.
a1=2
ak+1=3ak-5
Find the first five terms of the recursively defined infinite sequence.
a1=2
ak+1=3ak-5
a)
2, 1, -2, -11, -38
b)
2, 1, 2, 11, 38
c)
1, -3, 5, -10, -35
d)
1, -11, -38, -119
33.
11.2 Ellipses
Find the equation for the ellipse with center at the origin, Foci(±3,0) and minor axis length 2.
Find the equation for the ellipse with center at the origin, Foci(±3,0) and minor axis length 2.
a)
x2/3 + y2/2 =1
b)
(x+2)2 +(y-3)2 =1
c)
x2/10 + y2/1 =1
d)
x2/5 + y2/1 =1
34.
This review contains more than what is on the final. Be prepared! See OneDrive for the study guide of specific types of problems to focus on. Don't forget you can make a one sided notecard!
a)
Got it
b)
See other choice
35.
10.2 Arithmetic Sums
Find the sum of the first 10 terms of the arithmetic sequence in which the fourth term is 9 and the common difference is -5.
Find the sum of the first 10 terms of the arithmetic sequence in which the fourth term is 9 and the common difference is -5.
a)
11
b)
15
c)
17
d)
186
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