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Final Exam Review

Total questions: 50

Worksheet time: 2hrs 53mins

Name
Class
Date
1.
Which parabola opens down with a vertex at (-3, 4)?
a)
y = (x + 3)2 - 4
b)
y = -(x + 3)2 - 4
c)
y = (x + 3)2 + 4
d)
y = -(x+3)2 + 4
2.
Which function has a translation of 7 units down and reflects over the x-axis?
a)
f(x) = -(x - 7)2 + 1
b)
f(x) = (x + 7)2 + 1
c)
f(x) = -(x - 1)2 - 7
d)
f(x) = (x + 1)2 - 7
3.
What is the name of this form:
y = ax2 + bx + c
a)
vertex form
b)
standard form
c)
factored form
d)
zero form
4.
What is the vertex?
f(x) = -x2 - 4x + 12.
a)
(-2, 16)
b)
(2, 0)
c)
(2, 4)
d)
(-2, 4)
5.

What are the x-intercepts of the function?

y=(x-4)(x-2)

a)

x=4 and x=2

b)

x=-4 and x = -2

c)

x = 4 and x= -2

d)

x = -4 and x = 2

6.
Use the graph to determine the solutions.
a)
-1 and -3
b)
1 and -3
c)
1 and 3
d)
-1 and 3
7.
Expand
ln(xy2z3)
a)
6(lnx + lny - lnz)
b)
lnx + 2lny - 3lnz
c)
lnx + (1/2)lny + (1/3)lnz
d)
lnx + 2lny + 3lnz
8.

Condense log x + log y + 3log z

a)

logxyz3

b)

log(xy/z3)

c)

logx+logy+logz3

d)

logx3y3z3

9.

Write in logarithmic form

2-4 = 1/16

a)

log2(1/16) = -4

b)

log-4(1/16) = 2

c)

log -4 2 = 1/16

d)

log2(-4) = 1/16

10.
Rewrite the equation in exponential form:
 logvn = a
a)
va = n
b)
na = v
c)
vn = a
d)
an = v
11.
find the asymptote: y = log10 (x+3)
a)
x=-3
b)
x=3
c)
y=-3
d)
y=3
12.

Write the equation of the function f(x)=log3x after the following transformations:


Translate 6 units left and 4 units up.

a)

g(x)=log3(x+6)+4

b)

g(x)=log3(x+4)-6

c)

g(x)=log3(x-6)+4

d)

g(x)=3log(x+6)+4

13.

cos(150o)

a)

- ½

b)

-√3/2

c)

2√3 /3

d)

½

14.
 cos(30o)=
a)
1
b)
1/2
c)
(√3)/2
d)
(√2)/2
15.
 sin(90o)=
a)
1/2
b)
0
c)
-1
d)
1
16.
Using reference angles find sin 225o.
a)
√3
b)
√2/2
c)
-√2/2
d)
-√3
17.
 Find cosA
a)
30/16
b)
30/34
c)
30/15
d)
16/34
18.
 Find tanZ
a)
35/21
b)
21/28
c)
35/28
d)
28/21
19.
Find the length of the missing side. 
a)
25 cm
b)
42 cm
c)
52 cm
d)
48 cm
20.
Find the missing side
a)
48
b)
108
c)
83.6
d)
72
21.
What is the length of y in this picture?
a)
45
b)
5√2
c)
90
d)
5
22.
What is the length of y in this 45-45-90 triangle?
a)
8√2
b)
4√2
c)
4
d)
8
23.
What is the range of y = sin x  ?
a)
{-1 < y < 1}
b)
{-1 ≤ y ≤ 1}
c)
{-1 < x < 1}
d)
{-1 ≤ x ≤ 1}
24.
What is the period of g(x) = sin x + 5   ?
a)
185°
b)
365°
c)
180°
d)
360°
25.
Find all quadrants where sinx>0
a)
I and II
b)
I and III
c)
I and IV
d)
III and IV
26.
Find all quadrants where cosx>0
a)
I and II
b)
I and III
c)
I and IV
d)
III and IV
27.
Fully Factor the Following
216x3+125
a)
6(x+5)3
b)
(6x+5)3
c)
(6x+5)(6x2-30x+25)
d)
(6x+5)(36x2-30x+25)
28.
Fully Factor the Following
8x3-27
a)
(2x+3)(4x2-6x+9)
b)
(2x-3)(4x2+6x+9)
c)
(2x-3)(4x2+6x-9)
d)
(2x-3)(2x2+6x+9)
29.
Calculate (multiply):
(1 − 2i)(6 + 5i)
a)
16 − 7i
b)
-16 + 7i
c)
-16 − 7i
d)
16 + 7i
30.
Mulitply
(4 - 3i)(7 + 2i)
a)
28 - 6i
b)
28 + 6i
c)
34 - 13i
d)
22 - 13i
31.

Which answer choice below has a root of 3, multiplicity 5?

a)

(x+5)3

b)

(x-5)3

c)

(x-3)5

d)

(x+3)5

32.

Which of the following are roots of the polynomial

f(x)=(x+1)(x-3)(x-5)

Check ALL that apply!

a)

1

b)

-1

c)

3

d)

5

33.
Solve     8x2 - 6x + 1 = 0
a)
No Solution
b)
0 or 1
c)
-0.5 or -0.25
d)
0.25 or 0.5
34.
Solve    2x2 + 7x - 15 = 0
a)
-1.5 or 5
b)
No Solution
c)
-5 or 1.5
d)
0.7 or 5
35.
What is the Vertical Asymptotes? 
a)
x= -5
b)
x= 5
c)
x= 6
d)
x= -6
36.
State the vertical asymptote:  f(x)=(x-2)/(x+5).
a)
x = -2/5
b)
x = -5/2
c)
x = -5
d)
x = 2
37.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
38.
Simplify the exponential expression.
a)
2x6y12
b)
2x5y7
c)
8x6y12
d)
8x5y7
39.

sin (5π/4)

a)

√3/2

b)

-√2/2

c)

1

d)

-1

40.

Find the exact value of the trigonometric function. No decimal answers.


cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

41.

Find the exact value of the trigonometric function. No decimal answers.


sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

42.

Find the exact value of the trigonometric function. No decimal answers.


cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

43.
log2(x + 5) = 3
a)
3
b)
4
c)
5
d)
6
44.
Solve for x:
a)
1/4
b)
-4
c)
4
d)
-1/4
45.
Re-write the expression in radical form.
x2/3
a)
(∛x)2
b)
√x3
c)
(1/x)
d)
∛x
46.
Simplify:
a)
2
b)
8
c)
16
d)
32
47.
Expand ln xy2z3
a)
6(lnx + lny - lnz)
b)
lnx + 2lny - 3lnz
c)
lnx + (1/2)lny + (1/3)lnz
d)
lnx + 2lny + 3lnz
48.
Condense ln64 +ln65
a)
ln620
b)
ln69
c)
ln654
d)
ln62
49.
Rewrite the equation in exponential form:
log9(1/81) = -2
a)
ln(-2) = 1/81
b)
-2(1/81) = 9
c)
9-2 = 1/81
d)
9(1/81) = -2
50.
Rewrite the equation into logarithmic form:
62 = 36
a)
log6(2)= 36
b)
log6(36) = 2
c)
ln(36) = 2
d)
636 = 2

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