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Semester #1 Final (IM3)

Total questions: 40

Worksheet time: 3hrs 15mins

Name
Class
Date
1.
Find the slope of:
(12,-2) and (4, -6)
a)
-1/2
b)
5/7
c)
-2
d)
1/2
2.

Given the point (-1, 1) and the slope 4, write the equation of the line in slope-intercept form.

a)

y = 4x + 5

b)

y = 4x - 1

c)

y = 4x - 3

d)

none of these

3.

Determine whether the lines are parallel, perpendicular, or neither.

a)

parallel

b)

perpendicular

c)

neither

4.

Determine whether the lines are parallel, perpendicular, or neither.

a)

parallel

b)

perpendicular

c)

neither

5.

Write the equation of a line passing through the point, PERPENDICULAR to the given line.

a)

 y=3x+3y=3x+3 

b)

 y=−3x+3y=-3x+3 

c)

 y=13x−113y=\frac{1}{3}x-\frac{11}{3} 

d)

 y=−13x+113y=-\frac{1}{3}x+\frac{11}{3} 

6.

f(x) = 3(x-2) find f(5)

a)

9

b)

13

c)

21

d)

-9

7.
Factor Completely: x2-7x-8
a)
(x+1)(x-8)
b)
(x+1)(x+8)
c)
5(x+4)(x+5)
d)
(x-1)(x+8)
8.
Factor Completely: x4-9x2
a)
x2(x+3)(x-3)
b)
(x2+3x)(x2-3x)
c)
(x2+9)(x-3)(x+3)
d)
x2(x2-9)
9.
Factor Completely: 5x2-11x+6
a)
(5x+6)(x-1)
b)
(5x-6)(x-1)
c)
(2x-7)(x-3)
d)
(5x-6)(x+1)
10.
Evaluate.
log381
a)
4
b)
1/4
c)
-4
d)
-1/4
11.
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
12.
Write in exponential form.
log232 = 5
a)
2-5 = 32
b)
232 = 5
c)
25 = 32
d)
325 = 2
13.

Solve for x

log5(4x - 7) = log5(x + 5)

a)

3

b)

12

c)

4

d)

7

14.
The natural logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
15.
Log with a base "e" (loge) is the same thing as...
a)
"e"
b)
Natural Logarithm (LN)
c)
Common Logarithm (Log)
d)
Natural Log, base "e"
LNe
16.
Rewrite in exponential form:
ln(2) = x
a)
2x = 10
b)
102 = x
c)
ex = 2
d)
e2 = x
17.

When you get stuck in the logarithmic form, you switch to

a)

Natural logarithm form

b)

Exponential form

c)

Common logarithm

d)

Logarithm base b

18.
The common logarithm has what base?
a)
10
b)
0
c)
e
d)
-e
19.

Evaluate the following logarithm:

 log⁡2(18)\log_2\left(\frac{1}{8}\right)  

a)

3

b)

2

c)

-3

d)

1/3

20.

What is the end behavior of g(x)= -2x6+2x5-12x-6?

a)

up/down

b)

down/up

c)

down/down

d)

up/up

21.
The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 
a)
Leading Coefficient Positive
Degree - Even
b)
Leading Coefficient Positive
Degree - Odd
c)
Leading Coefficient Negative
Degree - Even
d)
Leading Coefficient Negative
Degree - Odd
22.
Which transformation maps the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
a translation shifting f(x) 4 units up
b)
a translation shifting f(x) 4 units down
c)
a translation shifting f(x) 4 units to the left
d)
a translation shifting f(x) 4 units to the right
23.
Describe the transformations of the graph y = (x - 3)3 -2
a)
Right 3, Down 2
b)
Left 3, Up 2
c)
Right 3, Up 2
d)
Left 3, Down 2 
24.

(4x2 - 24x + 35) ÷ (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

25.
Divide
(4b2 + b - 2) ÷ (4b + 5)
a)
b + 1 - 3/4b +5
b)
b - 1 + 3/4b - 5
c)
b + 1 + 3/4b + 5
d)
b - 1 + 3/4b + 5
26.

(27x3 + 9x2 - 3x - 10) ÷ (3x - 2)

a)

9x4+5

b)

9x2+9x+5

c)

9x2-9x+5

d)

9x2-9x

27.
2x3 - 5x - 7 ÷ x - 2
a)
2x3 - 4x2 + 3x - 13
b)
2x3 + 4x2 +3x - 1
c)
2x2 - 4x + 3 - 13/x-2
d)
2x2 + 4x + 3 - 1/x-2
28.
4x4+4x3-9x2-x+2 ÷ x-1
a)
4x3+8x2-7x-2
b)
4x3+19x2-x-2
c)
4x3+8x2-x-9
d)
4x3+8x2-x-2
29.
Which term is missing in this problem?
2x3 + 5x2 + 9 ÷
x + 3
a)
x4
b)
x3
c)
x2
d)
x
30.

What is the proper way to write the answer for the following problem?

a)

2x3-x2-25x+12

b)

2x4-x3-25x2-12x+0

c)

2x3-x2-25x-12

d)

2x4-x3-25x2-12x-0

31.
The degree of the polynomial determines the number of roots.
a)
True
b)
False
32.
All imaginary roots comes in pairs.
a)
True
b)
False
33.
Find all zeros for the polynomial function P(x) = x3 -3x2-5x+15
a)
3, √5 
b)
3, √5, -√5
c)
-3, √5, -√5
d)
-3, 5i, -5i
34.
Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root. 
a)
-3+5i
b)
-3-5i
c)
-5i
d)
3-5i
35.
Which of the following is a COMPLETE  list of all possible Rational Zeros?
f(x) = 2x3 + 5x2 - 9x + 5
a)
±1, ±5, ±1/2, ±5/2
b)
±1, ±2, ±5, ±1/2, ±5/2
c)
±1, ±5
d)
±1, ±2, ±5, ±1/2, ±5/2, ±2/5
36.
According to the Rational Root Theorem, what are the all possible rational roots? 
2x3 - 11x2 + 12x + 9 = 0
a)
±1,±2
b)
±1,±3,±9
c)
±1,±3±9,±1/2,±3/2,±9/2
d)
±1,±2,±1/3,±2/3,±1/9,±2/9
37.
Solve by using Rational Root Theorem: 
x3 + 3x2 - 6x - 8 = 0
a)
 -4, -1, 2
b)
-4, -1, ±√2
c)
1, 2, 4
d)
4,-1,√2
38.

Write in factored form using the following roots.


7, -2i

a)

(x-7)(x-2i)

b)

(x-7)(x+2i)(x-2i)

c)

(x-7)(x+2i)

d)

(x-7)(x+7)(x-2i)

39.
Factor:  27x3 + 8
a)
(3x + 2)(9x2 - 6x + 4)
b)
(9x + 2)(3x2 + 18x + 4)
c)
(3x2+4)(9x + 2)
d)
(27x + 8)(x2 - 216x + 64)
40.
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)

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