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Algebra 2 Midterm Review

Total questions: 56

Worksheet time: 2hrs 3mins

Name
Class
Date
1.

3+√-4

a)

1

b)

3-2i

c)

5

d)

3+2i

2.
Simplify: 
(10+ 15i) - (48 - 30i)
a)
58 - 45i
b)
58 - 15i
c)
-38 - 15i
d)
-38 + 45i
3.
Find the sum.
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
4.
(3+8i)(-2-i)
a)
2-19i
b)
23-i
c)
34+5i
d)
23-i
5.
Solve the following equation by completing the square:
n2 = 18n + 40
a)
{11 and -11}
b)
{16 and 2}
c)
{20 and -2}
d)
{10 and -4}
6.
Determine the values of
a, b, and c for
the quadratic equation: 
4x2 – 8x = 3
a)
a = 4, b = -8, c = 3
b)
a = 4, b =-8, c =-3
c)
a = 4, b = 8, c = 3
d)
a = 4, b = 8, c = -3
7.
Use the quadratic formula to solve 2x2 + 2x - 12?
a)
-2, 3
b)
2, 3
c)
2, -3
d)
-2, -3
8.
Factor the quadratic into binomials
x2+5x+6
a)
(x+1)(x-6)
b)
(x-3)(x+2)
c)
(x+3)(x+2)
d)
(x+4)(x+2)
9.
Factor Completely:
x2 - 36
a)
(x + 9)(x - 4)
b)
(x - 6)(x - 6)
c)
(x - 9)(x + 2)(x - 2)
d)
(x + 6)(x - 6)
10.
Simplify: (2i10)(-4i12)(-5i7)
a)
-40
b)
40i
c)
-40i
d)
40
11.
Factor.
a)
(3x²-3)
b)
3(x²-3)
c)
(3x-3)²
d)
3(2x²-3)
12.
Which polynomial has zeros at –3, 5 and 2?
a)
x3 – 4x2 – 11x + 30
b)
x3 + 4x2 + 11x – 30
c)
x2 – 19x – 30
d)
x3 + 19x + 30
13.
Classify the degree?
a)
Positive
b)
Negative
c)
Odd
d)
Even
14.
If you were finding all the zeroes of
 x6 + 4x3 + 2, how many times would you synthetically divide? 
a)
0
b)
2
c)
4
d)
6
15.
What are all the x-intercepts?
a)
(-2.55, 0), (2.55, 0)
b)
(-3,0), (-2,0), (2,0), (3,0)
c)
(0, 36)
d)
(-∞,∞)
16.
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
17.

Write the equation of the parabola in vertex form.

a)

y = 2(x - 1)2 - 2

b)

y = (x + 1)2 - 2

c)

y = 2(x + 1)2 - 2

d)

y = (x - 1)2 - 2

18.
Name the x-intercept(s)?
a)
(0, 0)
b)
(2, 4)
c)
(0, 0) and (0, 4)
d)
(0, 0) and (4, 0)
19.
What does i2 = ?
a)
-1
b)
√-1
c)
1
d)
-√1
20.
a)

2i√6

b)

8i√3

c)

-2√6

d)

-2i√6

21.

what is the value of i 3 * i 5 ?

**Hint - you can add exponents when multiplying**

a)

1

b)

-1

c)

i

d)

-i

22.

Factor completely:

3x2 + 18x +15

Hint: Assign x a value and check answers

a)

3(x2 + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

23.
What is the equation for the axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
24.
What is the green dot on the parabola called?
a)
maximum
b)
minumum
c)
roots
d)
zeros
25.
Find the y-intercept of f(x) = 2x2 - 2x + 1
a)
2
b)
-2
c)
1
d)
-1
26.
Does y = -4x2 have a maximum or minimum value?
a)
maximum
b)
minimum
27.
What is the vertex of the quadratic function:
y = x2 - 6x + 11?
a)
(3,2)
b)
(-3,-2)
c)
(-3,2)
d)
(3,-2)
28.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
none of these
29.
What is another name for the x-intercepts of a quadratic?
a)
y-intercepts
b)
zeros
c)
x-axis
d)
none of these
30.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
31.
Factor x2 + 12x + 20
WHAT TWO NUMBERS MULTIPLY TO 20
AND ADD UP TO 12? 
a)
(x + 2)(x + 10)
b)
(x + 7)(x + 5)
c)
(x + 6)(x + 6)
32.

Calculate the MEAN for the data set: 6, 7, 12, 8, 7, 4, 8, 8, 7

a)

7

b)

7.44

c)

8

d)

7 and 8

33.

Calculate the MEDIAN for the data set: 6, 7, 12, 8, 7, 4, 8, 8, 7

a)

7

b)

7.44

c)

8

d)

7 and 8

34.

Calculate the MODE for the data set: 6, 7, 12, 8, 7, 4, 8, 8, 7

a)

7

b)

7.44

c)

8

d)

7 and 8

35.

The POPULATION in statistics is best described by...

a)

a collection, or set, of individuals, objects, or events whose properties are to be analyzed

b)

the total number of people that live in a particular city

c)

the incomplete collection of individuals or objects that are of interest to the sample collector

d)

a collection of people that are being analyzed for membership on a list of particular elements to be studied

36.

A sample is...

a)

a subset of a population

b)

an infinite selection of a population

c)

a characteristic of a population

d)

a data value generated by the statistical information

37.

An experiment is...

a)

a planned activity whose results yield a set of data

b)

a numerical value that summarizes all of the data of an entire population

c)

the set of values collected from the variable from each of the elements that belong to the sample

d)

A numerical value summarizing the sample data

38.

A parameter is...

a)

a planned activity whose results yield a set of data

b)

a numerical value that summarizes all of the data of an entire population

c)

the set of values collected from the variable from each of the elements that belong to the sample

d)

A numerical value summarizing the sample data

39.

A statistic is...

a)

a planned activity whose results yield a set of data

b)

a numerical value that summarizes all of the data of an entire population

c)

the set of values collected from the variable from each of the elements that belong to the sample

d)

A numerical value summarizing the sample data

40.

Which of the following describes a stratified sample?

a)

Divide the population into groups and randomly select some people from each group

b)

Divide the population into groups, randomly select a few groups, and select everyone in those groups

c)

Randomly choose some people from the population

d)

Randomly choose one person from the population and then select every 10th person after that.

41.
A marketing survey compiled data on the number of cars in households. If X = the number of cars in a randomly selected household,and we omit the rare cases of more than 5 cars, then X has the following probability distribution:
What is the probability that a randomly chosen household has at least two cars?
a)
0.19
b)
0.20
c)
0.39
d)
0.61
42.
What is the expected value of the number of cars in a randomly selected household?
a)
2.5
b)
0.167
c)
1.45
d)
1
43.

What percent of people are 3 standard deviations above the mean?

a)

.15

b)

34

c)

68

d)

2.35

44.

What percent of people within 1 standard deviation of the mean?

a)

99.7

b)

34

c)

68

d)

95

45.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?
a)
68%
b)
99.7%
c)
95%
d)
84%
46.
The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.
a)
 28,000 km and 32,000 km.
b)
24,000 km and 34,000 km.
c)
26,000 km and 34,000 km.
d)
27,000 km and 31,000 km.
47.
The average waist size for teenage males is 29 inches with a standard deviation of 2 inches. 
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.  
a)
2
b)
1
c)
-2
d)
-1
48.
The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees.  What is the z-score for a temperature of 17 degrees?  
a)
1 
b)
1.43
c)
-1.43
d)
11.5
49.
What shape is a normal distribution curve?
a)
Half curve
b)
Round curve
c)
Bell curve
d)
Square curve
50.
The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?
a)
0.6915
b)
0.1762
c)
0.8238
d)
-0.93
51.
The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between  2.9 and 3.8? 
a)
81.5%
b)
47.5%
c)
68%
d)
95%
52.

What is the binomial expansion of (x + 1)8 ?

a)

x8 + 1

b)

x8 + 8x7 + 16x6 + 24x5 + 32x4 + 24x3 + 16x2 + 8x + 1

c)

x8 + 7x7 + 21x6 + 35x5 + 35x4 + 21x3 + 7x2 + 1

d)

x8 + 8x7 + 28x6 + 56x5 + 70x4 + 56x3 + 28x2 + 8x + 1

e)

x8 + 8x7 + 28x6 + 70x4 + 56x3 + 28x2 + 8x + 1

53.

What is the Binomial expansion of (x + 1)5 ?

a)

x5 + 5x4 + 10x3 + 10x2 + 5x + 1

b)

x5 + 5x4 + 15x3 + 15x2 + 5x + 1

c)

x5 + 6x4 + 15x3 + 15x2 + 6x + 1

d)

x5 + 1

54.

What is the Binomial expansion of (a − b)7 ?

a)

a7 − b7

b)

a7 + 7a6b + 21a5b2 + 35a4b3 + 35a3b4 + 21a2b5 + 7ab6 + b7

c)

a7 + 7a6b − 21a5b2 + 35a4b3 − 35a3b4 + 21a2b5 − 7ab6 + b7

d)

a7 − 7a6b + 21a5b2 − 35a4b3 + 35a3b4 − 21a2b5 + 7ab6 − b7

55.

How many terms are the in the expansion of (1+b)5

a)

5

b)

6

c)

25

d)

50

e)

3

56.

How is the binomial expansion of (1+b)n different from (1-b)n ?

a)

They have a different number of terms.

b)

Their coefficients have alternate + and - signs.

c)

They have different degrees.

d)

There is no difference

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