Log in
Sign up for FREE
arrow_back
Library

MC IM 2 Semester 1 Study Guide

star
star
star
star
star
Last updated about 2 hours ago
89 questions
Required
10
Required
4
Required
4
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
10
Required
40
Required
10
Required
8
10
Required
10
Required
10
Required
10
Required
10
Required
5
Required
5
Required
5
Required
5
Required
5
Required
10
Required
5
Required
5
Required
2
Required
2
Required
2
Required
12
Required
12
Required
20
Required
20
Required
8
Required
8
Required
20
Required
8
Required
5
Required
5
Required
12
Required
40
Required
40
Required
40

Simplifying Radicals


Required
10
Question 1
1.

Simplify this radical.

Multiplying Radicals


Required
10
Question 2
2.

Simplify this expression that contains radicals.

Required
10
Question 3
3.

Simplify this expression that contains radicals.

Square Roots with Variables

Required
5
Question 4
4.

Simplify each radical

Required
5
Question 5
5.

Simplify each radical

Simplifying Expressions by Multiplying Exponents (Product Rule)


Required
5
Question 6
6.

Simplify. Your answer should not have negative exponents.

Required
5
Question 7
7.

Simplify. Your answer should not have negative exponents.

Simplifying Expressions by Dividing Exponents

(Quotient Rule)


Required
5
Question 8
8.

Simplify. Your answer should not have negative exponents.

Required
5
Question 9
9.

Simplify. Your answer should not have negative exponents.

Simplifying Expressions by raising Exponents by another Exponent (very meta)

(Power Rule)


Required
5
Question 10
10.

Simplify. Your answer should not have negative exponents.

Required
5
Required
5

Simplifying Expressions (mixed practiced)

Using all three rules: Product Rule, Quotient Rule, and the Power Rule


Required
10
Question 13
13.

Simplify. Your answer should not have negative exponents.

Required
10
Required
10

Simplifying Negative Exponents


Required
5
Question 16
16.

Simplify this expression. Your answer should not have negative exponents.

Required
5
Required
5
Question 19
19.

Use the properties of exponents to match each expression to its simplified version.

Draggable itemarrow_right_altCorresponding Item
arrow_right_alt
arrow_right_alt
arrow_right_alt
arrow_right_alt
arrow_right_alt

Identifying Parts of Expressions/Simplifying Expressions

Required
10
Question 20
20.

Identify the variable terms, constant terms, and coefficients

Question 21
21.
Use page 6 in your notes to identify and classify the parts of this polynomial:



Degree (first, second, third, etc.)_______
# of Terms (1, 2, 3, etc.):_______
Question 22
22.
Use page 6 in your notes to identify and classify the parts of this polynomial:


Degree (first, second, third, etc.)_______

# of Terms (1, 2, 3, etc.):_______
Question 23
23.

Directions: Simplify each expression by combining like terms. (Write your answer in standard form)

Question 24
24.

Directions: Simplify each expression by combining like terms. (Write your answer in standard form)

Question 25
25.

Directions: Simplify each expression by combining like terms. (Write your answer in standard form)

Question 26
26.

Directions: Simplify each expression by combining like terms. (Write your answer in standard form)

Monomial times a Polynomial

Question 27
27.

Find the product of these expressions. Final answers must be in standard form.

Question 28
28.

Find the product of these expressions. Final answers must be in standard form.

Question 29
29.

Find the product of these expressions. Final answers must be in standard form.

Distribute then Combine Like Terms

Question 30
30.

Distribute, then simplify the remaining expression. Final answers must be in standard form.

Question 31
31.

Write an expression in simplest form to represent the area of the shaded region.

Multiplying Binomial X Binomial

Question 32
32.

Find the Product of this binomial * binomial using the box method.

Question 33
33.

Find the Product of this binomial * binomial using the box method.

Question 34
34.

Find the Product of this binomial * binomial using the box method.

Question 35
35.
Simplify this expression using F.O.I.L.


First-_______
Outside-_______
Inside-_______
Last-_______

Combine the four terms together for your answer
_______
Question 36
36.
Simplify this expression using F.O.I.L.


First-_______
Outside-_______
Inside-_______
Last-_______

Combine the four terms together for your answer
_______

Special Product: Sum and a Difference

Question 37
37.

Find the Product of these polynomials.

Special Products: Square of a Binomial

Question 38
38.

Find the square of this binomial.

Question 39
39.

Find the square of this binomial.

Question 40
40.
A rectangular garden is being constructed in a rectangular patio. The remaining area of the patio forms a walkway around the garden.

The dimensions of the entire rectangular patio are given by the binomials: Length: (4x + 3) meters Width: (2x + 5) meters

What is the area of the patio?
_______

The dimensions of the rectangular garden inside the patio are given by the binomials: Length: (3x + 1) meters Width: (x + 2) meters

What is the area of the garden?
_______


Find the area of the walkway around the garden represented by a polynomial.
_______

If x=5 meters, what actual area of the walkway in square meters?
_______m ²

Inequalities and Interval Notation

Question 41
41.

Put the interval notations and graphs in the right category.

  • Both
Question 42
42.

Match the inequailty and graph with the correct interval notation.

Question 43
43.
Use interval notation to describe the domain and range of this function.

Domain (Left to Right):_______
Range (Lowest to Highest):_______
Question 44
44.
Use interval notation to describe the domain and range of this function.

Domain (Left to Right):_______
Range (Lowest to Highest):_______
Question 45
45.
Use interval notation to describe the domain and range of this relation.

Domain (Left to Right):_______
Range (Lowest to Highest):_______
Question 46
46.
For what interval of x is the function f(x):

Increasing?
_______
Decreasing?
_______
Question 47
47.
For what interval of x is the function f(x):

Negative?
_______

Positive?
_______
Question 48
48.

Write the following in interval notation.

Question 49
49.

Write the following in interval notation.

Question 50
50.

Write the following in inequality notation.

[-4,3)

Question 51
51.

Write the following in inequality notation.

(-∞,-3]

Question 52
52.

Write the following in inequality notation.

(-∞,2)U[4,∞)

Sketching Functions

Question 53
53.

Use the graph to create a function with the following features:

1) As x gets smaller; the function approaches infinity. x→ - ∞; f(x)→- ∞
2) As x gets larger; the function approaches infinity. x→ ∞; f(x)→ ∞
3) The graph of the function passes through the x-axis at -6
4) The graph of the function passes through the y-axis at -6
5) The graph of the function passes through the x-axis at 4

Absolute Value

Question 54
54.

The definition of absolute value is...

Question 55
55.

Explain why this is not possible:

|x|= - 9.5

Question 56
56.

Find the absolute value of this expression:

Question 57
57.

Find the absolute value of this expression:

Question 58
58.

Find the absolute value of this expression:

Question 59
59.

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

  • x<-4 or x>4
  • -3≤x≤13
Question 60
60.

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

  • x<-2 or x>2
  • -2<x<2

Solving Absolute Value Equations

Required
10
Question 61
61.
Required
10
Required
10
Required
10

Compound Inequalities

Required
10
Question 65
65.
Solve and graph the compound inequality for the given variable.

_______ or _______
Required
10
Question 66
66.
Solve and graph the compound inequality for the given variable.

_______

Solving Absolute Value Inequalities

Question 67
67.

Solve and graph the inequality


Question 68
68.

Solve and graph.

Graphing Absolute Value Functions

Question 69
69.
How is the absolute function below different than the parent function y=|x|:

y=2|x+6|-2


Opens (Upward or Downward) _______

Horizontal Shift (write none if there is none) _______

Vertical Shift (write none if there is none) _______

Compression (0<|a|<1), Stretch (|a|>1), or None _______.
Question 70
70.
How is the absolute function below different than the parent function y=|x|:

y=-5|x-8|+3


Opens (Upward or Downward) _______

Horizontal Shift (write none if there is none) _______

Vertical Shift (write none if there is none) _______

Compression (0<|a|<1), Stretch (|a|>1), or None _______.
Question 71
71.
What are the critical values of this absolute value function:

y=|x-1|+2

Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______

Use the critical values of this equation to graph it.
Question 72
72.
What are the critical values of this absolute value function:




Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______

Use the critical values of this equation to graph it.

Graphing Quadratic Functions

Question 73
73.

What is the vertex of this parabola? Name the coordinate.

Question 74
74.

What is the axis of symmetry of this quadratic function? It should be in the form of x=h.

Question 75
75.
Describe the transformation of:

Stretch or Compression?(If a=1 or a=-1, then write none)_______
Opens upward or downward?_______
Horizontal shift? (If there is no shift write none)_______
Vertical shift? (If there is no shift write none)_______
Axis of Symmetry? (x=h)_______
Vertex (h,k)_______
Question 76
76.
Graph each quadratic function and each of its linear factors. Then identify the x-intercepts and the axis of symmetry of each parabola.

Left x-intercept
_______
Right x-intercept
_______
Axis of Symmetry
_______
Vertex
_______
Question 77
77.
What is the graph of this quadratic function?


Axis of Symmetry
x=_______
Vertex (h,k)
_______
Question 78
78.
What is the graph of this quadratic function?

a=_______
b=_______
c=_______

Axis of Symmetry
x=_______
Vertex (h,k)
_______

Solving Quadratics

Solving Quadratic Equations by Graphing

Required
40
Question 79
79.
Solve this quadratic equation graphing.

x=_______
x=_______
Required
20
Question 80
80.
Solve this quadratic equation graphing.

x=_______
x=_______

Solving Quadratics by Factoring

Required
10
Question 81
81.
Solve the following Quadratic function:
(7x + 3)(2x + 6) = 0

x=_______

x=_______
Required
10
Required
10

Solving Quadratic Using Square Roots

Required
10
Question 84
84.
Solve this quadratic equation by taking the square root
x=_______ and_______
Required
10
Required
10
Required
10

Solving Quadratic Word Problem

Calculating Room Areas

People frequently need to calculate the area of rooms, boxes or plots of land. An example might involve building a rectangular box where one side must be twice the length of the other side.

For example, if you have only 4 square feet of wood to use for the bottom of the box, with this information, you can create an equation for the area of the box using the ratio of the two sides. This means the area -- the length times the width -- in terms of x would equal x times 2x, or 2x2. This equation must be less than or equal to four to successfully make a box using these constraints.
Required
10
Question 88
88.
For this rectangle with the area given, determine the binomial factors that describe the dimensions.




Length
_______
Width
_______

Objects Affected by Gravity

Required
50
Question 89
89.
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = -16t²+ 16t + 500 , where t is the time in seconds and h is the height in feet.

Round your answers to the nearest tenth.

How long did it take for Jason to reach his maximum height?_______

What was the highest point that Jason reached?_______

Jason hit the water after how many seconds?_______
Question 11
11.

Simplify. Your answer should not have negative exponents.

Question 12
12.

Simplify. Your answer should not have negative exponents.

Question 14
14.

Simplify. Your answer should not have negative exponents.

Question 15
15.

Simplify. Your answer should not have negative exponents.

Question 17
17.

Simplify this expression. Your answer should not have negative exponents.

Question 18
18.

Simplify this expression. Your answer should not have negative exponents.

[3.5]
(-∞,-9)
[5,∞)
(3,5)
(3,5]
[3,5)
Open Interval
Closed Interval
|x|<4
|x-5|<8
(-3,13)
x≤-4 or x≥4
|x|>4
[-3,13]
(-∞,-4)∪(4,∞)
|x|≤2
(-2,2)
-2≤x≤2
(-∞,-2)∪(2,∞)
|x|<2
|x|≥2
|x|>2
Solve this absolute Value equation:


+ Case
_______
- Case
_______
Question 62
62.
Solve this absolute Value equation:

+ Case
_______
- Case
_______
Question 63
63.
Solve this absolute Value equation:
+ Case
_______
- Case
_______
Question 64
64.
Solve this absolute Value equation:

+ Case
_______
- Case
_______
Question 82
82.
Solve the following Quadratic function:
x2 + 2x - 15 = 0

x=_______
x=_______
Question 83
83.
Solve the following Quadratic function:
2x2 + 5x + 2 = 0

x=_______
x=_______
Question 85
85.
Solve this quadratic equation by taking the square root.
x=_______ and_______
Question 86
86.
Solve this quadratic equation by taking the square root.
x=_______ and_______
Question 87
87.
Solve this quadratic equation by taking the square root.
x=_______ and_______