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IM 2 Semester 1 Study Guide (Due 12/11/23)

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Day 1 12/6/23

Simplifying Radicals


Question 1
1.

Simplify this radical.


Multiplying Radicals


Question 2
2.

Simplify this expression that contains radicals.


Question 3
3.

Simplify this expression that contains radicals.


Square Roots with Variables

Question 4
4.

Simplify each radical


Question 5
5.

Simplify each radical


Simplifying Expressions by Multiplying Exponents (Product Rule)


Question 6
6.

Simplify. Your answer should not have negative exponents.

Question 7
7.

Simplify. Your answer should not have negative exponents.

Simplifying Expressions by Dividing Exponents

(Quotient Rule)


Question 8
8.

Simplify. Your answer should not have negative exponents.


Question 9
9.

Simplify. Your answer should not have negative exponents.


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

(Power Rule)


Question 10
10.

Simplify. Your answer should not have negative exponents.


Question 11
11.

Simplify. Your answer should not have negative exponents.


Question 12
12.

Simplify. Your answer should not have negative exponents.


Simplifying Expressions (mixed practiced)

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


Question 13
13.

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.


Simplifying Negative Exponents


Question 16
16.

Simplify this expression. 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.


Question 19
19.

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

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Identifying Parts of Expressions/Simplifying Expressions

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.

Special Product: Sum and a Difference

Question 35
35.

Find the Product of these polynomials.

Special Products: Square of a Binomial

Question 36
36.

Find the square of this binomial.

Question 37
37.

Find the square of this binomial.

Day 2 12/7/23

Inequalities and Interval Notation

Question 38
38.

Put the interval notations and graphs in the right category.

  • Both
Question 39
39.

Match the inequailty and graph with the correct interval notation.

Question 40
40.
Use interval notation to describe the domain and range of this function.

D:_______
R:_______
Question 41
41.
Use interval notation to describe the domain and range of this function.

D:_______
R:_______
Question 42
42.
Use interval notation to describe the domain and range of this relation.

D:_______
R:_______
Question 43
43.
For what interval of x is the function f(x):

Increasing?
_______
Decreasing?
_______
Question 44
44.
For what interval of x is the function f(x)


Negative?
_______

Positive?
_______
Question 45
45.

Write the following in interval notation.

Question 46
46.

Write the following in interval notation.

Question 47
47.

Write the following in inequality notation.

[-4,3)

Question 48
48.

Write the following in inequality notation.

(-∞,-3]

Question 49
49.

Write the following in inequality notation.

(-∞,2)U[4,∞)

Sketching Functions

Question 50
50.

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 51
51.

The definition of absolute value is...

Question 52
52.

Explain why this is not possible:

|x|= - 9.5

Question 53
53.

Find the absolute value of this expression:

Question 54
54.

Find the absolute value of this expression:

Question 55
55.

Find the absolute value of this expression:

Solving Absolute Value Equations

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Question 56
56.
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Compound Inequalities

Question 60
60.
Solve and graph the compound inequality for the given variable.



_______ or _______
Question 61
61.
Solve and graph the compound inequality for the given variable.



_______ and _______
Question 62
62.

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

  • (-2,2)
  • -2≤x≤2
Question 63
63.

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

  • x≤-4 or x≥4
  • [-3,13]

Solving Absolute Value Inequalities

Question 64
64.

Solve and graph the inequality




Question 65
65.

Solve and graph.



Graphing Absolute Value Functions

Question 66
66.

Use a set of x values to graph the function y=|x-3|+ 2

Question 67
67.
1)What are the critical values of this absolute value function:

y=|x-1|+2

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

2) Use the critical values of this equation to graph it.
Question 68
68.
What are the critical values of this absolute value function:




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

2) Use the critical values of this equation to graph it.
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) _______

Stretched (0<|a|<1), Compressed (|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) _______

Stretched (0<|a|<1), Compressed (|a|>1), or None _______.

Day 4 (12/11/23)

Features of Quadratic Functions

Question 71
71.

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

Question 72
72.

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

Question 73
73.
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 74
74.

Graph the function and state the vertex.


Vertex
_______
Question 75
75.

What is the graph of the function?



Be sure to include relevant graph detail: use the axis of symmetry and vertex to sketch the graph and use arrows to represent end behavior.

Solving Quadratic Equations by Graphing

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.


Solve this quadratic equation graphing.

x=_______
x=_______
Question 78
78.


Solve this quadratic equation graphing.

x=_______
x=_______

Solving Quadratics

Question 79
79.

Solve the following Quadratic function:
(7x + 3)(2x + 6) = 0

x=_______

x=_______
Question 80
80.

Solve the following Quadratic function:
x2 + 2x - 15 = 0

x=_______
x=_______
Question 81
81.

Solve the following Quadratic function:
2x2 + 5x + 2 = 0

x=_______
x=_______

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 82
82.
For each rectangle with area given, determine the binomial factors that describe the dimensions.




Length
_______
Width
_______

Objects Affected by Gravity

Required
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Question 83
83.

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 + 480 , where t is the time in seconds and h is the height in feet.

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?_______
(3,5)
[3,5)
[5,∞)
[3.5]
(3,5]
(-∞,-9)
Open Interval
Closed Interval
Solve this absolute Value equation:


+ Case
_______
- Case
_______


Question 57
57.
Solve this absolute Value equation:

+ Case
_______
- Case
_______


Question 58
58.
Solve this absolute Value equation:
+ Case
_______
- Case
_______


Question 59
59.
Solve this absolute Value equation:

+ Case
_______
- Case
_______


-2<x<2
(-∞,-2)∪(2,∞)
|x|≤2
|x|>2
|x|≥2
|x|<2
x<-2 or x>2
|x|<4
|x-5|<8
|x|>4
(-∞,-4)∪(4,∞)
-3≤x≤13
(-3,13)
x<-4 or x>4