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IM 2 Semester 1 Study Guide (12/15/2025)

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Last updated about 2 hours ago
61 questions
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Simplifying Radicals


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Question 1
1.

Simplify this radical.

Multiplying Radicals


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Question 2
2.

Simplify this expression that contains radicals.

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10
Question 3
3.

Simplify this expression that contains radicals.

Square Roots with Variables

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Question 4
4.

Simplify each radical

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Question 5
5.

Simplify each radical

Simplifying Expressions by Multiplying Exponents (Product Rule)


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10
Question 6
6.

Simplify. Your answer should not have negative exponents.

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Question 7
7.

Simplify. Your answer should not have negative exponents.

Simplifying Expressions by Dividing Exponents

(Quotient Rule)


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Question 8
8.

Simplify. Your answer should not have negative exponents.

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10
Question 9
9.

Simplify. Your answer should not have negative exponents.

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

(Power Rule)


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Question 10
10.

Simplify. Your answer should not have negative exponents.

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Simplifying Expressions (mixed practiced)

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


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Question 13
13.

Simplify. Your answer should not have negative exponents.

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Simplifying Negative Exponents


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Question 16
16.

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

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Exponent Rule Recap

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Day 2 12/11/25

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Monomial times a Polynomial

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Question 27
27.

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

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Question 28
28.

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Distribute then Combine Like Terms

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Question 30
30.

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

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10
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

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10
Question 37
37.

Find the Product of these polynomials.

Special Products: Square of a Binomial

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10
Question 38
38.

Find the square of this binomial.

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10
Question 39
39.

Find the square of this binomial.

Inequalities and Interval Notation

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

Domain (Left to Right):_______
Range (Lowest to Highest):_______
Question 41
41.
Use interval notation to describe the domain and range of this function.

Domain (Left to Right):_______
Range (Lowest to Highest):_______
Question 42
42.
Use interval notation to describe the domain and range of this relation.

Domain (Left to Right):_______
Range (Lowest to Highest):_______
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?
_______

Graphing Quadratic Functions

Question 45
45.

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

Question 46
46.

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

Question 47
47.
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 48
48.
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 49
49.
What is the graph of this quadratic function?


Axis of Symmetry
x=_______
Vertex (h,k)
_______
Question 50
50.
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

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Question 51
51.
Solve this quadratic equation graphing.

x=_______
x=_______
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Question 52
52.
Solve this quadratic equation graphing.

x=_______
x=_______

Solving Quadratics by Factoring

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Question 53
53.
Solve the following Quadratic function:
(7x + 3)(2x + 6) = 0

x=_______

x=_______
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Solving Quadratic Using Square Roots

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Question 56
56.
Solve this quadratic equation by taking the square root
x=_______ and_______
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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.
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Question 60
60.
For this rectangle with the area given, determine the binomial factors that describe the dimensions.




Length
_______
Width
_______

Objects Affected by Gravity

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Question 61
61.
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.

Question 19
19.

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

Draggable itemarrow_right_altCorresponding Item
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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)

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.

Question 54
54.
Solve the following Quadratic function:
x2 + 2x - 15 = 0

x=_______
x=_______
Question 55
55.
Solve the following Quadratic function:
2x2 + 5x + 2 = 0

x=_______
x=_______
Question 57
57.
Solve this quadratic equation by taking the square root.
x=_______ and_______
Question 58
58.
Solve this quadratic equation by taking the square root.
x=_______ and_______
Question 59
59.
Solve this quadratic equation by taking the square root.
x=_______ and_______