MC IM 2 Semester 1 Study Guide

Simplifying Radicals

Required

10

Simplify this radical.

Multiplying Radicals

Required

10

Simplify this expression that contains radicals.

Required

10

Simplify this expression that contains radicals.

Square Roots with Variables

Required

5

Simplify each radical

Required

5

Simplify each radical

Simplifying Expressions by Multiplying Exponents (Product Rule)

Required

5

Simplify. Your answer should not have negative exponents.

Required

5

Simplify. Your answer should not have negative exponents.

Simplifying Expressions by Dividing Exponents 
(Quotient Rule)

Required

5

Simplify. Your answer should not have negative exponents.

Required

5

Simplify. Your answer should not have negative exponents.

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

Required

5

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

Simplify. Your answer should not have negative exponents.

Required

10

Required

10

Simplifying Negative Exponents

Required

5

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

Required

5

Required

5

Required

10

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

Draggable item		Corresponding Item

Identifying Parts of Expressions/Simplifying Expressions

Required

10

Identify the variable terms, constant terms, and coefficients

Required

4

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.):_______

Required

4

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.):_______

Required

10

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

Required

10

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

Required

10

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

Required

10

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

Monomial times a Polynomial

Required

10

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

Required

10

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

Required

10

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

Distribute then Combine Like Terms

Required

10

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

Required

10

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

 Multiplying Binomial X Binomial

Required

10

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

Required

10

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

Required

10

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

Required

10

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


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

Combine the four terms together for your answer
_______ 

Required

10

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

Required

10

Find the Product of these polynomials.

Special Products: Square of a Binomial

Required

10

Find the square of this binomial.

Required

10

Find the square of this binomial.

Required

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

Required

10

Put the interval notations and graphs in the right category.

Both

Required

8

Match the inequailty and graph with the correct interval notation.

10

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

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

Required

10

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

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

Required

10

Use interval notation to describe the domain and range of this relation.

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

Required

10

For what interval of x is the function f(x):

Increasing?
_______ 
 Decreasing?
_______ 

Required

10

For what interval of x is the function f(x):

Negative?
_______ 

Positive?
_______ 

Required

5

Write the following in interval notation.

Required

5

Write the following in interval notation.

Required

5

Write the following in inequality notation.

[-4,3)

Required

5

Write the following in inequality notation.

(-∞,-3]

Required

5

Write the following in inequality notation.

(-∞,2)U[4,∞)

Sketching Functions

Required

10

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

Required

5

The definition of absolute value is...

Required

5

Explain why this is not possible:

|x|= - 9.5

Required

2

Find the absolute value of this expression:

Required

2

Find the absolute value of this expression:

Required

2

Find the absolute value of this expression:

Required

12

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

Required

12

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

Required

10

Required

10

Required

10

Compound Inequalities

Required

10

Solve and graph the compound inequality for the given variable.

_______  or _______ 

Required

10

Solve and graph the compound inequality for the given variable.

_______

Solving Absolute Value Inequalities

Required

20

Solve and graph the inequality

Required

20

Solve and graph.

Graphing Absolute Value Functions

Required

8

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  _______.

Required

8

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  _______.

Required

20

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.

Required

8

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

Required

5

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

Required

5

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

Required

12

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)_______ 

Required

40

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
_______ 

Required

40

What is the graph of this quadratic function?


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

Required

40

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

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Required

20

Solve this quadratic equation graphing.

x=_______ 
x=_______ 

Solving Quadratics by Factoring

Required

10

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

x=_______ 

x=_______ 

Required

10

Required

10

Solving Quadratic Using Square Roots

Required

10

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

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

Length
_______
Width
_______

Objects Affected by Gravity

Required

50

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?_______