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IM 1 Semester 1 Study Guide

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Day 1 and 2: Unit 1 Quantities and Modeling

Mathematical Phrases into Expressions

Question 1
1.

Translate this expression.

“eighteen less than a number”

Question 2
2.

Translate this expression.

“the product of a number and six”

Question 3
3.

Translate this expression.

“triple a number”

Question 4
4.

Translate this expression.

“a number increased by nine”

Question 5
5.

Translate this expression.

“the quotient of a twenty and a number”

Expressions into Mathematical Phrases

Question 6
6.

Write each expression in words

-12+n

Question 7
7.

Write each expression in words

-2/n

Question 8
8.

Write each expression in words

9x

Question 9
9.

Write each expression in words

k-14

Simpliying Expressions

Question 10
10.

Directions: Simplify each expression.

Question 11
11.

Directions: Give the perimeter of each figure as a simplified expression.

Parts of an Expression

Notes Page 1-Parts of an Expression


Question 12
12.


1. How many terms does the expression have?
_______
2. What are the variables?
_______ and _______
3. What are the coefficients?
_______ and _______
4. What is the constant?
_______
Question 13
13.


1. How many terms does the expression have?
_______
2. What are the variables?
_______ and _______ and _______
3. What are the coefficients?
_______ and _______ and _______
4. What is the constant?
_______

Evaluating Expressions

Notes Page 2-Evaluating Expressions

Question 14
14.

Evaluate each expression using the variable replacements.


Question 15
15.

The cost of either a can of gourmet chili is $2.25 and a can of hearty soup is $1.75. Ton Nam bought cans of chili and soup. He wrote an expression to describe the purchase where c represents the number of cans of chili and s represents the number of cans of soup. Write an expression to present how much he might spend based on the number of cans of each that he bought.

Using Distributive Property

Question 16
16.

Simplify each expression by distributing.


Question 17
17.

Simplify each expression by distributing.


Question 18
18.

Simplify each expression by distributing and combining like terms.


Question 19
19.

Simplify each expression by distributing and combining like terms.


Solving Equations


Notes Page 4- Solving Equation Basics

Question 20
20.

Match the operation with its inverse.

Draggable itemarrow_right_altCorresponding Item
inverse of addition
arrow_right_alt
subtraction
inverse of multiplication
arrow_right_alt
addition
inverse of division
arrow_right_alt
arrow_right_alt
Question 21
21.

Put these operations in the order by which you perform them to simplify an expression. (first to last)

  1. subtraction
  2. addition
  3. exponents
  4. multiplication
  5. division
  6. parentheses ( )
Question 22
22.

To solve an equation we need to undo operations to isolate a variable. So, we need to undo PEMDAS. This means we need to work in a different order.

Put these operations in the order by which you perform them to solve an equation. (first to last)

  1. parentheses ( )
  2. addition and subtraction (outside parentheses)
  3. multiplication and division
Question 23
23.

Put the steps to solving this equation in the right order.

  1. add 7 to both sides of the equation
  2. Before we start solving, we identify the variable a, so we can solve for it the variable
  3. the result is x=7
  4. divide both sides of the equation by 3
Question 24
24.

Solve this equation.


Question 25
25.

What is the first step to solving this equation?

Question 26
26.

What is the second step to solving this equation?

Question 27
27.

Solve this equation.

17 + 3k = 26


Question 28
28.

Solve this equation.

15h - 9 = - 54

Question 29
29.

Solve this equation.

Question 30
30.

Solving Multi-Step Equations


Notes Page 5-Solving Multi-Step Equations

Question 31
31.

Put the steps in the correct order to solve this multistep equation.


  1. The solution is a = 5
  2. undo multiplying by -28 by dividing by both sides of the equation by -28 to get a = 5
  3. undo subtract 20 by adding 20 to both sides of the equations to get -28a = -140
  4. Use distribution to multiply (7a+5) by -4 to get -28a - 20
  5. Check the solution by evaluating the original expression -4(7a+5) to verify that it equals -160
Question 32
32.

Solve this multi-step equation. Show your work (SYW)

Question 33
33.

Put the steps in the correct order to solve this multistep equation.


  1. undo multiplying by -7 by dividing by both sides of the equation by -7 to get x = -4
  2. Simplify like terms to get the equation -7x - 3 = 25
  3. The solution is x = -4
  4. Check the solution by evaluating the original expression -4x -7 - 3x +4 to verify that it equals 25
  5. undo subtract 3 by adding 3 to both sides of the equations to get -7x = 28
Question 34
34.

Solve this multi-step equation. Show your work (SYW)

Question 35
35.

Solve this multi-step equation. Show your work (SYW)

Solving Equations with Variables on Both Sides of the Equal Sign


Notes Page 6: Solving Equations with Variables on Both Sides of the Equal Sign

Question 36
36.

Solve this equation

Question 37
37.

Solve this equation

Solving Proportions



Question 38
38.
Cross multiply and fill in each box with the right product.

a. _______

b. _______
Question 39
39.

Solve each proportion. Show your work! Or suffer the consequences...


Question 40
40.

Solve each proportion. Show your work! Or suffer the consequences...


Question 41
41.
Cross multiply and fill in each box with the right product.
a. _______

b. _______

Question 42
42.

Solve each proportion. Show your work! Or suffer the consequences...


Question 43
43.

Solve each proportion. Show your work! Or suffer the consequences...


Question 44
44.


Jasmine bought 1000 robux for $8 with her parents' money. At the same exchange rate, how many robux can Lisa buy if she stole $24 from her parents?

Solving Literal Equations



Question 45
45.

Directions: Solve this equation for the specific letter. SHOW ALL STEPS!

Question 46
46.

Directions: Solve this equation for the specific letter. SHOW ALL STEPS!

Solving Inequalities


Notes Page 9-Solving Inequalities

Question 47
47.

Solve and graph the inequality for the given variable.

Question 48
48.

Solve and graph the inequality for the given variable.

Day 3: Unit 2 Understanding Functions

Main Idea: Representing Relations and Functions

Question 49
49.

Use the set of ordered pairs to complete the relation table, relation mapping, and coordinate graph.

Relations vs. Functions

Page 11-What are Functions?

Question 50
50.

Determine whether the given relation is a function. (Function or Not a Function)

Question 51
51.

Determine whether the given relation is a function. (Function or Not a Function)

Question 52
52.

Determine whether the given relation is a function. (Function or Not a Function)

Question 53
53.

Determine whether the given relation is a function. (Function or Not a Function)

Vertical Line Test

Page 11-What are Functions?

Question 54
54.

Determine whether the given relation is a function. (Function or Not a Function)

Question 55
55.

Determine whether the given relation is a function. (Function or Not a Function)

Question 56
56.

Determine whether the given relation is a function. (Function or Not a Function)

Equations as Functions--Graphing by Functions

Question 57
57.

Directions: Complete each function table, then graph the function.


Evaluating Functions

Notes Page 12 Equations as Functions

Question 58
58.

Evaluate each function for the given value.

For questions 60 and 61, use the functions to the left.

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Question 59
59.

Evaluate each function for the given value.

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Question 60
60.

Evaluate each function for the given value.

Arithmetic Sequences

Page 13-Arithmetic Sequences


Question 61
61.
Find the next three terms of each sequence.




3, 7, 11, 15, _______ ,_______ ,_______
Question 62
62.
Find the next three terms of each sequence.




10, 6, 2, _______ ,_______ ,_______
Question 63
63.


What does f(1) mean?

Question 64
64.


What does f(n) mean?

Question 65
65.


What does d mean?

Question 66
66.


What does n mean?

Question 67
67.

What is the explicit rule of this arithmetic sequence?

Question 68
68.

What is the explicit rule of this arithmetic sequence?


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Day 4: Unit 3 Linear Equations

Finding Slope


Notes Page 14 Rate of Change and Slope

Question 77
77.

Find the slope of this line:

Question 78
78.

Find the slope of this line:

Slope-Intercept Form


Notes Page 15 Slope-Intercept Form

Slope-Intercept Form



Slope (m)

y-intercept (b)

Question 79
79.

Write the equation in slope intercept form with the given information:

Question 80
80.

Write the equation in slope intercept form with the given information:

Question 81
81.

Write the equation of this line in slope-intercept form. (10pts)

Question 82
82.

Write the equation of this line in slope-intercept form. (10pts)

Question 83
83.

Given the slope and y-intercept of the line, write the equation
in slope-intercept form:

slope = 3; y-intercept = -4

Question 84
84.

Given the slope and y-intercept of the line, write the equation
in slope-intercept form:

slope = -3/2; y-intercept = 7

Slope Formula

Notes Page 16 Slope Formula

Question 85
85.

Directions: Find the slope between each pair of points:

(-5, 8) and (-7, 5)


Question 86
86.

Directions: Find the slope between each pair of points:

(1, 3) and (3, 9)


Graphing Slope-Intercept Form


Page 17 Graphing Linear Equations--Using Slope-Intercept Form

Question 87
87.
Use the slope and the y-intercept of each equation to graph the equation.

y=mx+b

y=-2x-2


slope:
_______
y-intercept:
_______


Question 88
88.
Use the slope and the y-intercept of each equation to graph the equation.

y=mx+b




slope:
_______
y-intercept:
_______


Graphing Using x and y Intercepts


Notes Page 19 Graphing Using x and y Intercepts

Question 89
89.
What are the x and y-intercepts of this function?

x-intercept
_______

y-intercept
_______
Question 90
90.
What are the x and y-intercepts of this equation:

x-int
_______
y-int
_______
Question 91
91.

Use x and y-intercepts of this equation to graph it.

Question 92
92.

Use x and y-intercepts of this equation to graph it.

division
inverse of subtraction
multiplication

Question 69
69.
Find the first term and common difference in this sequence:

1, 3, 5, 7, ...

a₁=_______

d=_______


Question 70
70.

Write the explicit formula to find the nᵗʰ term of this sequence (you can use either notation):

1, 3, 5, 7, ...

Question 71
71.

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:

1, 3, 5, 7, ...


Question 72
72.
Find the first term and common difference in this sequence:

-1, -4, -7, -10, ...

a₁=_______

d=_______


Question 73
73.

Write an equation to find the nᵗʰ term of this sequence (you can use either notation):

-1, -4, -7, -10, ...

Question 74
74.

Use the explicit formula you created from the last problem to find the 24ᵗʰ term of this sequence:

-1, -4, -7, -10, ...

Question 75
75.

Charlie deposited $115 in a savings account. Each week thereafter, he deposits $35 into the account.

Write a formula to represent this sequence.

Question 76
76.

Charlie deposited $115 in a savings account. Each week thereafter, he deposits $35 into the account.



How much total money has Charlie
deposited after 30 weeks?