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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

Simplifying Expressions

Question 10
10.

Directions: Simplify each expression.

Question 11
11.

Directions: Simplify each expression.

Question 12
12.

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

Parts of an Expression

Notes Page 1-Parts of an Expression


Question 13
13.


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 14
14.


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 15
15.

Evaluate each expression using the variable replacements.


Question 16
16.

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 17
17.

Simplify each expression by distributing.


Question 18
18.

Simplify each expression by distributing.


Question 19
19.

Simplify each expression by distributing and combining like terms.


Question 20
20.

Simplify each expression by distributing and combining like terms.


Solving Equations


Notes Page 4- Solving Equation Basics

Question 21
21.

Match the operation with its inverse.

Draggable itemarrow_right_altCorresponding Item
inverse of subtraction
arrow_right_alt
subtraction
inverse of multiplication
arrow_right_alt
addition
inverse of addition
arrow_right_alt
arrow_right_alt
Question 22
22.

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

  1. subtraction
  2. division
  3. exponents
  4. multiplication
  5. parentheses ( )
  6. addition
Question 23
23.

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. addition and subtraction (outside parentheses)
  2. multiplication and division
  3. parentheses ( )
Question 24
24.

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

  1. the result is x=7
  2. add 7 to both sides of the equation
  3. Before we start solving, we identify the variable a, so we can solve for it the variable
  4. divide both sides of the equation by 3
Question 25
25.

Solve this equation.


Question 26
26.

What is the first step to solving this equation?

Question 27
27.

What is the second step to solving this equation?

Question 28
28.

Solve this equation.

17 + 3k = 26


Question 29
29.

Solve this equation.

15h - 9 = - 54

Question 30
30.

Solve this equation.

Question 31
31.

Solving Multi-Step Equations


Notes Page 5-Solving Multi-Step Equations

Question 32
32.

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


  1. Check the solution by evaluating the original expression -4(7a+5) to verify that it equals -160
  2. The solution is a = 5
  3. undo multiplying by -28 by dividing by both sides of the equation by -28 to get a = 5
  4. undo subtract 20 by adding 20 to both sides of the equations to get -28a = -140
  5. Use distribution to multiply (7a+5) by -4 to get -28a - 20
Question 33
33.

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

Question 34
34.

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


  1. Simplify like terms to get the equation -7x - 3 = 25
  2. undo multiplying by -7 by dividing by both sides of the equation by -7 to get x = -4
  3. Check the solution by evaluating the original expression -4x -7 - 3x +4 to verify that it equals 25
  4. The solution is x = -4
  5. undo subtract 3 by adding 3 to both sides of the equations to get -7x = 28
Question 35
35.

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

Question 36
36.

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 37
37.

Solve this equation

Question 38
38.

Solve this equation

Solving Proportions



Question 39
39.
Cross multiply and fill in each box with the right product.

a. _______

b. _______
Question 40
40.

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


Question 41
41.

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


Question 42
42.
Cross multiply and fill in each box with the right product.
a. _______

b. _______

Question 43
43.

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


Question 44
44.

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


Question 45
45.


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 46
46.

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

Question 47
47.

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

Solving Inequalities


Notes Page 9-Solving Inequalities

Question 48
48.

Solve and graph the inequality for the given variable.

Question 49
49.

Solve and graph the inequality for the given variable.

Day 3: Unit 2 Understanding Functions

Main Idea: Representing Relations and Functions

Question 50
50.

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 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)

Question 54
54.

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

Vertical Line Test

Page 11-What are Functions?

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)

Question 57
57.

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

Equations as Functions--Graphing by Functions

Question 58
58.

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


Evaluating Functions

Notes Page 12 Equations as Functions

Question 59
59.

Evaluate each function for the given value.

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

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Question 60
60.

Evaluate each function for the given value.

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10
Question 61
61.

Evaluate each function for the given value.

Arithmetic Sequences

Page 13-Arithmetic Sequences


Question 62
62.
Find the next three terms of each sequence.




3, 7, 11, 15, _______ ,_______ ,_______
Question 63
63.
Find the next three terms of each sequence.




10, 6, 2, _______ ,_______ ,_______
Question 64
64.


What does f(1) mean?

Question 65
65.


What does f(n) mean?

Question 66
66.


What does d mean?

Question 67
67.


What does n mean?

Question 68
68.

What is the explicit rule of this arithmetic sequence?

Question 69
69.

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 78
78.

Find the slope of this line:

Question 79
79.

Find the slope of this line:

Slope-Intercept Form


Notes Page 15 Slope-Intercept Form

Slope-Intercept Form



Slope (m)

y-intercept (b)

Question 80
80.

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

Question 81
81.

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

Question 82
82.

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

Question 83
83.

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

Question 84
84.

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

slope = 3; y-intercept = -4

Question 85
85.

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 86
86.

Directions: Find the slope between each pair of points:

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


Question 87
87.

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

y=mx+b

y=-2x-2


slope:
_______
y-intercept:
_______


Question 89
89.
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 90
90.
What are the x and y-intercepts of this function?

x-intercept
_______

y-intercept
_______
Question 91
91.
What are the x and y-intercepts of this equation:

x-int
_______
y-int
_______
Question 92
92.

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

Question 93
93.

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

division
inverse of division
multiplication

Question 70
70.
Find the first term and common difference in this sequence:

1, 3, 5, 7, ...

a₁=_______

d=_______


Question 71
71.

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

1, 3, 5, 7, ...

Question 72
72.

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

1, 3, 5, 7, ...


Question 73
73.
Find the first term and common difference in this sequence:

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

a₁=_______

d=_______


Question 74
74.

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

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

Question 75
75.

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

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

Question 76
76.

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

Write a formula to represent this sequence.

Question 77
77.

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?