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

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91 Nsɛmmisa

Day 1 Monday (12/8/25)

Day 2 Tuesday (12/9/25)

Day 3 Wednesday (12/10/25)

Day 4: Thursday (12/11/25)

Mathematical Phrases into Expressions

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1.

Translate this expression.

“eighteen less than a number”

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2.

Translate this expression.

“the product of a number and six”

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3.

Translate this expression.

“triple a number”

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Expressions into Mathematical Phrases

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6.

Write each expression in words

-12+n

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7.

Write each expression in words

-2/n

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8.

Write each expression in words

9x

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9.

Write each expression in words

3k-14

Parts of an Expression

Notes Page 1-Parts of an Expression

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10.

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?

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11.

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?

Simplifying Expressions

^^^^Video link^^^^

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12.

Directions: Simplify each expression.

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13.

Directions: Simplify each expression.

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14.

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

Using the Distributive Property

^^^^Video link^^^^

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15.

Simplify each expression by distributing.

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16.

Simplify each expression by distributing and combining like terms.

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17.

Simplify each expression by distributing and combining like terms.

Evaluating Expressions

Notes Page 3-Evaluating Expressions

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18.

Evaluate each expression using the variable replacements.

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19.

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.

How much will it cost to buy 6 cans of chili and 7 cans of soup?

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Solving Multi-Step Equations

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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

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Solving Equations with Variables on Both Sides of the Equal Sign

Notes Page 5: Solving Equations with Variables on Both Sides of the Equal Sign

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36.

Solve this equation

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37.

Solve this equation

Solving Proportions

>>>Video Link<<<

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38.

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

a.

b.

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Solving Inequalities

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43.

Solve and graph the inequality for the given variable.

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44.

Solve and graph the inequality for the given variable.

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45.

Solve and graph the inequality for the given variable.

Main Idea: Representing Relations and Functions

>>>Video Link<<<

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46.

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

Relations vs. Functions

Page 7-What are Functions?

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47.

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

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48.

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

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Vertical Line Test

Page 7-What are Functions?

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51.

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

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52.

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

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Equations as Functions--Graphing by Functions

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54.

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

Evaluating Expressions and Functions

Notes Page 3 Equations as Functions

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55.

Evaluate each function for the given value.

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56.

Evaluate each function for the given value.

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57.

Evaluate each function for the given value.

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Arithmetic Sequences

Page 8-Arithmetic Sequences

>>>Video Link<<<

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66.

Find the first term and common difference in this sequence:

1, 3, 5, 7, ...

a₁=

d=

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

Find the 70ᵗʰ term of this sequence:

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67.

Find the first term and common difference in this sequence:

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

a₁=

d=

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

Find the 24ᵗʰ term of this sequence:

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Finding Slope

Notes Page 9 Rate of Change and Slope

>>>Video Link<<<

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69.

Find the slope of this line:

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70.

Find the slope of this line:

Slope-Intercept Form

Notes Slope-Intercept Form

Slope-Intercept Form

Slope (m)

y-intercept (b)

>>>Video Link<<<

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72.

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

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Slope Formula

Notes Page 10 Slope Formula

>>>Video Link<<<

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76.

Directions: Find the slope between each pair of points:

(1, 9) and (3, 9)

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77.

Directions: Find the slope between each pair of points:

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

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78.

Directions: Find the slope between each pair of points:

(-4, 8) and (-4, 5)

Graphing Slope-Intercept Form

Notes Graphing Linear Equations--Using Slope-Intercept Form

>>>Video Link<<<

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79.

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

y=mx+b

y=-2x-2

slope:

y-intercept:

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80.

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

y=mx+b

slope:

y-intercept:

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Graphing Using x and y Intercepts

Notes Page Graphing Using x and y Intercepts

>>>Video Link<<<

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82.

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

x-intercept

y-intercept

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83.

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

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84.

Graphing Using Point-Slope Form

Notes Page 11--Point Slope Form

>>>Video Link<<<

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85.

Write the equation of the line that passes through the given two points. Write all final answers in slope-intercept form.

Slope-

Slope-intercept Form-

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86.

Write the equation of the line that passes through the given two points. Write all final answers in slope-intercept form.

Slope-

Slope-intercept Form-

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87.

Write the equation of the line that passes through the given two points. Write all final answers in slope-intercept form.

Slope-

Slope-intercept Form-

Linear Word Problems

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88.

A city parking garage charges a flat rate of $10.00 for parking 2 hours or less, and $0.50 per hour for each additional hour.

Write a linear model that gives the total charge if you parked more than 2 hours.

How much does it cost to park a car in the parking gargage for 7 hours?

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89.
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4.

Translate this expression.

“a number increased by nine”

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5.

Translate this expression.

“the quotient of a twenty and a number”

Solving Equations

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20.

Match the operation with its inverse.

Draggable itemarrow_right_altCorresponding Item

inverse of subtraction

arrow_right_alt

subtraction

inverse of division

arrow_right_alt

addition

inverse of addition

arrow_right_alt

division

inverse of multiplication

arrow_right_alt

multiplication

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21.

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

  1. division

  2. addition

  3. exponents

  4. multiplication

  5. parentheses ( )

  6. subtraction

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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. Undo subtraction and addition

  2. Combine like terms

  3. Undo division and multiplication

  4. parentheses ( )

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23.

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

  1. add 7 to both sides of the equation

  2. divide both sides of the equation by 3

  3. Before we start solving, we identify the variable a, so we can solve for it the variable

  4. the result is a=7

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24.

Solve this equation:

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25.

What is the first step to solving this equation?

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26.

What is the second step to solving this equation?

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27.

Solve this equation:

17 + 3k = 26

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28.

Solve this equation:

15h - 9 = - 54

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29.

Solve this equation:

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30.

Solve this equation:

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32.

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

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33.

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

  1. The solution is x = -4

  2. undo multiplying by -7 by dividing by both sides of the equation by -7 to get x = -4

  3. Simplify like terms to get the equation -7x - 3 = 25

  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

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34.

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

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35.

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

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39.

Solve each proportion. Show your work!

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40.

Solve each proportion. Show your work!

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41.

Solve each proportion. Show your work!

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42.

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?

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49.

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

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50.

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

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53.

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

Arithmetic Sequences

Page 8-Arithmetic Sequences

>>>Video Link<<<

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58.

Find the next three terms of each sequence.

3, 7, 11, 15, , ,

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59.

Find the next three terms of each sequence.

10, 6, 2, , ,

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60.

What does f(1) mean?

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61.

What does f(n) mean?

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62.

What does d mean?

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63.

What does n mean?

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64.

What is the explicit rule of this arithmetic sequence?

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65.

What is the explicit rule of this arithmetic sequence?

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68.

Charlie deposited $300 in a savings account. Each week thereafter, he deposits $35 into the account.

Write a formula to represent this sequence.

How much total money has Charlie

deposited after 30 weeks?

How many weeks would it take to save at up at least $2000

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71.

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

in slope-intercept form:

slope = 3; y-intercept = -4

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73.

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

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74.

Write the equation of this line in slope-intercept form.

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75.

Write the equation of this line in slope-intercept form.

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81.

Write the equation of of the line represented on the graph.

slope:

y-intercept:

Equation of the line:

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

Sarah is saving money to buy a e-bike that costs $900. She already has $120 saved, and she plans to save an additional $30 each week from her job working at Del Taco.

Write a linear equation that shows how much money she is saving.

How much money will she have saved in 2 months?

How many weeks will it take Sarah to save enough money to buy the bicycle?

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90.

The cost for 7 dance lessons is $82. The cost for 11 lessons is $122.

Write an equation that can calculate the cost of dance lessons. (Use point-slope form)

Find the cost of 4 lessons.

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91.

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet.

How many feet can he climb in 1 hour? (Find the slope)

Write an equation that can calculate the how many feet a climber can climb in a given amount of hours. (Use point-slope form).

How many feet can this person climb in 12 hours of climbing?