S1: Math 1 Study Guide Name ______________________________
Period _________
Show all of your work on a separate piece of paper!
Chapter 1: Quantities and Relationships
Identify the independent quantity and the dependent quantity in each scenario.
1.
Hector knows there is a relationship between the number of cars he washes and the time it takes him to wash those cars.
2.
Jason is driving to visit his grandmother who lives 325 miles away from Jason's home. He travels an average of 60 miles per hour. Identify the independent quantity and the dependent quantity.
3.
The height of bean plants is recorded daily for 2 weeks. Identify the independent quantity and the dependent quantity.
Sketch a graph for each with the given characteristics.
4.
Is a smooth curve, is continuous, has a minimum, and is quadratic.
5.
Is linear, is discrete, and is decreasing.
6.
Is linear, is continuous, is neither increasing nor decreasing, and does not pass through the origin.
7.
Is discrete, has a maximum, does not pass through the origin, and is quadratic.
Evaluate the following expressions.
8.
1
3
3
4
11.
5
4
9
3
9.
1
5
12.
0
8
2
3
Simplify each of the following expressions.
(6−8) 2
14.
56÷4∗2
15.
(1 + 2 3 ) − 75 + 25 ÷ 5
Determine if each graph represents a function. Why or why not?
17.
18.
19.
10.
1
13.
4
0
4
3
4
16.
−3|3 3 − 33| − 3

Chapter 2: Functions and Equations
Solve each of the following scenarios.
20.
The function 𝐴(𝑡) = 7𝑡 represents the total amount of money in dollars Laura earns babysitting as a function of time in hours. Solve for 𝐴(5) and describe the answer in words.
21.
The function 𝐴(𝑡) = 7𝑡 represents the total amount of money in dollars Laura earns babysitting as a function of time in hours. Find when 𝐴(𝑡) = 42 and describe what the answer means in words.
Solve each equation.
22.
2𝑥 + 1 = 7
24.
|𝑥 − 5| = 7
23.
25.
2 − 5(𝑥 − 3) = −7𝑥 + 9
|𝑥 + 3| + 2 = 11
Solve & Graph each inequality.
26.
10 − 2𝑥 < 18
28.
|4𝑥 + 2| < 22
27.
29 .
|2𝑥 + 3| > 5
|𝑥 − 3| + 5 ≥ 2
Chapter 3: Quantities and Relationships
Rewrite the equation from standard form to slope-intercept form.
30.
4𝑥 + 6𝑦 = 48 31.
3𝑥 − 5𝑦 = 25
Rewrite the equation from slope-intercept form to standard form.
32.
𝑦 = 5𝑥 − 3 33.
𝑦 = −
2
3 𝑥 − 6
Find the slope of the line given two points.
34.
(2 , 7) & (−3 , 5) 35.
(11 , −5) & (12 , 3)
Graph each of the following by using the x- and y-intercepts.
36.
4𝑥 + 6𝑦 = 48 37.
3𝑥 − 5𝑦 = 15
State the slope and y-intercept and graph the line for each of the following.
2 1
38.
𝑦 = 𝑥 39 .
𝑦 = 𝑥 − 2
3 4
Chapter 4: Sequences
Describe each pattern and draw the next two figures. Then write a numeric sequence.
40.
41.

Write a numeric sequence to represent the situation.
42.
The school cafeteria begins the day with a supply of 1000 chicken nuggets. Each student
that passes through the lunch line is given 5 chicken nuggets. Write a numeric sequence to
represent the number of chicken nuggets left from the first seven students.
Determine the common difference for each arithmetic sequence.
43.
10, 3, −4, −11, … 44.
1
3
,
2
3
, 1,
4
3
, …
Determine the common ration (common multiple) for each geometric sequence.
9 9
45.
2, −8, 32, −128, … 46.
45, 9, , , …
5 25
Determine whether each given sequence is arithmetic, geometric, or neither. Then write the next 3 terms of the sequence.
47.
4, 8, 12, 16, __ , __ , __ 48.
−15, −18, −21, −24, __ , __ , __
Chapter 5: Exponential
49.
Suppose that Goliath deposits $15,000 into an account that earns 6.25% simple interest.
The general formula for simple interest is 𝑃(𝑡) = 𝑃
0
+ (𝑃
0
∙ 𝑟)𝑡 a) Use the formula to calculate his account balance after 15 years.
50.
Suppose that Thelma deposits $700 into an account that earns 6% compound interest. The general formula for compound interest is 𝑃(𝑡) = 𝑃
0
(1 + 𝑟) 𝑡 a) Use the formula to calculate her account balance after 8 years.
Create a table for each function with x values of -2, -1, 0, 1, 2, 3.
Then graph each function using the table of values.
51.
𝑓(𝑥) = (
1
3
) 𝑥
52.
𝑓(𝑥) = −3 ∙ 2 𝑥
Given the parent function (𝒙) = 𝟓 𝒙
, (a) describe each transformation, (b) name new critical point, and (c) make a sketch of the graph.
53.
𝑓(𝑥) = 5 𝑥+4 − 3 54.
𝑓(𝑥) = 5 −𝑥
55 .
𝑓(𝑥) = −5 𝑥
Simplify.
56. 𝑥 3 ∙ 𝑥 5 ∙ 𝑦 0
57 . (𝑥 6 ) 4
58. 𝑦 𝑦
8
2 𝑥
59.
(𝑥
4
∙𝑥
−2
3
) −5

Chapter 6: Systems of Equations
Solve each system of equations by Graphing.
60. 𝑦 = 3𝑥 − 4 𝑦 = −
1
2 𝑥 + 3
61. 𝑦 = −𝑥 + 1 𝑦 =
1
3 𝑥 − 3
Solve each system of equations by Substitution.
62. 𝑥 = −3𝑦 + 1 𝑥 + 𝑦 = 5
63.
−2𝑥 − 3𝑦 = −7 𝑦 = 6𝑥 − 11
Solve each system of equations by Elimination.
8𝑥 + 𝑦 = −16
64.
−3𝑥 + 𝑦 = −5
65.
−4𝑥 + 9𝑦 = 9 𝑥 − 3𝑦 = −6
For each scenario: a) define the variables, b) write a system of equations, c) solve.
66. Kelly gets paid at home for doing extra chores. Last week, she did 2 loads of laundry and 7 loads of dishes, and her parents paid her $18. The week before, she finished 2 loads of laundry and 4 loads of dishes, earning a total of $12. How much does Kelly earn for completing each type of chore?
Chapter 6: Systems of Equations
Simplify each of the radical expressions.
67. √𝟓𝟏𝟐𝒙 68. √𝟗𝟖𝒙 𝟓
Simplify each of the radicals based on its index.
𝟒
69. √𝟒𝟎𝟓𝒙 𝟒
70.
𝟑
√𝟐𝟒𝒎 𝟓
Find the prime factorization.
71. 𝟏𝟓𝟑𝟔𝒙 𝟐
72. 𝟐𝟖𝒙𝒚𝒛 𝟑