1. Integrated Math One
Semester One Reveiw

2. Graph the system 𝑦≤ 3 4 𝑥+2 𝑦≥−3𝑥−2

3. Graph the line 𝑦=− 3 4 𝑥−6

4. Write the equation of the line that has a slope of 3 and contains the point 4,−3 .

5. Which table represent the function that increases most rapidly? Why?
Label if the table is arithmetic, geometric, or neither. Then write the recursive and explicit formulas.(if neither just state neither)
Which table represent the function that increases most rapidly? Why?
Which tables have a constant rate of change. x y 2 1 5 8 3 11

6. Graph the inequality 𝑦<−3𝑥+3

7. Graph the equation 2𝑥−3𝑦=12

8. A cell phone company charges $55 per month for unlimited minutes plus 25 cents per text sent. Write an equation to represent how much money you will spend on your phone bill each month if you use this company.

9. Your extended family will be sending you money for Christmas this year
Your extended family will be sending you money for Christmas this year. You would like to spend all your money on sports equipment and electronics. You decide to represent how much you will spend on each item on a graph. Describe the appropriate labels you will use on your graph. (What would you label the x-axis and what would you label the y-axis?)

10. Your math teacher asks you to draw a graph of the number of texts you send each day over the period of 2 weeks, you are to use most of your paper. If you send between 100 and 500 texts a day what would be the best scale to use for the y- axis?

11. Chris makes 365 cookies in 8 hours, and he uses 5 pounds of butter
Chris makes 365 cookies in 8 hours, and he uses 5 pounds of butter. He divides 365 by 5 to get a rate of 77. Give the units that correspond to this rate.

12. You have nickels, dimes, and quarters in your pocket write an expression and describe what each piece of the expression means.

13. Mrs. Acker sold 150 tickets for the Christmas play and made $1000
Mrs. Acker sold 150 tickets for the Christmas play and made $1000. Adult tickets were $10 and student tickets were $5. Write a system of equations that can be used to determine the number of adult and student tickets sold.

14. 𝑠=5𝑏+45 Rearrange the formula to show b in terms of s.

15. Rewrite the following equation to solve for d.
𝑘=𝑝+𝑑𝑎

16. Jesse was asked to solve an algebra problem
Jesse was asked to solve an algebra problem. She submitted the following solution. Is Jesse’s solution correct? If it is correct, justify each step of her solution. Find the mistake and explain to Jesse what she did wrong.
−2 5𝑥+3 = 𝑥−1 2
Step 1
6 −2 5𝑥+3 = 𝑥−1 2
Step 2
−12 5𝑥+3 =10+3 4𝑥−1
Step 3
−60𝑥+3=10+12𝑥−1
Step 4
−60𝑥+3=12𝑥+9
Step 5
−72𝑥+3=9
Step 6
−72𝑥=6
Step 7
𝑥=− 6 72 =− 1 12

17. Does the solution set for the following inequality contain the number −2.
3 5 𝑥+2≤1

18. Solve 3 4𝑥−2 =12𝑥+6
Solve −2 3𝑥+4 =−6𝑥−8

19. Brenda’s school is selling tickets to a spring musical
Brenda’s school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. How much did they make on the third day if they sold 2 senior citizen tickets and 6 child tickets.

20. Solve the system 2𝑥−3𝑦=8 −4𝑥+6𝑦=−16

21. Graph the inequality and give one solution. 𝑦< 3𝑥−2

22. The cost to enter a carnival is $15
The cost to enter a carnival is $15. The Zipper costs an additional $3 per ride. Graph the equation that shows the sequence of the total cost for rides on the Zipper including the cost to enter the carnival.

23. Sierra got a puppy for her birthday, she was curious about how the puppy would grow so she measures the mass of the puppy each day. The equation 𝑦=15𝑥+150 represents the puppy’s growth, where x is the independent variable and y is the dependent variable. What units would be reasonable for x and y.

24. There were 3 bacteria in the petri dish
There were 3 bacteria in the petri dish. After that the bacteria grow as shown in the table below. Assume that the pattern in the table continues. Write the equation that can be solved to find when the number of bacteria has increased to 250.
Time (minutes)
Number of Bacteria 3 1 6 2 12 24

25. Describe how you would solve this system of equations using elimination. 2𝑥+3𝑦=9 3𝑥−𝑦=8

26. Anna is going to save pennies each week according to a sequence she learned. She has saved 5 pennies to start week 0. Each week after that, she will save 8 pennies each day, for a total of 13, 21, 29, 37,… write an explicit formula for (d) days.

27. A linear function crosses the x-axis when 𝑥=4 and the y-axis when 𝑦=−6
A linear function crosses the x-axis when 𝑥=4 and the y-axis when 𝑦=−6. What is the equation for this line?

28. Rearrange the formula 𝑦=𝑚𝑥+𝑏 to find the formula for the slope.

29. Dr. Ramirez is driving to San Diego, a trip of 428 miles
Dr. Ramirez is driving to San Diego, a trip of 428 miles. He hopes to drive no more than 263 miles after lunch. If Dr. Ramirez drives 55 miles per hour, how many hours must he drive before he stops for lunch? 428−55ℎ≤263

30. Graph the function 𝑓 𝑥 = 3 𝑥−2

31. Write the explicit formula for the sequence -10, - 7, -4, -1,…?

32. Mr. Walsh started a savings account for his son that earns interest, which is added to his account each year. If he does not add to or withdraw from the account then the growth of the account can be modeled by the expression 𝑥 . Describe what each piece of the expression represents.

33. What is the explicit formula for the perimeter of step n in the pattern

34. Mrs. Viney has small bag of dimes and quarters
Mrs. Viney has small bag of dimes and quarters. She knows that she has less than $20 in the bag. Write an inequality that models this situation.

35. What is the recursive formula for this explicit formula 𝑓 𝑥 =3𝑥−6?

36. Solve 4 2𝑥−1 ≥5