Algebra I Review Test

Try to do these exercises without looking at the review material. Show your work! If you get stuck, refer to the MathPlanet links in the Algebra I Review Homework.

  1. Define variables and write an equation to model the relationship in each table.
    1. NumberCost
      1$2.30
      2$4.60
      3$6.90
    2. PaymentChange
      $1$9
      $2$8
      $3$7
  2. Simplify each expression.
    1. 3 + 5 - 4
    2. 8 - 24 ÷ 2
    3. (2 x 3 - 1) ÷ 32
    4. 36 - (4 + 5 x 4)
  3. Decide whether each statement is true or false. If true, explain why. If false, provide a counterexample.
    1. All rational numbers are integers.
    2. The absolute value of a number is always positive.
  4. Write an expression for each phrase.
    1. Ten times the result of eleven minus two
    2. The quantity p minus five eighths times the result of one fourth plus p
  5. Write four rational numbers. Use a number line to order them from least to greatest.
  6. The price p of a CD is $17.95. The sales tax rate r is 7.5%. Use the formula C = p + rp to find the total cost C of the CD. 
  7. Use the scatter plot for the next three exercises Scatterplot of Climate Data - Daily Mean Temperature vs Location in latitude
    1. Is there a positive correlation, negative correlation, or no correlation between daily mean temperature and latitude?
    2. What is the daily mean temperature for the location at latitude 58º N?
    3. What is the range of daily mean temperatures?
  8. Explain why | a/b | = a/b is not always true. Use complete sentences. 
  9. Use the table below for the next two exercises. This table represents the percentage of people who speak a language other than English at home. (Source: U.S. Census Bureau)
    StatePercent
    Connecticut15
    Massachusetts15
    Maine9
    New Hampshire9
    New Jersey20
    New York23
    Pennsylvania7
    Rhode Island17
    Vermont6
    1. Make a stem-and-leaf plot for the data.
    2. Find the mean, median, mode, and range of the data. 
  10. The price of a turkey depends on its weight. This week, whole turkeys sell for $1.59 per lb. 
    1. Write a rule to describe the function. Define any variables used. 
    2. What is the price of a 14-lb turkey?
    3. If you had $10 to buy a turkey, how big a turkey could you buy?
  11. Identify the independent and dependent variables and write a function rule to describe each situation.
    1. The amount of money you earn mowing lawns at $15 per lawn
    2. The profit you make by selling flowers at $1.50 each when each flower costs you $.80
  12. Write a function rule for the relationship shown in the table below.
    1. Number of WeeksTotal Savings
      1$52
      2$64
      3$76
      4$88
    2. Use the function to find the total savings after 7 weeks.