zMath Intervention Math  - Unit 2: Expressions, Sequences, and Logic
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Order of Operations

1) Find the value of the expression.

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2) Find the value of the expression.

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3) Find the value of the expression.

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4) Find the value of the expression.

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5) Find the value of the expression.

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6) Find the value of the expression.

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7) Janie bought 14 pairs of socks at $2.00 each. She paid for the socks with two twenty-dollar bills. Calculate the money Janie received back after making the purchase? (Note: Janie’s state does not apply sales tax to clothing.) (a) State a math expression that represents this problem. (b) What is the amount of change?

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8) Darren works 40 hours a week at a construction company and makes $24.00 an hour. Calculate Darren’s take-home pay if $275 is withheld for taxes and insurance? (a) State a math expression that represents this problem. (b) What is Darren’s take-home pay?

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Math Expressions

For the next four problems, determine a math expression to represent the given phrase. State the letter of the correct answer.

9) What math expression represents the following phrase? “the sum of eight and a number”

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10) What math expression represents the following phrase? “twelve divided by a number”

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11) What math expression represents the following phrase? ‘ten less than a number”

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12) What math expression represents the following phrase? “the product of 15 and a number”

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Properties of Real Numbers

For the next five problems, review the explanation of the properties of real numbers in the content link to “Properties of Real Numbers”, and then determine which property fits each of the given descriptions.

13) Which property fits this description? When adding several whole numbers, the result is the same no matter which two numbers are added first. In other words, (2 + 7) + 9 is the same as 2 + (7 + 9).

14) Which property fits this description? When adding two whole numbers, the result will be a whole number also.

15) Which property fits this description? When multiplying two whole numbers, the result is the same regardless of the order the numbers are multiplied. In other words, 7(8) = 8(7).

16) Which property fits this description? The product of any whole number and one is that number. In other words, 19(1) = 19.

17) The given figure is a model of the distributive property. What is the numerical representation of the model?

Evaluating Expressions

18) Find the value of the expression if n = 4 and p = 3.

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19) Find the value of the expression if a = 3, b = 7, and c = 4.

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20) Find the value of the expression if a = 5, b = 2, and c = 9.

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21) Find the value of the expression if a = 6, b = 3, and c = 8.

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22) What number is the product of six and eight subtracted from nine-squared?

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Arithmetic Sequences

23) Define an arithmetic sequence.

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24) What is the common difference in the given arithmetic sequence?

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25) What are the next three terms in the sequence in the previous problem?

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26) What are the next three terms in the given sequence?

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27) Which sequence is arithmetic?

28) Complete the arithmetic sequence.

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29) Sarah signed up for typing class at her high school. Her typing skills improved the first four weeks as shown below. If Sarah continues to improve her typing skills at this rate, what week will she be able to type 56 words per minute (wpm)?

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30) The Fibonacci sequence is a special sequence that occurs in both natural and man-made creations. It is not an arithmetic sequence; but, addition may used to determine the next term. (a) What are the next three terms? (b) Describe the pattern that connects the terms in the Fibonacci sequence.

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Matrix Logic

For the next two problems, complete a matrix logic table to help solve the problems.

31) Kristen, Amy, and Larissa have chosen careers as a mechanical engineer, a teacher, and a physician’s assistant. Amy does not have patience with children. Kristen likes to analyze and design equipment. Which career has each person probably chosen?

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32) Four friends like four different kinds of music. Jay does not like heavy metal. Mike does not like jazz. Cory does not like jazz or rap. Luke does not like rap, jazz, or rock. Each boy likes which kind of music?

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33) Five friends live in apartments on the same side of the street. The apartment numbers are #510 through #514. Darrel’s apartment number is #512. Laura’s apartment is right before Ray’s. Darrel’s closest neighbors are Jim and Laura. Dianne’s apartment number is not #512 through #514. What is each person’s apartment number? (Hint: Draw a matrix table to solve the problem.)

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