MATHCP Algebra I  - Unit 01: Expressions, Variables, and Properties
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Sets of Numbers

1) Which number is an element of the whole numbers but is not an element of the natural numbers?

2) Is 2.88 rational or irrational?

3) Is "pi" rational or irrational?

4) Name all sets of numbers to which 21/7 belongs.

In the following problems, use the order of operations to evaluate the problems.

5) Evaluate.

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6) Evaluate.

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7) Evaluate.

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8) Evaluate.

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9) Evaluate.

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10) Evaluate.

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Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the worksheet.

Extra Practice Challenge:  Check with you instructor to see if s/he would like for you to do some extra practice challenge problems.  Click here to view the worksheet.

Introduction to Variables and Expressions

11) Evaluate.

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12) Evaluate.

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In the following problems, evaluate the expressions for a = 5, b = 3, and c = 4.

13) Evaluate.

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14) Evaluate.

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15) Evaluate.

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16) Evaluate.

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Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the worksheet.

Parts of an Algebraic Expression

17) In the algebraic expression 3xy + 13 – 5a, name a term, the constant, and a coefficient.  Select the letter of the answer that has the term first, the constant second, and the coefficient last.                  

18) Which algebraic expression has a coefficient of 5?

19)

Translate the following phrase into an algebraic expression: “the quotient of a number and 6.”


20)

Select the correct translation for the following phrase: “x decreased by 14.”


21)

Select the correct translation for the following phrase: “four times a number increased by 3.”


22)

Translate the following phrase into an algebraic expression: “two more than twice last month’s sales.”


23)

Select the correct translation for the following phrase: “twice the sum of two and y.”


Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the worksheet.

Properties of Real Numbers

In the following problems, state “True” if the property given is illustrated in the example. State “False” if it is not, and then give the correct property illustrated or state a counterexample.

24) 5x + 0 = 5x, Multiplicative Property of Zero

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25) 9 + 8 = 8 + 9, Commutative Property of Addition

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26) x(3y) = (3y)x, Associative Property of Multiplication

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27) 251 = 251 × 1, Commutative Property of Multiplication

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28) (5 + a) + 6 = 5 + (a + 6), Associative Property of Addition

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29) mn(0) = 0, Identity Property of Multiplication

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30) (3 + 5) + m = (5 + 3) + m, Commutative Property of Addition

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31) The set of whole numbers is closed under division.

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32) The set of real numbers is closed under multiplication.

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