Name ____________________________

Unit 3 Review

Use the Distributive Property to simplify the following expressions.

1. \frac{1}{2} (4z + 6)

2. (4 + 5) - (5 + 2)

3. \frac{3y + 2}{6}

4. - \frac{6z - 2}{3}

Evaluate each expression according to the order of operations.

5. 2 + 3 \times 4 + 7 = \underline{\;\;\;\;\;\;\;}

6. 7^3 - 100 + (3 + 4) - 9 = \underline{\;\;\;\;\;\;\;}

Check each answer using order of operations. Write whether the answer is true or false.

7. 4 + 5 \times 2 + 8 - 7 = 15

8. 4 + 3 \times 9 + 6 - 10 = 104

Insert grouping symbols to make each a true statement.

9. 4 + 5 - 2 + 3 - 2 = 8

10. 2 + 3 \times 2 - 4 = 6

Name the base and exponent in the following examples. Then write in expanded form and write how to “read” the exponential notation, for example: "four to the fifth power".

11. 4^5

12. 3^2

 Evaluate each expression.

13. . 3^3

14. 3^2+4^2

Simplify the following variable expressions.

15. (y^5 )(y^3)

16. (a^5 )^4

Choose an appropriate variable to describe each situation.

17. The height of an object over time

18. The area of a square

 Write an expression to describe each situation.

19. Avocados are sold for $1.50 each

20. A car travels 50 miles per hour for a certain number of hours

Underline the math verb(s) in the phrase.

21. Six times v

22. Four plus y minus six

Simplify each sum or difference by combining like terms.

23. 13b-9b

24. 22x+19x

Simplify each product or quotient.

25. 9x(2)

26. 14y(2y)

27. \frac{25x}{x}

28. \frac{45a}{9a}

Simplify each variable expression involving multiple operations.

29. 19x-5x \cdot 2

30. 16y-12y \div 2

Use the order of operations to evaluate each numerical expression.

31. 5 + 3 \times 4

32. 8 - 15 \div 3 + 4 \times 5

Use what you have learned to answer the following questions as either true or false.

33. Parentheses are a grouping symbol.

34. Exponents can’t be evaluated unless the exponent is equal to three.

35. If there is multiplication and division in a problem you always do the division first.  

Evaluate each expression if the given value of r=9.

36. \frac{r}{3}

37. r+5r

38. 12r-1

Evaluate the following variable expressions if x=4, y=2, z=3

39. x^2+ y

40. 2y^2+ 5-2

Use what you learned about variables and real-life situations for the next problems. Choose a variable to represent the number and write an algebraic expression for the following phrases.

41. 19 decreased by a number

42. four less than the product of four and a number