Name: Algebra 1 Review

Name: _______________________________________________

Algebra 1 Review: Packet #1

Topic #1: The Real Number System

THE REAL NUMBERS (____): ___________________________________

IRRATIONAL NUMBERS (____): ______________________ RATIONAL NUMBERS (____): __________________________

INTEGERS (____): ____________________________

WHOLE NUMBERS (____): ____________________________

NATURAL NUMBERS (____): _________________________

Name all sets to which each number belongs.

1. 2 3

2. 50

4. 9 4

5. 28 7

3. 0 6.

Topic #2: Properties Give two examples of each property.

COMMUTATIVE:

____________________________________________

____________________________________________

ASSOCIATIVE: ____________________________________________ ____________________________________________

IDENTITY: ____________________________________________ ____________________________________________

INVERSE: ____________________________________________ ____________________________________________

ZERO PRODUCT: ____________________________________________

____________________________________________

DISTRIBUTIVE: ___________________________________________

___________________________________________

REFLEXIVE: ____________________________________________ ____________________________________________

SYMMETRIC: ___________________________________________ ___________________________________________

TRANSITIVE: _________________________________________________________________________________________________ _______________________________________________________________________________________________

Name the property that justifies each statement.

7. 5x + 1 = 1 + 5x

8. 17 = 17

9. 10y2 0 = 0

10. -3(m + 8) = -3m ? 24

11. If 25 = 32 and 32 8 4 , then 25 8 4

12. 8k + 0 = 8k

13. If -2x = 20, then 20 = -2x

Topic #3: Square & Cube Roots

Give the value of each expression.

15. 25

16. 324

19. 3 27

20. 3 343

14. 4 9 1 94

17. 144 21. 3 64

18. 16 49

22. 3 1000

Topic #4: Evaluating Expressions

Evaluate each expression. Use the variable replacements when given.

23. 23 (9 2) 12 5 4

24. 8 12 400 25 11

25. 53 42 6 38

26. w2 5xy

(if x = -3, w = -2, and y = 1)

27. 2 m n2 k3

(if k = -2, m = -7, and n = 4)

28.

bc (c a)2

b

(if a = 1, b = -20, and c = -5)

Topic #5: Translating Equations & Inequalities

Translate using an equation or an inequality. Do not solve.

29. The quotient of twice a number and 7 is 20.

30. Five less than the product of a number and 3

is 14.

31. Seven times the difference of a number and 4 is 32. The product of a number and four, increased by

no more than 10.

one, is at least 7.

Topic #6: Solving Equations Solve each equation. 33. 18 3 3a

34. 4 1 n 12 2

35. 3 x 17 23 4

36. 9 y 4( y 1) 31

37. 6(w 4) 8w 2(w 9)

38. 3m (7m 12) 2(m 3)

39. 2x 2(4x 3) 6 6x

40.

7

3

x8 x

41. Solve A 1 bh for h.

2

42. Solve c a2 3b for b. 4

Topic #7: Solving & Graphing Inequalities Solve and graph each inequality. 43. 11x 13 20

44. 2x 6 3x 34

-8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

45. 3x 7(x 3) 13

46. 4 8x 2(5 3x)

-8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

47. x 7 2 or x 14 3 4

48. 3x 5 16 or 5x 8 13

-8 -6 -4 -2 0 2 4 6 8

49. 2 3x 2 10

50. 3 2x 1 13

-8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

Topic #8: Properties of Equality/Justifying Steps when Solving Equations

Properties of Equality: Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, Division Property of Equality, Substitution Property of Equality

Use a property to justify each step of the equations solved below.

51. Step

Property/Reason

1. 1 x 16 11 3

2. 1 x 5 3

1. Given 2.

3. x 15

3.

52. Step

1. 5 2(3x 5) 47

2. 5 6x 10 47 3. 6x 5 47 4. 6x 42 5. x 7

1. Given 2. 3. 4. 5.

Property/Reason

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