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Accelerated Algebra I
Unit 1 Review
List of Properties
(A) Identity Property of Addition
(B) Identity Property of Multiplication
(C) Property of Reciprocals
(D) Commutative Property
(E) Multiplicative Property of Zero
(F) Distributive Property
(G) Associative Property
(H) Symmetric Property of Equality
(I) Transitive Property of Equality
(J) Reflexive Property of Equality
(K) Substitution Principle
(L) Properties of Opposites in Products
I. Name the property illustrated by each statement. An answer may be used more than once.
_________ 1. If b  2  4 then, 4  b  2.
_________ 2. 3r  s   3r  3s
_________ 3.  93  27
_________ 4. 3  a  a  3
_________ 5. 6 
1
1
6
_________ 6. x  0  0
_________ 7. If 9  5  4 , then 5  4  9
_________ 8. 9  (1  6)  9  7
_________ 9. 56x  5  6x
_________ 10. 6  0  6
_________ 11. If a = b and b = c, then a = c
_________ 12. a 1  a
_________ 13. 7 
1
1
7
_________ 14. Every real number is equal to itself
II. Classify each of the following using the appropriate symbolism:
16.
8
_________________
9
17.  _________________
18.
19.
9
_________________
3
20.
21. 0. 3 _________________
36 _________________
5 _________________
III. Refer to the number line below to answer the following questions:
Name the coordinates for the given points.
22. B _________
23. A _________
24. E _________
25. F _________
List the letters for the points whose coordinates are given.
26. 3 _________
27.  2.5 _________
28.  4 _________
29. 6 _________
IV. On a horizontal number line, point P has a coordinate  1 and point Q has a coordinate 3. Write
the coordinate of each point described.
30. 3 units to the left of P _________
31. 2 units to the right of Q. _________
V. Give the solution set of each equation over the set of real numbers. If there is no solution, explain
why.
32. x 
1
______________________
3
33. q  1 ______________________
VI. Simplify.
34.  9   4
37.
14
1

2
35.  (5  14)
36.  (3)  9
38.  3(2 x  7 y )
39.  3x 2 y 
1
15a  21b 
3
40. 5  16x  11  8x
41.
43. 3( x  2)  8( x  3)  6 x
1
44.  (35)
7
45. 6 x  2( x  3)
46. 4x  2x  7  x
47. (13  6)  (36  12)
48.
1
50.  (35a  60b)
5
51. 3  2  5  4
49.
 13
1
6
42. (104  96)  (8)
74  25
3(5  3)
VII. Evaluate each expression if x  2, y  4, z  6 and b  5
52.
9x  z
xz
53. 6 x( yz  b)
54.
9y  z
5(b  y )