Department Of Math
Houston Community College
Review for Exam II: Math 0312
The following review problems will help you pass test II. The problem
is based on the lectures. You are to know how to solve all the
problems. Print a copy for your practice. Use your class note,
textbook, and Mymathlab for extra help. Chapters 4.1 to 6.2
Solve the following system of equation using any method.
1.
5x - 4y = 9
3 - 2y = - x
5.
2x - 5y = 11
3x + y = 8
2.
3x - y = 10
2x + 5y = 1
6.
4x + 3y = 1
3x + 2y = 2
3.
⅔x - ½x = 7/6
3x - y = 6
7.
5x - 5y = 3
x - y = 12
4.
2x - 5y = 4
5x + 2y = 10
8.
2x - y = 3
6x - 3y = 9
9.
Simplify: (x4)0
9x- 3
13.
t- 3
t- 6
10.
Simplify: 3x0
14.
x0
x- 10
11.
Simplify: 4a5 (a- 1)3
(a- 2)- 2
15.
Simplify: 5- 2
16.
Simplify: - (- 5)- 2
12.
Simplify: 22y4 (y-3)- 1
25 y- 2
17.
Evaluate: 5 x 10- 3
25x 102
18.
Divide and write scientific notation for the result: 1.1 x 10- 4
2.0 x 10- 7
19.
Write in scientific notation: 0.0000000617
20.
Write 6.28 x 10- 5 without exponent
1
21.
Multiply and write scientific notation for the result:
(9.1 x 10- 17)(8.2 x 103)
22.
Simplify: (2- 3)- 2
23.
Simplify: x4
3
24.
Simplify: - 3s2t(15s3t4)
37.
25.
Simplify: 5x2(- 4x2 + 3x - 2)
38.
26.
Multiply: (3x- 4)(2x2 + x)
39. Factor: x2+ x - 6
27.
Multiply:
(2k- 5m)(3k+ 2m) 40. Expand: (x + 2)2
28.
Multiply:
5x(2x - 1)(x + 4)
29.
Multiply:
(3x - 7y)(3x + 7y)
30.
Multiply:
(p + 7)(p - 7)
31.
Expand: (m+ 7)2
32.
Expand: (p - 4)2
33.
Expand:
34.
Expand:
[(x - y) + z][(x-y) - z]
35.
Expand:
[(3m - 2) + k]
36.
(x – 5)(x + 5)
43.
Divide: 8x5 - 6x3 + 2x2
2x2
44.
Divide: (x3 - 1) ÷ x - 1
45.
Factor completely: 3x2 - 6x - 4x + 8
-2
41.
Factor completely: x2 + 3x – x - 3
Factor : x2 – 7x + 12
multiply: (3y3 – 7)(2y2 – 2y +5)
(3x - 5y)2
42. Expand: (4x + 5y)2
2
46.
Factor completely: 2x3 + 10x2 + 8x
47.
Divide: 4x3 + 3x - 8 by x + 2
48.
Divide: 3x3 - 2x + 5 by x - 3
49.
Divide: x5 + 1 by x + 1
50.
Divide: 5m3 - 9m2 + 10m by 5m2
3
Keys
1.
(5,4)
2. (3, - 1)
3.
(11/5, 3/5)
4.
(2,3)
5. (3, - 1)
6.
(4, - 5)
7.
Ø
8. Infinite number of solution
9.
x3/9
10. 3
12. y9/8
13. t3
15. 1/25
16. -1
25
17. 2 x10- 6
11. 4/a2
14. x10
18. 5.5x 102
19. 6.17x10- 8
20. 0.0000628
21. 7.462x10- 13
22. 64
23. 9/x8
24. - 45s5t5
25. - 20x4+ 15x3 - 10x2
26. 6x3 - 5x2 - 4x
4
27. 6k2 - 11mk - 10m2
28. 10x3 + 35x2 - 20x
29. 9x2 - 49y2
30. p2 - 49
31. m2 + 14m + 49
32. p2 - 8p + 16
33. 9x2 - 30xy + 25y2
34. x2 - 2xy + y2 - z2
35. 9m2 - 12m + 4 + 6mk - 4k + k2
36. x2 - 25
37. (x- 1)(x+3)
38. (x-4)(x-3)
39. (x+3)(x- 2)
40
x2 + 4x + 4
41. 6y5 - 6y4 + 15y3 - 14y2 + 14y - 35
42. 16x2 + 40xy + 25y2
43. 4x3 - 3x + 1
44. x2 + x + 1
5
45. (3x- 4)(x - 2)
46. 2x(x+1)(x+4)
47. 4x2 - 8x + 19 + (-46/(x+2)
48. 3x2 + 9x + 25 + 80/(x-3)
49. x4- x3 + x2 - x + 1
50. m + 2/m - 9/5
6