Algebra/Calculus Review

Algebra/Calculus Review

ALGEBRA REVIEW

Add as indicated:

1. (2ac) +(–6ac) +(9ac) 2. 3x +(–7x)

3. (–8a) –(–3a) –(2a) 4. (5x) –(6x) –(7x)

Add the two expressions in each problem

5. x +2y –8 6. 11m –7n +13

3x –4y +9 3m –8n –21

Subtract the two expressions in each problem

7. x +2y –8 8. 11m –7n +13

3x –4y +9 3m –8n –21

9. 10a –17b +24c; 13a +14b –16c

Add the three expressions in each of the problems:

10. 7a –3b +11c; –14a +10b +10c; 8a +8b +13c

Combine like terms:

11. 3x +7y –3z +6xc –8y –7z +5 –1

12. 9xy +3x +4a –5ax +10a –7x +3yx +6xa

Remove the symbols of grouping and simplify by combining terms:

13. 3a –(b +c) +(a +b –c) 14. –[x +(3 –x) –(4 +3x)]

15. –{5a –b –[3b –(c –2b +a) –4a] +c}

Multiply as indicated:

16. (5)(-4)(-2) 17. (3ab)(2a)

18. (6a2b)(3ab2) 19. (3xy2)(5x2y)(xy)

20. 3x2y(2xy2 +y) 21. –4mn(3 –5m +6mn +3n)

22. (a +3b)(3a2 +6ab +4b2) 23. (3a +2)(a –2)(2a +1)

Divide as indicated:

24. x2/x2 25. –y3/y3

26. a8/a5 27. acz/ac

28. 12a4/6a 29. –9c3d4/3c5d3

30. 34a3b2/17a2b 31. (9x2 –6x3 –3x4)/(-3x2)

Perform the indicated operations, giving the results in the lowest term:

32. 33. 34.

35. 36. 37.

38. 39.

Simplify the complex fractions and other expressions;

40. 41. 42. 43.

Solve for x, and check by substitution:

44. 8x –15 = 3x 45. x –4 = 5 +2x

46. 47. (3x –1)(x +1) = 3x2

Solve the following systems:

48. – 4x +5y +14 = 0 49. 4xy – 2y –11 = 0

– 2x +2y – 7 = 0 2xy –3y – 4 = 0

50. 3x + y – 6 = 0 51. 4x –5y = 9

4x–3y –21 = 0 3x –4y = 8

Simplify the complex fractions;

52. 53.

54. 55.

CALCULUS REVIEW

Differentiate the following functions

56. Y = X2 57 y = 6x3

58. Z = 20Y0.5 59. Z =.

60. y = 30 61. t = 3x + 6x3

62. y = 7x0.5 + 12x1.5 63. Y = 6X(6 + 2X2)

64. y = (2 + 6x)(2 + 5x2) 65. y = (x2 – 3x3)(x3 + 5)

66. f(x) = 67. y =

Find the maximum and/or minimum values of the following functions. Be sure to state the first and second order conditions.

68. y = 10 + 10x – 0.5x2 69. T = – 2000S + 10S2

70. Z = 145 – 4Y – 0.3Y2 71. X = – 145 + 4Y + 0.3Y2

Find the maximum and/or minimum values and the inflection point of the following functions. Be sure to state the first and second order conditions. (Hint: the roots of the quadratic equation: aX2 + bX + c = 0 are

.)

72. y = 5000 + 500x + 20x2 –0.1x3 73. z = -2000 +30x +10x2 – 0.3x3

74. y = 5000x –100x2 –0.5x3 75. y = 400x – 25x2 + 0.2x3