Honors Precalculus Summer Packet

Fractions Review: Perform the indicated operation and simplifying completely as needed: 1.

2 4   3 5

2.

6 2   7 3

3.

7 6  8 5

4.

2 3   15 4

2 4 5. 1  2  3 5

6.

5 7   24 x 12 x 2

7. Turn into a percentage: 0.0054

8. Turn into a decimal: 0.0054%

Exponents Review: Product Rule:

a m  a n  __________

Quotient Rule:

Negative Exponent: a  n  __________

Zero Exponent: a0  __________ Power Rules:

 am   __________, n

9. a) Rewrite in Exponential form:

7

am  __________ an

m

a    __________ b

 ab   __________, m

x4

b) Rewrite in Radical form: 6

1

5

Simplify each expression completely as needed: 10. 24 

 27  14.    64 

11.

 2 

4

2/3



12. 32

2

2

5

 2 13.   =  3b 

=



15.

s 2t 3 6sr 3   2r 2 t

16.

 2x y z 

 32 c  17.  3  =  c 

18.

8 x3 y 5/3 z 4  2 x 2 y 2/3 z

19.

 3x y

3

3

3 2

2/3 4

z

(3x 2 yz 0 )3 

5x y z   2

3/2

Radicals Review: Simplify completely as needed. No decimal answers – exact answers only! 20. 108

21.

52  32

22.

3

108

Perform the indicated operation and simplifying completely as needed: 23. 2 3  4 3 

26. 2 6



24. 2 5  2 6 

2 3 = 2

3 7



25. 2 8  3 18 

27.



29. 2  3 2  3 

28.

2  3

30. Rationalize the denominator:

2



2 2

Polynomials Review: Perform the indicated operation: 31.  x3  3x 2  x    2 x 2  3x  5

33.  2 x  y  3x  4 y 

32. 5x  x 2  7 xy  3 y   2 x  2 y  19 xy  2 x 2 

34.

 7 x  6

2

35.

 2 x  3  x 2  4 x  5 

Factoring Review: Factor, if factorable, the following polynomials completely: 36. x2  5x  6

37. 10r 4 s3t  16r 2 s 2t 3

38. 2 x2  5x  12

39. 4 x 2  25

40. 6 x2  17 x  12

41. x3 y  9 xy

42. 4 p 2  3 pq  1q 2

43. x 2  64

44. x3  6 x 2  9 x

Rational Expressions:

Simplify each expression completely as needed: 45.

2 y 2  5 y  12 3 y 2  14 y  8

46.

x2 1 2 x  x2 4 x  4

47.

2r 3 8r 3  9r 3 6r

48.

2 x 2  x  6 x3  3x 2  2 x  x2  4 x  5 4 x2  6 x

49.

3 x  2 x 1 x 1

50.

5 1  2 9x 6x

1 2  51. 2 3 4 2  5 7

1 1  52. x x  1 1 x 1

Linear Functions: Fill in the following formulas:

Slope: _________________________ Slope-intercept form: _______________________ Point-slope form: _________________________

What is the relationship of the slope of 2 parallel lines? __________________________________ What is the relationship of the slope of 2 perpendicular lines? _______________________________

53. Write the equation of the graph given to the right: ________________________

54. Find the equation of the line containing the points (–4, 3) and (2, –5).

55. Write an equation that is perpendicular to 3x + 2y = 12 and goes through the point (2, 3).

56. Write an equation that is parallel to 3x + 2y = 12 and goes through the point (2, 3).

57. Find the equation of the line containing the points (7, 4) and (7, –9).

58. Identify the slope, intercepts, and sketch the graph: 2x + 3y = –18 slope: ______________ x-intercept: ______________ y-intercept: ______________

Additional Algebra Review: 59. Solve the system:

x  2 y  1 2x  y  4

60. Given the functions, f  x   2 x 2  x  7 and g  x   4 x  5 , evaluate the following: a)

f  3

b) f  2   g  4 

c)

f  x  g  x

d) f  2  g  2 

e)

f  g  1 

f) g  f  1 

1   x  13 , x  3 61. Given the function f ( x)   find : a) f  3 x  2, x  3 

b) f 11

62. What’s the quadratic formula? ____________________________________________

63. What is the vertex formula? ______________________________ 64. Find the vertex of f  x   2 x 2  6 x  1

Solving Equations: 65. Solve for h: V   r 2 h

67. Solve for g: h 

69.

1 2 gt  v0t  h0 2

3 1  r  5   r  24   0 2 4

66. Solve for u: u 2  d  0

68. 0.275x  0.725  500  x   300

70.

100  4 x 5 x  6  6 3 4

71.  x  2   x 2  4  x  1

72. 2 x2  32  0

73. x2  x  12

74. x2  4 x  2  0

75. 3x2  7  20 x

76. 6 x2  3x  0

77. 3  5x  2 x2  0

78.

2

79. x2  2ax  a 2  0

 x  13

2

 21

80. Suppose you invest $12000 in two funds paying 10.5% and 13% simple interest. Where the formula for simple interest is equal to I = Prt (P = Principle amount, r = rate, and t = time in years). The total annual interest is $1447.50. How much was invested in each fund?