Entering

Pre-Calculus

Summer Assignment

TKCS-2020

Name:____________________________

2. ,4

3. 60 x

Use interval notation to describe the set.

_____________4. y is no more than 25

_____________5. t is at least 10 and at most 22

_____________6. k is less than 5 but no less than –3

Entering PreCalculus Summer Packet

Name ___________________

This assignment will be graded on completion as well as accuracy and will count as your first math grade. All work must be shown to receive full credit. Write your answers in the space provided. These problems are reflective of the knowledge that is prerequisite to the PreCalculus course.

Sketch each subset on the real number line.

1. x 5

Evaluate the expression for the given value of x.

_____________7. x2 – 3x + 4 ; x = –2

_____________8. 33x ; x = 2

_____________9. 43x ; x = –2

Simplify each expression. Each answer should only have positive exponents (no negative

exponents).

_____________10. 433zz

_____________11. 3

27

x

x

_____________12. 1332 42

xx

_____________13.

343

5

yx

_____________14. 362362 55

zxzx

Evaluate each expression without a calculator.

_____________15. 3

1

27

_____________16. 4

3

81

16

Simplify each radical expression. Rationalize the denominator of any fractions. Leave

answer in simplified radical form (no decimals).

_____________17. 454xy

_____________18. 5 48160 zx

_____________19. 812502

_____________20. 214

5

_____________21. 3 2

8

Find the product.

_____________22. (3x – 5)(2x + 1)

_____________23. (2x – y)3

_____________24. (u + 2)(u – 2)(u2 + 4)

Perform the multiplication or division and simplify.

_____________25. 4

3

96

622

2

t

t

tt

tt

_____________26. xx

xx

x

x

2

232 636

Perform the addition or subtraction and simplify.

_____________27. xx

2

5

2

3

_____________28. xxxx

11

1

232

Simplify the complex fraction.

_____________29. 2

12

x

x

_____________30. x

xx

2

1

_____________31.

3

2

2

1

1

x

x

x

x

_____________32.

2

11

11

x

x

Completely factor the expression.

_____________33. 2x3 – 6x

_____________34. 16x2 –

9

1

_____________35. 3x2 – 5x +2

_____________36. 6x3 – 2x + 3x

2 – 1

_____________37. 89

2

81

1 24 xx

Write the rational expression in simplest form.

_____________38. x

x

10

15 2

_____________39. 510

84 2

y

yy

_____________40. 4

652

23

x

xxx

Solve the quadratic equation by factoring.

_____________41. x2 – 12x + 35 = 0

_____________42. 2x2 = 19x + 33

Solve the quadratic equation by completing the square.

_____________43. x2 + 4x – 32 = 0

_____________44. 4x2 – 4x – 15 = 0

Use the Quadratic Formula to solve the equation.

_____________45. 2 + 2x – x2 = 0

_____________46. 8t = 5 + 2t2

Solve using the square root method.

_____________47. 9x2 = 36

_____________48. (2x – 1)2 = 18

Find all real solutions of the equation. Check your solutions in the original equation.

_____________49. x4 – 81 = 0

____________50. x3 – 3x

2 – x + 3 = 0

____________51. 0102 x

_____________52. 512 x

Solve the inequality and sketch the solution on the real number line. (some inequalities

have no solutions)

_____________53. – 2x > – 3

_____________54. 2

5318

2

1 xx

_____________55. 132318 x

_____________56. 15 x

_____________57. 42

3

x

Solve for the indicated variable.

_____________58. Solve 202

5 bA for b

_____________59. Solve

4

203

qp for q

_____________60. Solve p

c

x

pc for x

Logarithms and Exponents. Solve for x.

_____________61. logx81 = 4

_____________62. log3x = 5

_____________63. 2x = 8

_____________64. Write 3x = 27 in logarithmic form.

_____________65. Convert log255 = ½ to an exponential equation.

Evaluate the function at each specified value of the independent variable and simplify.

h(t) = t2 – 2t

_____________66. h(2)

_____________67. h

2

3

_____________68. h(x+2)

Check for symmetry with respect to both axes and the origin. Answer Yes or No.

69. y = 2x3 x-axis: _________

y-axis: _________

origin: _________

70. x – y2 = 1 x-axis: _________

y-axis: _________

origin: _________

Plot the points. Find the distance between the two points and the midpoint of the line

segment between the two points. Leave answer in simplified radical form (no decimals).

71. A

1,

2

1,B

3,

2

5 Distance = ____________ Midpoint = _____________

Find the second endpoint of a line segment if the coordinates of the first endpoint and

midpoint are, respectively:

_____________72. (1,– 2), (4,– 1)

Find the domain of the function and write answer in interval notation.

_____________73. 3 4)( ttf

_____________74. 5

3)(

y

yys

_____________75. x

xxf

6

6)(

Find the x and y intercepts.

76. y = 16 – 4x2 x-intercept(s): __________

y-intercept(s): __________

77. y = x3 – 4x x-intercept(s): __________

y-intercept(s): __________

Solve the system of equations.

_____________78. 2r + s = 11

6r – 2s = – 2

_____________79. 4x – 5y = 17

3x + 4y = 5

_____________80. Find the slope of the line passing through points (– 2,0) and (3,1).

_____________81. Find the equation of the line passing through the point (2, – 1) and

parallel to the line 2x – 3y = 5. Write in slope-intercept form.

_____________82. Find the equation of the line passing through the point (– 3,2) and

perpendicular to the line x + y = 7. Write in slope-intercept form.

_____________83. Find the equation of the line passing through the points (– 4, – 4)

and (4,3). Write in slope-intercept form.

For each problem, write an equation and solve.

_____________84. The measure of an angle is 8 degrees less than three times the

measure of the angle’s supplement. Find the measure of the angle.

_____________85. A rectangle has a perimeter of 26 meters. If the length is 4 meters

longer than twice the width, find the length and the width.

_____________86. Find two consecutive odd integers whose product is 195.

_____________87. The Lance Company has 78 female employees, which represents

52% of the total work force of the company. How many employees

does the company have?

_____________88. An airplane flies from Naples, Italy in a straight line to Rome, Italy,

which is 120 km north and 150 km west of Naples. How far does

the plane fly?(round answer to nearest tenth km)

Graph each of the following lines:

89. y = ½ x + 1

90. 5 – y = 3x

91. A line passing through the point (6,– 1) with an undefined slope.

92. y + 3 = 0

Graph each of the following inequalities. Remember to shade.

93. 53

1 xy

94. 42

93

yx

yx