Entering Pre-Calculus - The King's Christian School Library
Transcript of Entering Pre-Calculus - The King's Christian School Library
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