PreCalculus GT - Howard High

Howard HS: PreCalculus GT Summer Review Name ______________________________
HOWARD HIGH SCHOOL
PreCalculus GT
Summer Pre-View Packet
DUE THE FIRST WEEK OF SCHOOL
The problems in this packet are designed to help you review topics from previous mathematics courses that are
important to your success in PreCalculus GT.
Show all work that leads you to each solution on separate sheets of paper. You may use your notes from
previous mathematics courses to help you. You may use a calculator for all problems, unless otherwise
indicated.
ALL work should be completed and ready to turn in by the end of the FIRST WEEK of school. You will be
assessed on this material!
ENJOY YOUR SUMMER! WE ARE LOOKING FORWARD TO SEEING YOU IN THE FALL.
Reference Information
Quadratic Formula: Given , then .
Factoring:
Laws of Exponents:
Changing between Logarithmic and Exponential Form:
Basic Properties of Logarithms:
Properties of Logarithms: Product Rule:
Quotient Rule:
Power Rule:

Howard HS: Precalculus GT Summer Review Name __________________________
Simplify each expression.
SHOW ALL WORK ON A SEPARATE SHEET OF PAPER.
Unless otherwise specified, if a decimal approximation is used,
it must be accurate to three places after the decimal point.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
€
Simplify each expression.
13. 14. 15.
17.
⎛⎛ 1 ⎞⎞ ⎛⎛
2 ⎜⎜ 2x ⎟⎟ ⎜⎜ 3x
⎜⎜ 2 ⎟⎟ ⎜⎜
⎜⎜ 3 ⎟⎟ ⎜⎜
⎝⎝ y ⎠⎠ ⎝⎝
−2
3
1
2 y
⎞⎞
⎟⎟
⎟⎟
⎟⎟
⎠⎠
€
Factor Completely.
€
18.
p 2 q 4 ( ) 1 2
27q 3 p 6 ( ) 1 3
€ 19. € 20.
1
(3−i)(2+i)
2012 1
⎛⎛
⎜⎜ 8m
⎝⎝
3 1
2
3
2 4 n
21. 22. 23. 24.
25. 26. 27. 28.
Solve using the quadratic Formula.
29. 30.
⎞⎞
⎟⎟
⎠⎠
€
16.
(Hint: Rationalize the
Denominator.)
⎛⎛
⎜⎜
⎝⎝
−8x 6
y −3
2
3
⎞⎞
⎟⎟
⎠⎠
x m ( ) n
• x n ( ) n−m

Howard HS: Precalculus GT Summer Review Name __________________________
Solve by completing the square.
31. 32.
Solve each quadratic equation for x using any method.
33. 34.
35. 36.
Given and , determine each of the following.
37. 38. , when x = ? 39. 40.
41. 42. 43.
Simplify. Write your answer as a single fraction.
44. 45. 46.
47. 48. 49.
Find the solution(s) of the given systems of equations. Write answers in the form (x, y).
50. 51. 52.
Solve for the missing side of the triangle using the Pythagorean Theorem a 2 + b 2 = c 2 :
a
53. a = 6 ft., b = 8 ft.
54. b = 17 ft., c = 19 ft.
c
2012 2
b

Howard HS: Precalculus GT Summer Review Name __________________________
Solve for x and y using a 45-45-90 or a 30-60-90 triangle .
55.
45°
x y
56.
4 in
x
57.
60°
y
x
3 ft
Given the right triangle, determine the trigonometric ratios.
B
58. 59.
36
39
C A
15
60. 61.
Use trig ratios to solve for x and y (to the nearest thousandth) in each right triangle.
62.
x
63.
y
12
20°
18
Solve each equation or inequality.
64. 65. 66. 67.
Find an equation in slope intercept form for the line described.
y
68. The line through ( 3, -2 ) with slope m =
€
2012 3
4
69.
5
The line through the points ( -1, -4 ) and ( 3, 2 )
70. The line through ( -2, 4 ) with a slope m =0
71. The line through ( 2, -3 ) and parallel to the line 2x +5y =3
72. The line through ( 2, -3 ) and perpendicular to the line 2x +5y =3
73. Tangent to the circle (x −3) €
€
€
€
2 +( y +5) 2 =36 at ( 7, 2 )
x
28
30°
m
y
c