Pre-Calculus - [PDF]

Bensalem High School
Trig and Pre-Calculus
Summer Math Packet
DUE THE FIRST DAY OF SCHOOL
Student Name: ____________________________________

This packet has been designed to help you review various mathematical
topics that will be necessary for your success in Trig &/or Pre-Calculus.
Instructions:
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 must do all work without any help from another person.
You may use the online textbook for Algebra 2 by going to
www.phschool.com. If you need a log in for this website, please contact
Mrs. Mielke at the email below.
Additional copies of this packet may be obtained from the Bensalem
High School website, www.bensalemsd.org
ALL work should be completed and ready to turn in on the FIRST
DAY of school.
If you have questions regarding the summer math packet, please email
Mrs. Mielke at cmielke@bensalemsd.org.
ENJOY YOUR SUMMER!! WE ARE LOOKING FORWARD TO
SEEING YOU IN THE FALL.

I. Polynomials and operations on real and imaginary numbers.
A. Simplify these expressions
1. − 100
2. (3+2i) + (5+7i)
3. 2i(3 – i ) 4. (3+2i)(3 - 2i)
5. (3 + i 5 ) 2 6.
5i
6 − 21
B. Factor Completely
2
7. t − 4t
− 21
8. 2x 2 – 9x – 5
9. 2x 2 – x – 3 10. 2x 2 – 11x + 15
11. 3x 2 + 4x + 1 12. 6x 2 – 41x + 30
C. Simplify the following expressions.
13. 5x 2 • 2x 5 14. (-2c 3 ) 2
15.
4
4
h−k
h+
k
6
10x
16.
−2
8x

D. Divide and simplify these expressions. Use synthetic division.
17.
x
2
+ 2x
−1
x + 3
18.
x
2
− 5x
+ 16
x − 8
E. Solve each quadratic equation for x
19. (x - 1)(5x + 3) = 0 20. 2x(x – 4) = 3(1 - x)
21. 2x 2 + 4x = - 3 22. 2x 2 - 32x = 0
F. Graph the functions using a table of values, symmetry, or other properties to plot points.
State the domain and range of each function
23. y = ln x
24.
y =
2
x
Domain:
Range:
Domain:
Range:

25.
3
y = x
26.
x
y = e
Domain:
Range:
Domain:
Range:
27. y = x
28. y = x
Domain:
Range:
Domain:
Range:
II. Function Operations
If f(x) = x 2 – 4 and g(x) = 2 x + 4 , determine
29. f(3) 30. f(x) = 0 when x = ?
31. f(g(4)) 32. f(g(x))
33. Domain of f(g(x) ) 34. f − 1 (x) Is the inverse of f(x) a function?

III.
Rational Expressions and Rational Functions
A. Graph each of the following functions using a table of values. Identify the intercepts
and any asymptotes.
35.
2x
f ( x)
= 36.
x + 4
3x
h ( x)
= 37.
x 2 + 1
2
4x
k ( x)
= x
2
− 9
Asymptotes: Asymptotes: Asymptotes:
Intercepts: Intercepts: Intercepts:
B. Simplify. Write your answer as a single fraction in simplest form.
38.
36x
2 + 45x
9x
3
39.
2
x − 25
2
x + 7x
+ 10
40.
2
2x
6x
÷
x + 5 2x
+ 10
4x
41. + 2
x + 6
42.
x − 2 x + 4
+
x 2x
43.
2x
x
−
x − 3 x + 3

C. Solve each equation. Check for extraneous roots.
44.
x x − 5
=
2x
+ 7 x −1
5
45. 6x − = −7
46.
x
x + 3
−
4
7
=
x + 2
2
4x
+ 8
IV.
Pythagorean Theorem and Trigonometric Ratios
A. Solve for the missing side of the triangle using the Pythagorean Theorem:
47. a = 6 ft. b = 8 ft.
B
48. b = 17 ft. c = 19 ft.
C
A

B. Solve for x and y using a 45-45-90 (ratio of sides 1:1: 2 ) or a 30-60-90 triangle
(ratio of sides 1: 3 :2)
49.
.
50.
.
51.
.
C. Given the right triangle, determine the trigonometric ratios.
52.
..
53.
.
54.
..
B
A C
1
21
8
10
°
D. Use trig ratios to solve for x and y in each right triangle. Round answers to three
places.
55.
..
56.
..

V. Exponential and Logarithmic Equations
Find the exponential function that satisfies the given condition.
59. initial value 5000 increasing at a rate of 5.5 % every year
60. Compare the balance after 5 years of a $8,000 investment earning 4.5% compounded:
r t
A. Continuously ( A= Pe )
⎛⎛ r ⎞⎞
B. Monthly ( A = P ⎜⎜ 1 + ⎟⎟ )
⎝⎝ n ⎠⎠
nt
Evaluate each of the following:
1
61. log 4
=
62. log .001 =
63.
256
log3.5
10
Page 9 of 10

Solve each of the following equations. Check your answers.
64. log 5
x = 3
65. log x = 3
66.
1
−
2
log 25
x =
3
2
67. 8 2 x
e + 6 = 9
68. 3 x = 80
Page 10 of 10