Principal
Brian Stranieri
Southington High School
Assistant Principals
Richard Aroian
Michael Halloran
Diane Holst-Grubbe
Jeffrey Shaw
Dear students,
Enclosed you will find a comprehensive set of problems which reflect critical math skills
that must be mastered prior to entering your PreCalculus class at Southington High
School. You are encouraged to develop a wide range of ways for finding the correct
answer, including techniques both with and without the aid of a calculator. Working
with a friend, sibling, or parent might be a helpful way to complete this assignment!
On the second day of school, your teachers will check your packets for completion and
count it as your first three homework grades. In order to receive full credit for the
assignment, you must attempt each problem and show all work used to complete it. The
answers are provided as a means to assess your own work. During the first few days of
school, your teachers will provide you with an opportunity to review your work from this
packet. Soon thereafter, you will be given your first quiz that addresses these skills.
As an additional means of support, I will be in school on Tuesday August 30th (3:00 pm –
5:00 pm in room E288) and will be available for extra help in completing the packet.
Please have a parent/guardian call or email me in advance if you plan to attend on this
date. (860-628-3229 ext. 243 or [email protected]). Note: You may stay
the entire time or for any portion of the extra help session.
Our goal is for you to have a successful and enjoyable transition into your PreCalculus
class at Southington High School. This packet is meant to facilitate this process. Try
your best and remember your teachers will help you upon your return.
Sincerely,
Mr. Robert Lasbury
Mathematics Department Chair
Southington High School
860-628-3229 ext 243
Mr. Brian Stranieri
Principal
**Copies of this packet may be found on the Southington High School Website. Go to
www.southingtonschools.org and click on the link to Parent Resources.
Summer Packet Pre-Calculus
Name:___________________
Part I : Use the exponent rules to simplify each expression.
1) (3x
4) 5
4
3

5
0
6x ) =
4
y
 8
x
3
4
x

x4
8)
Part II : Multiply the following binomials:
10) (x + 8)(x + 7)=
12) (7x + 12)(x – 5)=
3) (3xy) =
2
5) (-4x y
=
12
7)
3
2) (8x) =
3
) =
6) (3m

 

2
2
)
2
=
a a

a6
5
9)
3
n)(5m n
8
11) (x – 8)(3x – 2)=
13) (4x – 15)(x + 9)=
2
2
14) (x – 9) =
15) (2x + 11) =
Part III : Factor the following expressions.
2
16) x +12x + 35 =
2
18) 3x + 15x – 72 =
2
20) 5x – 13x – 28 =
3
22) 64x – 125 =
17)
19)
21)
23)
2
x – 8x – 48 =
2
2x – 26x + 72 =
2
64x – 121 =
4
16x + 54x =
Part IV : Graph the following functions and state the domain.( Show roots and turning points)
2
3
24) f(x)=(x + 1) – 9
2
25) y = x + 4x – 12x –18
Part V : Solve each quadratic by the indicated method.
2
2
26) 15x + 7x – 2 = 0 by factoring.
27) 3x – 6x – 24 = 0 by quadratic form.
2
28) 6x = 150 by any method.
Part VI : Simplify each expression.
2
29)
32)
30) 27 3 =
18 + 32 =
x
1
5
x
3
5
=
33)
31)
4 x y  5x y
3
4
3
=
3
34)
54
–
98 x 4
2x2
3
250 =
=
Part VII : Evaluate each expression.
35) log
38) log
5
3
2
e7 =
125 =
36) e
1
=
27
39) log 81 =
37)
x
40) 6
3
Part VIII : State whether each expression is True or False without a calculator.
41) ____
3
45
=
3
4
+
3
5
42)_____
34
5
=
3
5
+
4
5
43)_____
16e8
log6 4
=
=
35  4
5
=3+4
44)_____
35  45
5
=3+4
45)_____
1
 1
 
3
=3
46)_____
1
1
4
3
=3+4
Part IX : Simplify each rational expression.
47)
x  3 6 x 2  96


2x  8 x2  9
48)
x 2  13x  40
 x 2  5 x  24 
2
x  2 x  15
49)
5x
4x  9
 2

x  8 x  5 x  24
50)
x2  5
x3


2
x  5 x  14 x  7
Part X : Graph each rational function.
51)
x3
y
x 3
2x2
52) y  2
x 9
3
3
53) The figure above shows the graph of w(x) – 6. What is the value of w(0)?
A) – 6
B) – 3
C) 0
2
D) 3
E) 9
D) 16
E) 24
2
54) If x – 4x – 12 = 0, what is the value of 2x – 8x?
A)0
B) 4
C) 12
55) If z ≥ 0 and √𝑥 + 𝑦 = 𝑧, which of the following must be true?
I.
II.
III.
(A)
(B)
(C)
(D)
(E)
x ≥0
y≥0
x+y≥0
I only
II only
III only
I and III only
I, II, and III
Answer Key
1. 18x 9
30. 9
2.
31.
1
 23 2
3
5
3. 27x 3 y 3
32.
x
x
4. 1/125
33.
2 x3 y 2 5 y
5. -64x 6 y 12
8
6. 75m n
7. x
8.
34. 7x
5
35. 3
8
36. e
y12
x 24
5
37. 4e
9. a 7
4
38. –3
10. x  15x  56
39. 4x
11. 3x  26 x  16
40. 4
12. 7 x  23x  60
41. False
13. 4 x 2  21x  135
42. True
14. x  18x  81
43. False
2
2
2
2
15.
16.
17.
18.
4 x  44 x  121
44. True
(x + 7)(x + 5)
45. True
(x – 12)(x + 4)
46. False
3(x + 8)(x – 3)
47. 3(x + 4)/(x + 3)
2
2
19. 2(x – 9)(x – 4)
48. 1/(x + 3)
20. (5x + 7)(x – 4)
21. (8x + 11)(8x – 11)
49. (5x –11x – 9)/[(x + 8)(x – 3)]
2
50. (-x + 1)/[(x + 7)(x – 2)]
2
22. (4x – 5)(16x + 20x + 25)
23. 2x(2x + 3)(4x 2 – 6x + 9)
24.
51.
25.
26. x = 1/5, -2/3
27. x = 4, –2
28. x = 5, –5
52.
29. 7 2
53. D
54. E
55. C