NAME________________________
Advanced Algebra/Trigonometry SUMMER PACKET
Introduction (12 – 2)
This packet is due on the first day of school in September. You are responsible to do and show work
for any 50 problems that you decide to do. You must show work on these 50 problems to receive credit.
If you choose a problem that only requires a calculator, you must write down the key strokes that you
used. This assignment will count as a quiz grade so this is a great opportunity to start your senior year
with an A in math.
There will be a separate file on the CHS math department website that will contain some notes, hints,
and worked out solutions that will help you complete this packet successfully. There are roughly 10
weeks in the summer before your senior year begins and we suggest that you try to do 5 problems a
week so you will not feel overwhelmed if you wait until summer is almost over. This packet will help you
review what you have already learned and give you a head start to having a great year in this course.
HAVE A GREAT SUMMER AND WE LOOK FORWARD TO HAVING YOU AS A STUDENT WHEN SCHOOL
STARTS IN SEPTEMBER!!!!
Summer Packet - 12 - 2
1. If a + 3b= 13 and a + b = 5, the value of b is
A) 1
B) 7
C) 4.5
D) 4
2. If a = 3 and b = –1, what is the value of ab – b 2 ?
A) –2
B) 2
C) –4
D) 4
3. The expression (2x2 + 6x + 5) – (6x2 + 3x + 5) is
equivalent to
A) –4x 2 + 3x
C) –4x 2 – 3x + 10
B) 4x 2 – 3x
D) 4x 2 + 3x – 10
4. If r = 2 and s = –7, what is the value of | r | – | s |
A) 5
B) –5
C) 9
D) –9
5. On February 18, from 9 a.m. until 2 p.m., the
temperature rose from –14°F to 36°F. What was the total
increase in temperature during this time period?
A) 50°
B) 36°
C) 32°
D) 22°
6. Which expression is equivalent to x –1•y 2?
C) 3 9
D) 3 24
14. The length of a rectangle is 3a 2b 4 ft and the width is 5a
3 b 2 ft. What is the area in ft 2 ?
A) 15a 5b 6
C) 15b 7a 4
B) 15a 6b 8
D) 15b 12a 4
15. What is the product of –2x 2y 3 and 5x 3y?
A) 10x 6y 4
C) -10x 5y 4
B) -10x 3y 3
D) -10x 6y 3
16. The expression (ab 4c 2)(a 2c 3) is equivalent to
A) a 2b 5c 6
C) a 3c 5
B) a 3b 4c 5
D) a 2b 3c 5
17. The expression (–4a 3b) 2 is equivalent to
A) –16a 6b 2
C) 16a 5b 2
B) 16a 6b 2
D) 8a 6b 2
B) 36x 5y 8
D) 6x 6y 12
19. What is the value of 30 + 3 –2?
A) 0
B) 2y 3
C) y 9
D) y 6
8. The expression (–2a 2b 3)(4ab 5)(6a 3b 2) is equivalent to
A) 8a 6b 30
C) –48a 6b 10
B) 48a 5b 10
D) –48a 5b 10
9. What is the product of 10x 4y 2 and 3xy 3?
A) 30x 4y 5
C) 30x 5y 5
B) 30x 4y 6
D) 30x 5y 6
10. Expressed in simplest form, (3x 3)(2y)2(4x 4) is
equivalent to
24x 12y 2
24x 7y 2
A)
C) 48x 12y 2
–9x 5
B)
D) 48x 7y 2
is divided by
A) –3x 2
C) –27x 15
–3x 3,
x
0, the quotient is
B) 3x 2
D) 27x 8
12. The product of 3x 5 and 2x 4 is
A) 5x 9
B) 27 24
A) 36x 6y 12
C) 12x 6y 12
7. The expression y 3 + y 3 is equivalent to
11. When
A) 27 9
18. The expression (6x 3y 6) 2 is equivalent to
A) xy
2
B) y
x
2
C) x
y
D) xy –2
A) 2y 6
13. The expression 3 2 • 33 • 34 is equivalent to
B) 5x 20
C) 6x 9
D) 6x 20
B)
C) 1
D) 6
20. The expression 8 –4 • 86 is equivalent to
A) 8 –24
B) 8 –2
C) 8 2
D) 8 10
21. The video of the movie Star Wars earned $193,500,000
in rental fees during its first year. Expressed in
scientific notation, the number of dollars earned is
A) 1935 × 10 8
C) 1.935 × 10 6
B) 193.5 × 10 6
D) 1.935 × 10 8
22. According to the 2000 census, the population of New
York State was approximately 18,900,000. How is this
number expressed in scientific notation?
A) 1890 x 10 4
C) 1.89 x 10 7
B) 18.9 x 10 6
D) 189 x 10 5
23. The expression 0.62 × 10 3 is equivalent to
A) 0.062
C) 6.2 x 10 4
B) 62,000
D) 6.2 x 10 2
24. In a year, there are approximately 530,000 minutes.
When this number is written in scientific notation, the
numerical value of the exponent is
A) 5
B) –5
C) 4
D) –4
Summer Packet - 12 - 2
25. The distance from Earth to the Sun is approximately 93
million miles. A scientist would write that number as
A) 9.3 × 10 6
C) 93 × 10 7
B) 9.3 × 10 7
D) 93 × 10 10
26. What is the value of n if the number 0.0000082 is
written in the form 8.2 × 10 n?
A) –6
B) –5
C) 5
D) 6
27. A micron is a unit used to measure specimens viewed
with a microscope. One micron is equivalent to
0.00003937 inch. How is this number expressed in
scientific notation?
A) 3.937 × 10 –5
C) 3937 × 10 –8
B) 3.937 × 10 5
D) 3937 × 10 8
28. What is the sum of 2m 2 + 3m – 4 and m2 – 3m – 2?
A) m 2 – 6
C) 3m 2 + 6m – 6
B) 3m 2 – 6
D) m 2 + 6m – 2
29. What is the sum of x 2 – 3x + 7 and 3x 2 + 5x – 9?
4x 2
A)
– 8x + 2
2
C) 4x – 2x – 2
4x 2
B)
+ 2x + 16
2
D) 4x + 2x – 2
30. The sum of 8x 2 – x + 4 and x – 5 is
A) 8x 2 + 9
C) 8x 2 – 2x + 9
B) 8x 2 – 1
D) 8x 2 – 2x – 1
31. When 3a 2 – 7a + 6 is subtracted from 4a2 – 3a + 4, the
result is
A) a 2 + 4a – 2
C) –a 2 – 4a + 2
32. The expression
equivalent to
(x 2
7x 2
A)
– 12x – 5
2
C) 7x + 2x + 1
B) a 2 – 10a – 2
D) 7a 2 – 10a + 10
– 5x – 2) –
(–6x 2
– 7x – 3) is
7x 2
B)
– 2x + 1
2
D) 7x + 2x – 5
33. When 3x 2 – 8x is subtracted from 2x 2 + 3x, the
difference is
A) – x 2 + 11x
C) – x 2 – 5x
B) x 2 – 11x
D) x 2 – 5x
34. The expression (3x 2 + 2xy + 7) – (6x 2 – 4xy + 3) is
equivalent to
A) –3x 2 – 2xy + 4
C) –3x 2 + 6xy + 4
B) 3x 2 – 2xy + 4
D) 3x 2 – 6xy – 4
35. Kaylie's rectangular backyard is fenced in on three
sides. The sum of the length of the fencing on these
three sides is 2x 2 + 6x + 7. Tomorrow, she will add a
fourth side to the fence, with a length of 2x – 5. What
will be the total length of the four sides?
A) 4x 3 + 6x + 2
C) 2x 2 + 8x + 2
B) 2x 2 + 8x + 7
D) 2x 2 + 6x + 7
36. What is the product of 2r 2 – 5 and 3r?
A) 6r 3 – 15r
C) 6r 2 – 15r
B) 6r 3 –5
D) 6r 2 – 1
37. Base your answer to the following question on the
following information: The width of a rectangle is 4
less than its length.
If x represents the length, which expression represents
the area of the rectangle?
A) x 2 – 4x
C) 4x 2
B) x 2 – 4
D) 2x 2 – 8x
38. The width of a rectangle is represented by 2x and the
length is represented by x 2 - x + 3. Which expression
represents the area of the rectangle?
A) 2x 3 - x + 3
C) 2x 2 + 2x + 6
B) x 2 + x + 3
D) 2x 3 - 2x 2 + 6x
39. What is the product of (c + 8) and (c - 5)?
A) c 2 + 3c – 40
C) c 2 + 13c – 40
40. What is the product of
x 2y B)
A)
3
B) c 2 + 3c – 40
D) c 2 – 40
x 2y and
x 3y C)
4
xy 3?
x 2 D)
y3
x3
y4
41. The expression (x – 3) 2 is equivalent to
A) x 2 – 9
C) x 2 – 6x + 9
B) x 2 + 9
D) x 2 + 6x + 9
42. Which trinomial is equivalent to (3x – 1)(x + 4)?
A) 3x 2 + 11x – 4
C) 3x 2 – 11x + 4
B) 3x 2 + 13x – 4
D) 3x 2 + 11x + 4
43. What is 6x 3 + 4x 2 + 2x divided by 2x?
A) 3x 2 + 2x
C) 4x 2 + 2x
B) 3x 2 + 2x + 1
D) 4x 2 + 2x + 1
44. The expression (50x3 – 60x2 + 10x) ÷ 10x is equivalent
to
A) 5x 2 – 6x +1
C) 5x 2 – 60x 2 + 10x
B) 5x 3 – 6x 2 + x
D) 5x 2 – 6x
Summer Packet - 12 - 2
45. When 3x 2 – 6x is divided by 3x, the result is
A) –2x
B) 2x
C) x + 2 D) x – 2
46. Expressed in factored form, the binominal 4a 2 – 9b 2 is
equivalent to
A) (2a – 3b)(2a – 3b) B) (2a + 3b)(2a – 3b)
C) (4a – 3b)(a + 3b) D) (2a – 9b)(2a + b)
47. Which expression is a factor of
A) (x – 81)
C) (x + 9)
x2
– 81?
B) (x – 4)
D) (x – 3)
B) (x – 1) and (x + 4)
D) (x + 2) and (x + 2)
undefined?
D) –5
C) 12
D) 14
55. Which expression is equivalent to 7
A) 16
C) 70
B) 21
D)
B) 5
D) 25
is equivalent to
B) 10
D) 2
B) 3
is equal to
C) 5
D) 5
B) 2
C) 9
D) 4
B) 2
C) 3
D) 4
?
B) 0.6
C) –5
D) –9
64. Kevin and Hunter have $273 in total. If Kevin has $27
more than Hunter has, how much money does Kevin
have?
A) $27
B) $123 C) $150 D) $177
65. What is the solution of the equation 3y – 5y + 10 = 36?
A) –13
54. Jamie is 5 years older than her sister Amy. If the sum of
their ages is 19, how old is Jamie?
B) 7
A) 12
A) 1
B) 24xy 2 C) 12xy 2 D) 2xy
53. For which value of x is the expression
A) 5
can be simplified to
63. What is the value of x in the equation
5(2x – 7) = 15x – 10?
B) 2(x - 50)2
D) (2x + 5)(2x - 5)
C) 5
D) 4
61. Robin spent $17 at an amusement park for admission
and rides. If she paid $5 for admission, and rides cost
$3 each, what is the total number of rides that she went
on?
A) 1
52. The greatest common factor of 12x 2y 3 and 24xy 2 is
B) –1
A) 2
C) 16
62. What is the value of x in the equation
13x – 2(x + 4) = 8x + 1?
51. Factor completely: 2x 2 - 50
A) 1
B) 4
60. The expression
x + (x + 1) = 156
(x + 1) + (x + 2) = 156
(x + 1)(x + 3) = 156
x(x + 1) = 156
A) 6xy
A) 12
A) 2
C) 100
50. When Albert flips open his mathematics textbook, he
notices that the product of the page numbers of the two
facing pages that he sees is 156. Which equation could
be used to find the page numbers that Albert is looking
at?
A) 2(x - 5)2
C) 2(x + 5)(x - 5)
57. If the area of a square garden is 48 square feet, what is
the length, in feet, of one side of the garden?
59. The expression
49. What are the factors of x 2 + 3x – 4?
A)
B)
C)
D)
B)
D)
A) 5
C) 2
48. Which is a factor of x 2 + 5x – 24?
A) (x + 1) and (x – 4)
C) (x + 3) and (x – 4)
A)
C) 0.3333
58. The expression
B) (x – 18)
D) (x + 18)
A) (x + 4)
C) (x + 3)
56. Which number is irrational?
B) 2
C) 4.5
D) 13
66. Three times as many robins as cardinals visited a bird
feeder. If a total of 20 robins and cardinals visited the
feeder, how many were robins?
A) 5
B) 10
C) 15
D) 20
67. If 6x + 2y = 3x + 8y, which of the following must be
true?
A) x = 2y
C) y = x + 2
B) y = 2x
D) y = x – 2
Summer Packet - 12 - 2
68. What is the value of n in the equation 0.6(n + 10) =
3.6?
A) –0.4
B) 5
C) –4
D) 4
69. A girl can ski down a hill five times as fast as she can
climb up the same hill. If she can climb up the hill and
ski down in a total of 9 minutes, how many minutes
does it take her to climb up the hill?
A) 1.8
B) 4.5
C) 7.2
D) 7.5
70. What is the value of p in the equation 8p + 2 = 4p –
10?
A) 1
B) –1
C) 3
D) –3
71. What is the value of n in the equation 3n – 8 = 32 – n?
A) –10
B) –6
C) 6
D) 10
72. If c = 2m + d, then m is equal to
A)
B)
C)
D) d – 2c
73. Which equation represents the line whose slope is 2 and
whose y-intercept is 6?
A) y = 2x +6
C) 2y + 6x = 0
B) y = 6x +2
D) y + 2x = 6
74. If a line is horizontal, its slope is
A) 1
C) undefined
B) 0
D) negative
75. What is the y-intercept of the graph of the line whose
equation is y = – x + 4?
A)
B)
C) 0
D) 4