Download PRE-CALCULUS SUMMER PACKET IINTRODUCTION 12

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PRE-CALCULUS SUMMER PACKET IINTRODUCTION
12 - 3
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 - 3
1. The width, w, of a rectangular rug is 4 less than its
length, . Which expression represents the area of the
rug?
A)
C)
B)
D)
2. If a machine that prints designs on T-shirts prints 500
shirts in 3 hours, how many hours will it take to print
designs on 1,800 shirts?
A) 6
B) 9.8
C) 10.8
D) 12
3. The larger of two consecutive integers is represented by
x + 4. Which expression represents the smaller integer?
A) x + 2 B) x + 3 C) x + 5 D) x + 6
4. If x represents a given number, the expression "5 less
than twice the given number" is written as
A)
C)
B)
D)
5. The sum of Scott's age and Greg's age is 33 years. If
Greg's age is represented by g, Scott's age is represented
by
A) 33 – g B) g – 33 C) g + 33 D) 33g
A)
B)
C)
D)
(–1.8 + 2) –0.4
–16 –0.4
–5 0.2
6 –2
16. What is the product of –2x 2y 3 and 5x 3y?
17. What is the value of xy 2 if x = –3 and y = –7?
18. Find the product of –6a 7, –7a 8, and –8a 9.
19. Find the product of – xy 2 and –12xy 7.
20. If -18x 4y is divided by -2xy, what is the quotient?
21. What is the product of x 3y and xy 2?
22. The distance from the planet Pluto to the sun is
approxiamately 3,700,000,000 miles. A scientist will
write the distance as 3.7 x 10 n. What is the value of n?
23. If 0.000043 is expressed as 4.3 × 10n , what is the value
of n?
24. 0.00074 meter is the width of an unusually thin blade of
grass. When expressed in the form 7.4 × 10n, what is
the value of n?
6. Find the value of 3x 2y when x = 2 and y = -1
7. If x = 4 and y = -1, find the value of 3x 2y.
8. A football team assigns jersey numbers to its players by
using the formula of 7y - 3x where x and y are randomly
chosen. What number will a player get if x = -2 and y =
4?
25. Subtract 2x 2 – 5x + 8 from 6x 2 + 3x – 2 and express
the answer as a trinomial.
26. What is the sum of x 2 – 3x + 7 and 3x 2 + 5x – 9?
A) 4x 2 – 8x + 2
C) 4x 2 – 2x – 2
9. Find the value of a 2 - b if a = 3 and b = -5.
10. Find the numerical value of 4xy 2 when x =
15. Find the quotient.
and y = -3
11. Given the formula t = rv 2, find t if r = 3 and v = –2.
12. The expression 3x 2 + y represents the number of babies
born on an exotic tropical island each month. How
many babies were born in June if x =1 and y = –3.
13. Write an irrational number and explain why it is
irrational.
14. Seth is thinking of a number between 20 and 30. The
number is prime and not more than 2 away from a
perfect square. What is the number?
B) 4x 2 + 2x + 16
D) 4x 2 + 2x – 2
27. 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
28. The expression 2x 2 – x 2 is equivalent to
A) x 0
B) 2
C) x 2
D) –2x 4
29. When 3a 2 – 7a + 6 is subtracted from 4a2 – 3a + 4, the
result is
A) a 2 + 4a – 2
C) –a 2 – 4a + 2
B) a 2 – 10a – 2
D) 7a 2 – 10a + 10
Summer Packet - 12 - 3
30. The expression (x 2 – 5x – 2) – (–6x 2 – 7x – 3) is
equivalent to
7x 2
7x 2
A)
– 12x – 5
2
C) 7x + 2x + 1
B)
– 2x + 1
2
D) 7x + 2x – 5
31. 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
32. Express (x – 7)(x + 3) as a trinomial.
33. Express (2x – 4)(x + 7) as a trinomial.
34. Find the product of
4x 2
– 2 and itself.
35. Find the product of 3 + 6a and 5 – 7a.
36. Find the product of 7x – 6 and 11x + 9.
37. Express the product (x + 5)(x - 3) as a trinomial.
38. 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
39. 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
40. When 3x 2 – 6x is divided by 3x, the result is
A) –2x
B) 2x
C) x + 2 D) x – 2
41. 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)
42. Written in factored form, the binomial 4x 2 – 9 is
equivalent to
A) (2x – 3)(2x – 3)
C) (4x – 9)(x + 1)
B) (2x – 3)(2x + 3)
D) (4x + 1)(x – 9)
43. One of the factors of 4x 2 – 9 is
A) (x + 3)
C) (4x – 3)
B) (2x + 3)
D) (x – 3)
44. Which expression is a factor of x 2 – 81?
A) (x – 81)
C) (x + 9)
B) (x – 18)
D) (x + 18)
45. Which is a factor of x 2 + 5x – 24?
A) (x + 4)
C) (x + 3)
B) (x – 4)
D) (x – 3)
46. What are the factors of x 2 + 3x – 4?
A) (x + 1) and (x – 4)
C) (x + 3) and (x – 4)
B) (x – 1) and (x + 4)
D) (x + 2) and (x + 2)
47. Which expression is a factor of x 2 + 2x – 15?
A) (x + 5)
C) (x – 5)
B) (x + 3)
D) (x – 15)
48. Which expression is a factor of x 2 + 11x + 10?
A) (x + 5)
C) (x – 5)
B) (x + 10)
D) (x – 10)
49. Which expression is a factor of x 2 – 7x + 10?
A) (x + 5)
C) (x + 2)
B) (x + 10)
D) (x – 2)
50. Which expression is a factor of 3x 2 + 2x – 8?
A) (3x – 4)
C) (3x + 4)
B) (x – 2)
D) (3x + 2)
51. 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)
B)
C)
D)
x + (x + 1) = 156
(x + 1) + (x + 2) = 156
(x + 1)(x + 3) = 156
x(x + 1) = 156
52. Factor completely: 2x 2 - 50
A) 2(x - 5)2
C) 2(x + 5)(x - 5)
B) 2(x - 50)2
D) (2x + 5)(2x - 5)
53. Which expression is the complete factorization of 32 –
18y 2?
A) 2(16 – 9y 2)
C) 2(3y + 4)(3y – 4)
B) 2(4 – 3y) 2
D) 2(4 – 3y)(4 + 3y)
54. Which expression is a factored form of
2x 2 - 2x - 12?
A) 2(x + 2)(x - 3)
C) 2(x + 3)(x - 2)
B) 2(x + 6)(x - 1)
D) 2(x + 1)(x - 6)
Summer Packet - 12 - 3
55. The greatest common factor of 4a 2b and 6ab 3 is
B) 2ab 2
D) 24a 3b 4
A) 2ab
C) 12ab
56. What is the least common denominator of ,
?
A) 9x
B) 12x
, and
57. Which number is irrational?
A)
58. If x <
A) 0
B) .0
C)
D)
, x could be
B) 2
C)
59. The expression
D) 4
is equivalent to
A) 3
C) 8
B) 2
D) 4
60. If the area of a square garden is 48 square feet, what is
the length, in feet, of one side of the garden?
A) 12
B) 4
C) 16
61. The expression
can be simplified to
A) 5
C) 2
is equivalent to
A) 2
C) 100
is equal to
B) 3
C) 5
64. The expression
B) 5
D) 10
65. The sum of
and
B) 7
67. What is the sum
A)
C) 9
and
?
C) 9
+
D) 29
?
B) 20
D)
70. The sum of
C) 6
and
A)
C) 3
D) 18
is
B) 9
D) 6
71. What is the value of m in the equation
2m – (m + 1) = 0?
A) 1
B) –1
C) 1
3
D) 0
72. What is the value of x in the equation
13x – 2(x + 4) = 8x + 1?
A) 1
A) 1
A) $27
B) 2
C) 3
D) 4
B) 0.6
C) –5
D) –9
B) $123 C) $150 D) $177
75. What is the solution of the equation 3y – 5y + 10 = 36?
A) –13
A) –0.4
B) 9
D) 4
66. What is the sum of
B)
is equivalent to
B) 2
C) 4.5
D) 13
76. What is the value of n in the equation 0.6(n + 10) =
3.6?
is
A)
C) 3
A)
D) 5
is equivalent to
A) 50
C) 10
+
74. Kevin and Hunter have $273 in total. If Kevin has $27
more than Hunter has, how much money does Kevin
have?
B) 10
D) 2
63. The expression
B) 11
D) 8
69. The expression
A) 9
?
73. What is the value of x in the equation
5(2x – 7) = 15x – 10?
B) 5
D) 25
62. The expression
A) 2
D) 4
and 3
A) 9
C) 60
D) 14x 2
C) 14x
68. What is the sum of 5
B) 5
C) –4
D) 4
77. 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
78. What is the value of x in the equation
2(x – 3) + 1 = 19?
A) 6
B) 9
C) 10.5
D) 12
Summer Packet - 12 - 3
79. If 3(x + 2) – 2(x + 1) = 8, the value of x is
A) 1
B)
C) 5
D) 4
80. What is the value of x in the equation
6(x – 2) = 36 – 10x?
A) –6
B) 1.5
C) 3
D) 6
81. If 12x = 4(x + 3) then x equals
A) 5
B)
82. Solve for s:
A) 1
C)
D) 1.5
7s + 4(3 - s) = 18
B) 2
C) -2
D) 3
83. What is the value of p in the equation 8p + 2 = 4p –
10?
A) 1
B) –1
C) 3
D) –3
84. What is the value of n in the equation 3n – 8 = 32 – n?
A) –10
B) –6
C) 6
D) 10
85. If c = 2m + d, then m is equal to
A)
B)
C)
D) d – 2c
86. If the temperature in Buffalo is 23° Fahrenheit, what is
the temperature in degrees Celsius? [Use the formula
C = (F – 32).]
A) –5
B) 5
C) –45
D) 45
87. What are the factors of x 2 – 5x + 6?
A) (x + 2) and (x + 3)
C) (x + 6) and (x – 1)
B) (x – 2) and (x – 3)
D) (x – 6) and (x + 1)