Download PRECALCULUS SUMMER MATH 2014

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PRECALCULUS SUMMER MATH 2014
This packet is a review of the math concepts for Precalculus. Please do not wait until the last minute to work on this
assignment. Start early enough so that you will have time to review any problems that you may need assistance in
working. An assessment will be given within the first week of school. This will be your first test grade of the school
year 2014-2015 in your math course.
DIRECTIONS: DO NOT TURN THIS IN DURING REGISTRATION.
A. Write neatly and in pencil on your own notebook paper. Keep all problems in the order given. Please write on
the lines, and number all work. DO NOT SHOW YOUR WORK ON THIS HANDOUT.
B. Please be sure it is your own handwriting and work.
C. Simplify all answers and include units where necessary (perimeter, area, etc.).
D. Do not give decimals unless you are directed to do so.
E. Show your work (step-by-step). Circle your final answers.
F. Please bring this assignment with you the first day of class.
Evaluate the expression, given x = -2, y = 3, and a = -4.
1)
A) - 13/5
B) - 1
C)
D) 1
C) {x|x = - 4}
D) {x|x ≠ 5}
Find the domain of the variable x in the expression.
2)
A) {x|x ≥ - 4}
B) {x|x ≠ - 4}
Graph the numbers on the real number line.
3) x ≤ -6
A)
B)
C)
D)
Find the length of the missing side of a right triangle.
4) Given the length of the hypotenuse of a right triangle is 15 cm, and one of the other sides is 4 cm, find the
length of the third side, rounded to two decimal places.
A) 15.52 cm
B) 11 cm
C) 14.45 cm
D) 14.46 cm
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Use the Pythagorean Theorem to find the length of the missing side. Then find the indicated trigonometric function of
the given angle. Give an exact answer with a rational denominator.
5) Find sin θ.
A)
B)
C)
Use a calculator to find the value of the acute angle θ to the nearest degree.
6) cos θ = 0.2286
A) 13°
B) 77°
C) 1°
7) sin θ = 0.8659
A) 1°
B) 76°
C) 31°
D)
D) 97°
D) 60°
Find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round your answer
to the nearest whole number.
8)
A) a = 12 cm
B) a = 10 cm
C) a = 27 cm
D) a = 1 cm
Solve the problem.
9) A radio transmission tower is 210 feet tall. How long should a guy wire be if it is to be attached 8 feet from
the top and is to make an angle of 25° with the ground? Give your answer to the nearest tenth of a foot.
A) 231.7 feet
B) 478.0 feet
C) 496.9 feet
D) 222.9 feet
Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the
given angle. Give exact answers with rational denominators.
10) Find cos A when a =
and c = 14
A)
B)
C)
D)
Simplify the expression. Write the result using positive exponents only.
11)
A)
B)
C)
D)
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Simplify the expression. Write answer with positive exponents only.
12)
A)
B)
Solve the right triangle.
13) Solve the right triangle given that
A) β = 55°
b = 12.85
c = 15.69
and
B) β = 55°
b = 15.69
c = 12.85
C)
D)
C) β = 60°
b = 12.85
c = 15.69
D) β = 60°
b = 15.69
c = 12.85
C) { -11, 22}
D) {-
.
Solve the quadratic equation by completing the square.
14) x2 + 12x + 11 = 0
A) { -11, -1}
B) { 1, 11}
,
Find the area.
15) Find the area of a triangle with height 7 cm and base 8 cm.
A) 56 sq. cm
B) 56 cm
C) 28 cm
D) 28 sq. cm
Evaluate the expression or indicate that the root is not a real number.
16)
A)
B) 8
C) 64
D) 14
Simplify the expression.
17)
A) 18
B) 3‰6
C) 10
D) 6‰3
B) 2 x10
C) -2 x10
D) -2 x27
B) 4
C)
D) 2
}
18)
A) -2x30
Solve the equation.
19)
=2
A)
Solve the problem.
20) For a culture of 60,000 bacteria of a certain strain, the number of bacteria N that will survive x hours is
modeled by the formula N = 6000
A) 36 hr
B) 52 hr
. After how many hours will 48,000 bacteria survive?
C) 92 hr
D) 64 hr
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Use a graphing utility to approximate the real solutions, if any, of the equation rounded to two decimal places.
21) x3 - 6x + 3 = 0
A) no solution
Solve the equation.
22) 7 x - 1 + 7( x + 1) = 6 x + 1
A) { -7/8}
B) {-0.48}
C) {2.67, -0.52, -2.15}
D) {2.15, 0.52, -2.67}
B) { -5/7}
C) { -5/8}
D) { - 1}
B)
C)
D)
B)
C)
D)
B) x = 2, x = 3
C) x = 0, x = - 4, x = 3
D) x = 0, x = 2, x = 3
B) x ≥ 9/31
C) x ≤ -9/31
D) x ≥ -34/31
Solve by factoring.
23) 3k2 - 23k - 8 = 0
A) {-3, 8}
24) 10m2 - 8m = 0
A) {0}
Solve the equation by factoring.
25) x3 + x2 - 12x = 0
A) x = - 4, x = 3
Solve the inequality algebraically.
26) 0.75(3x - 8) ≤ 2.5(4x + 1)
A) x ≤ -31/34
Perform the indicated operations.
27) (5x4 + 8x6 - 6 - 8x5) - (3 + 5x5 + 3x6 + 8x4)
A) 11x6 - 3x5+ 13 x4 - 9
C) 5 x6 - 3x5 + 13x4 - 3
B) 5 x6 - 13 x5 - 3x4 - 9
D) 11 x6 - 3x5 + 13x4 - 3
28) (6x2 - xy – y2) + (x2 + 5xy + 6y2)
A) 6x2 + 5xy + 6y2
B) x2 + 4xy + 5y2
C) 5 x2 - 6xy - 7y2
Multiply the polynomials. Express your answer as a single polynomial in standard form.
29) (13p + 8)(13p - 8)
A) 169p2 - 64
B) p2 - 64
C) 169p2 + 208p - 64
30) (w - 16)2
A) w2 + 256
D) 7 x2 + 6xy + 7y2
D) 169p2 - 208p - 64
B) w + 256
C) 256w2 - 32w + 256
D) w2 - 32w + 256
B) Prime
C) (x + 8)(x - 9)
D) (x + 1)(x - 72)
Factor the polynomial completely.
31) x2 - x - 72
A) (x + 9)(x - 8)
32)
-
- 4x + 3
A) x(64 x2 - 48x - 4x) + 3
C) (4x –
1)2(4x
- 3)
B) 16 x2 (4x - 3) + (-4x + 3)
D) (4x + 1)(4x - 1)(4x - 3)
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33) 9x2 - 39x - 30
A) 3(3x + 2)(x - 5)
B) Prime
C) ( 9x + 6)(x - 5)
D) 3(3x - 2)(x + 5)
If the following defines a one-to-one function, find the inverse.
34) {( 6, -10), ( 9, -9), ( 7, -8), ( 5, -7)}
A) {(-9, -10), ( -10, 7), ( 6, 9), ( -9, -8)}
C) Not a one-to-one function
B) {( -10, 6), ( -9, 9), ( -8, 7), ( -7, 5)}
D) {( -9, -10), ( -7, 7), ( 6, 7), ( -9, -8)}
Decide whether or not the functions are inverses of each other.
35) f(x) = 2x + 6; g(x) = 0.5(x - 6)
A) Yes
B) No
The function f is one-to-one. Find its inverse.
36) f(x) = 4x + 5
A)
B) f(x) =(x – 5)/ 4
(x) = (x – 5)/ 4
C)
(x) =(x + 5)/ 4
D)
(x) = - (x +4)/ 5
Solve the combined inequality. Write your answer in inequality notation.
37) 5 < 4 - 3x ≤ 13
A) -3 ≤ x < -1/3
B) -1/3 < x ≤ -3
C) -1/3 < x < - 3
D) 1/3 < x ≤ 3
Solve the inequality.
38) |5x - 1| ≥ 5
A) -4/5 < x < 6/5
B) x < -4/5 or x > 6/5
C) - 4/5 ≤ x ≤ 6/5
D) x ≤ - 4/5 or x ≥ 6/5
B) -(x3 + 1)/(5x + 5)
C) -(x2
D) (x + 1)/ (-5x – 5)
Multiply or divide as indicated.
39)
∙
A) -1/5
+ 1)/5
State the name of the property illustrated.
40) 1 ∙ (11 ∙ 5) = (11 ∙ 5) ∙ 1
A) Associative property of multiplication
B) Distributive property of multiplication over addition
C) Identity property of multiplication
D) Commutative property of multiplication
Solve the problem.
41) A train ticket in a certain city is $2.50. People who use the train also have the option of purchasing a frequent
rider pass for $17.25 each month. With the pass, each ticket costs only $1.75. Determine the number of times
in a month the train must be used so that the total monthly cost without the pass is the same as the total
monthly cost with the pass.
A) 22 times
B) 25 times
C) 24 times
D) 23 times
Evaluate the algebraic expression for the given value or values of the variable(s).
42) (x + 4y)2;
x = 4 and y = 3
A) 256
B) 64
C) 16
D) 32
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Rationalize the denominator.
43)
A) 5‰11
B)
C) 126
D)
Solve the linear equation.
44) x/4 = x/9 + 8
A) { 36}
B) { 72}
C)
D) { 32}
45) 4x - 2 = 18
A) { 20}
B) { 16}
C) { 5}
D) { 6}
B)
C)
D)
B) 9z - 12
C) 9z + 6
D) 15z + 12
Simplify the exponential expression.
46)
A)
Simplify the algebraic expression.
47) ( 12z + 9) - ( 3z - 3)
A) 9z + 12
Find the product.
48) ( 8x3 + 3)( x2 + 8)
A) 8 x5+ 64 x3 + x2+ 24
C) 8 x5+ 67x3 + 24
B) 8 x6+ 64 x3 + 3x2 + 24
D) 8 x5 + 67x2 + 24
Find the vertex and axis of symmetry of the graph of the function.
49) f(x) = 4x2+ 24x - 1
A) (-3, 107); x = -3
B) (3, 35); x = 3
C) (3, 107); x = 3
D) (-3, -37); x = -3
Solve the problem.
50) The manufacturer of a CD player has found that the revenue R (in dollars) is
when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue,
what is the maximum revenue to the nearest whole dollar?
A) $ 1,428,050
B) $ 714,025
C) $ 357,013
D) $ 178,506
51) The owner of a video store has determined that the cost C, in dollars, of operating the store is approximately
given by
dollar.
A) $ 878
where x is the number of videos rented daily. Find the lowest cost to the nearest
B) $ 622
C) $ 494
D) $ 238
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Use a graphing calculator to plot the data and find the quadratic function of best fit.
52) The number of housing starts in one beachside community remained fairly level until 1992 and then began to
increase. The following data shows the number of housing starts since 1992 (x = 1). Use a graphing calculator
to plot a scatter diagram. What is the quadratic function of best fit?
A) H(x) = -2.679 x2- 26.607x + 168.571
C) H(x) = 2.679 x2+ 26.607x + 168.571
B) H(x) = -2.679 x2+ 26.607x + 168.571
D) H(x) = -2.679 x2+ 26.607x - 168.571
Find the real zeros of the polynomial.
53) f(x) = x3 + 3x2 - 4x - 12
A) -3
B) -2
C) -3, -2, 2
D) -2, 2, 3
B) (88/61) – (8/61)i
C) 8 - 8i
D) 8/11- 8i
B) -4 + 6i
C) 12 - 2i
D) 12 + 2i
C) 2i
D) ±2
Perform the indicated operation. Write result in standard form.
54)
A) 8/61 + (88/61)i
55) (4 - 2i) + (8 + 4i)
A) -12 - 2i
Simplify. Write result in standard form.
56)
A) -i‰2
B) -2i
Use the discriminant to determine whether the quadratic equation has two unequal real solutions, a repeated real
solution, or no real solution without solving the equation.
57) t2 - 12t + 36 = 0
A) two unequal real solutions
B) no real solution
C) a repeated real solution
58) w2 + 2w + 4 = 0
A) two unequal real solutions
B) no real solution
C) a repeated real solution
Solve the quadratic equation by the method of your choice.
59) 3 x2 + 10x + 6 = 0
A)
B)
C)
D)
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60) On the first four exams, your grades are 77, 94, 59, and 78. You are hoping to earn a C in the course. This will
occur if the average of your five exam grades is greater than or equal to 70 and less than 80. What range of
grades on the fifth exam will result in earning a C?
A) [ 32, 82)
B) [ 42, 92)
C) ( 42, 92]
D) ( 32, 82]
Use the product rule to simplify the expression.
61)
A) 14
B) 4‰7
C) 2‰7
D)
Solve the absolute value inequality. Other than ∅, use interval notation to express the solution set and graph the
solution set on a number line.
62) |3(x + 1) +6| ≤ 12
A) ( -7, 1)
B) [ -5, 3]
C) [ -7, 1]
D) ( -5, 3)
Solve the problem.
63) Express the perimeter of the trapezoid as a single rational expression.
A)
B)
C) x + 12
D)
64) The average height of a boy in the United States, from birth through 60 months, can be modeled by
where y is the average height, in inches, of boys who are x months of age. What would be
the expected difference in height between a child 49 months of age and a child 16 months of age?
A) 48.9 inches
B) 20.3 inches
C) 8.7 inches
D) 10.7 inches
Solve the absolute value equation or indicate that the equation has no solution.
65)
= 5
A) { -3}
B) { -7, 3}
C) ∅
D) { 7, 3}
Add or subtract as indicated.
66)
_
B)
A)
C)
D)
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Simplify the exponential expression.
67)
A) 0
B)
C) 1
D)
Solve the quadratic equation by the method of your choice.
68) x2 + 6x = 5
A) {-1 – ‰14, -1 + ‰14}
C) {-3 - ‰14, -3 + ‰14}
B) {-3 - 2‰14, -3 + 2‰14}
D) {3 + ‰14}
Solve the formula for the specified variable.
69) I = Prt
for t
A) t =
B) t = P - Ir
C) t =
D) t =
B) { -11, -3}
C) {-7, 7}
D) { 53}
A) -
B)
C)
D) -
A)
B)
C)
D)
Solve the quadratic equation by the square root property.
70)
= 49
A) { -3, 11}
Simplify the exponential expression.
71)
∙
72)
Write an equation in point-slope form of the line satisfying the given conditions.
73) The line through the point ( -4, 5) and having the slope
A) y - 5 = (x + 4)
B) x + 5 = (y - 4)
C) y + 4 = (x - 5)
D) y + 5 = (x - 4)
Write the equation of the line satisfying the given conditions.
74) The horizontal line through the point (- , 2)
A) y = 2
B) y = -2
Write an equation for the line.
75) Through ( -4, -6), parallel to -8x + 9y = -4
A) -8x - 9y = -22
B) -4x + 9y = -4
C) y = 0
D) y = -
C) -8x + 9y = -22
D) 9x - 8y = -6
76) With y-intercept -6 and perpendicular to -2x - 5y = -1
A) -5x + 2y = 30
B) -2x - 5y = 30
C) -2x - 5y = 12
Decide whether the relation defines a function.
77) {( -7, 6), ( -7, -5), ( 1, 9), ( 3, -6), ( 8, 2)}
A) Function
B) Not a function
D) -5x + 2y = -12
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Determine whether the equation is a function.
78) y =
A) Yes
B) No
Evaluate the function.
79) Find f(k - 1) when f(x) = 3x2 + 3x + 3.
A) -3k2 + 3k + 3
B) 3k2 + 12k + 9
Find the value of the function.
80) Find the value of g(x) = -4
A) 73
+ 3x + 15, when x = -2.
B) -7
C) 3k2 - 3k + 3
D) 3k2 - 3k + 9
C) 7
D) -39
C) (-∞, ∞)
D) x ≤ 8
Give the domain of the function.
81) f(x) =
A) x >
B) x ≠ 8
Determine whether or not the graph represents a function.
82)
A) Not a function
83) The graph of y =
A) y =
B) Function
is shifted to the right by 3 units. Write the resulting equation.
B) y =
C) y = + 3
84) The graph of which function
=
A)
Find the requested function.
85) f(x) = 7x - 8, g(x) = 4x + 6
Find fg.
A) 28x2 - 48
86) Let f(x) = 16 - ,
A) 4 + x
below is the reflection of the graph of
=
B)
C)
= -(x/1)
B) 11x2 + 10x - 2
and g(x) = 4 - x. Find (f + g)(x).
B)
- 16x + 64
=
across the x-axis?
D)
= -(1/x)
C) 28x2 + 10x - 48
C)
D) y = 3
+ x + 12
D) 28x2 - 26x - 48
D)
- x + 20
Find the indicated composite for the pair of functions.
87) (g ∘ f)(x): f(x) = 4x2 + 5x + 3, g(x) = 5x - 5
A) 20x2 + 25x + 10
B) 4x2 + 25x + 10
Write the standard form of the equation for the circle.
88) Center at ( 1, -10), radius = 10
A) (x - 10)2 + (y + 1)2 = 10
C) (x - 1)2 + (y + 10)2 = 100
C) 20x2 + 25x + 20
B) (x + 1)2 + (y - 10)2 = 100
D) (x + 10)2 + (y - 1)2 = 10
D) 4x2 + 5x - 2
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Find the length of the missing side. Leave your answer in simplest radical form.
89.
18 m
11 m
Not drawn to scale
A.
B.
29 m
90.
445 m
C.
7m
D.
203 m
Find the length of the hypotenuse.
45°
3 2
A. 12
B. 6
91.
C. 5
D. 18
Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
16
45°
Not drawn to scale
A. 128
B. 8 2
C. 16
D. 2 2
92.
Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the
nearest tenth.
y
7
45°
x
Not drawn to scale
A. x = 7, y = 9.9
B. x = 9.9, y = 7
C. x = 4.9, y = 6.1
D. x = 6.1, y = 4.9
Page 12 of 12
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
93.
6
x
60°
12
Not drawn to scale
A. 2
B.
C. 1
2
D.
94.
x
y
30°
20
Not drawn to scale
A. x =
,y=
B. x = 10, y =
C. x =
, y = 10
D. x = 30, y =
95.
y
17
30°
x
Not drawn to scale
A. x = 17, y =
B. x = 34, y =
96.
Find the missing value to the nearest hundredth.
A. 44.67
97.
B. 89.67
B. 30
B. 85.41
tan
C. 4.59
= 86
D. 51.67
cos
C. 26.57
Find the missing value to the nearest hundredth.
A. 64.71
, y = 17
, y = 34
C. 89.33
Find the missing value to the nearest hundredth.
A. 39
98.
C. x =
D. x =
7
= 14
D. 60
sin
2
= 25
D. 4.57