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Algebra 2 with Trigonometry
Sample Test #4
Answer all 39 questions in this examination. Write your answers to the Part I multiple-choice questions
on the separate answer sheet. No partial credit will be allowed on the multiple-choice section.
For Parts II, III, and IV, clearly indicate the necessary steps, including appropriate formula substitutions,
diagrams, graphs, charts, etc. For all questions in these parts, a correct numerical answer with no work shown
will receive only 1 credit.
A reference sheet that you may need to answer some questions in this examination is included.
Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this
examination as scrap paper. Scrap graph paper is provided at the end of this examination for any question for
which graphing may be helpful but is not required. Any work done on this sheet of scrap graph paper will not be
scored. Write all your work in pen, except graphs and drawings, which should be done in pencil.
Note: A graphing calculator and a straightedge (ruler) must be available for you to use while taking this
examination.
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
Part I
Answer all 27 questions in this part. Each correct answer will receive 2 credits. No partial credit will
be allowed. For each question, write on the separate answer sheet the numeral preceding the word or
expression that best completes the statement or answers the question. [54]
1. Which of the following is not a solution to the equation 4sin 2 x 1 ?
(1) 30
(3) 150
(2) 210
(4) 120
4
2. Which of the following represents the middle term of the expansion of x 4 ?
(1) 96x 2
(3) 16x 4
(2) 96x 2
(4) 16x 4
3. Which of the following linear equations best fits the data set shown in the table below?
(1) y
2.7 x 7.1
(3) y
4.5x 1.2
(2) y
3.2 x 9.4
(4) y 1.8x 10.5
4. All values of x that solve the inequality x 2
x
3
1
5
8
10
y
20
3
4
15
25
5 are given by the set
(1) x | 3 x 3
(3) x | 7
x 3
(2) x | 3 x 7
(4) x | x
7 or x 3
5. When the complex number 4 3i is divided by its conjugate, the result can be expressed as
(3) 1 i
(1) 1
(2)
7
25
24
i
25
(4) 1
24
i
7
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
6. For what value of k will the equation log2 4k
(1) 12
(3) 19
(2) 9
(4) 24
2
(2) 10
2
5 be satisfied?
x 2 10 x 23 are given in exact form by
7. The x-intercepts of the parabola y
(1) 5
log2 3
(3) 4
3
(4) 7
3
8. Which of the following gives the common ratio of the geometric sequence starting with 9, 6, 4, ... ?
(1) r
2
(2) r
1
3
2
3
(3) r
(4) r
2
3
9. After a reflection in the x-axis, the parabola y
(1) y
x 2 10
(3) y 10 x 2
(2) y
x 2 10 x
(4) y 10
x 1
x 2 10 would have the equation
2
10. Accurate to the nearest degree, the third quadrant solution of 5cos x 2 0 is
(1) 224
(3) 114
(2) 66
(4) 246
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
11. On a tropical island, it reliably rains on 60% of all days. Which of the following gives the probability, to the
nearest percent, that it will rain exactly 5 out of 7 days when tourists visit it?
(1) 32%
(3) 71%
(2) 43%
(4) 26%
12. A sequence is defined recursively by the formula bk
5bk
1
20 , where b1
2 . Based on this definition,
4
bk =?
the summation
k 1
(1) 370
(3) 220
(2) 250
(4) 448
13. Which of the following represents the solution set of the inequality
(1)
4, 1
(2)
4, 1
2
2
(3)
, 4
1 ,
2
(4)
, 4
1 ,
2
14. An angle whose radian measure is
2x 1
x 4
0?
8
is drawn in standard position. In what quadrant does its terminal ray
3
lie?
(1) I
(3) III
(2) II
(4) IV
15. Which of the following functions, when mapping the real numbers to the real numbers, would be considered
one-to-one?
(1) y
x2
(3) y
x
(2) y
sin x
(4) y
x
2
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
16. Which of the following is not a factor of x 4 13x 2
(1) x 2
(3) x 3
(2) x 3
(4) x 6
36 ?
17. Of Mr. Weiler’s 16 math team members, he must pick five of them to be on his A-Team, where the order in
which he selects the five is not important. Which of the following gives the number of different five
member teams Mr. Weiler can form?
(1) 5!
(3) 16!
(2)
(4)
16
C5
16
P5
18. If a quadratic has two roots that are rational and unequal, then its discriminant could be
(1) 16
(3) 10
(2) 12
(4) 0
19. If f x
5x 10 and g x
2x 1 then f g
(1) 59
(3) 55
(2) 35
(4) 75
20. For a given angle
(1)
(2)
2
3
1
2
it is known that cos
(3)
(4)
4
?
1
. Which of the following could be the value of tan ?
3
2
2
2
2
3
21. If an angle drawn in standard position intersects the unit circle at
represents the sine of this angle?
(1) 0.96
(3) 0.28
(2) 1.25
(4) 0.68
0.28, 0.96 then which of the following
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
22. A triangle whose area is 15 has two sides of length 6 and 10. If the angle created by these two sides is
obtuse, then its measure must be
(1) 120
(3) 30
(2) 135
(4) 150
23. Which of the following represents the value of ln
b
a
(1)
(2)
(3)
b
a
(1)
a
2ab
(2)
a
b
b
a
a b
, for a
a
b
b
eb ?
a
b
(4) e
24. The expression
a
b , is the same as
(3)
a
b
(4)
a
3 b
25. Which of the following correlation coefficients shows the best linear fit between two variables?
(1) r
0.85
(3) r
(2) r
0.55
(4) r
0
0.98
26. Which of the following points falls in the solution set to y
(1)
x 2 12 x ?
(3) 2, 26
1,13
(2) 0, 0
(4) 7, 30
27. Which of the following equations represents the inverse of y
(1) y
log5 x 1
(2) y
1
(3) y
5x 1
(4) y
log 1 x 1
log5 x 1 ?
x 1
5
5
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
Part II
Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the
necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all
questions in this part, a correct numerical answer with no work shown will receive only 1 credit. [16]
28. The following mapping diagram shows how the set A is mapped to set B using the function f x
Explain why this mapping is one-to-one but not onto.
2x .
1
1
2
2
3
4
Set A
Set B
29. Mr. Richmond’s traffic engineering class is trying to determine people’s attitudes towards their evening
commute. Students in his class decide to stop drivers on their way home to conduct this survey. Why
would this survey method introduce bias into their results?
30. Solve the equation below for all values of x. State your answers in simplest a bi form.
x 2 10 x 29 0
31. Realtors in a Florida community have found that the average price of a four bedroom house varies inversely
with the distance that the house lies away from the beach. If, on average, a four bedroom house located 2
miles from the beach costs $750,000, what is the average cost of a house that lies 5 miles from the beach?
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
32. A radar is tracking the location of a plane. Initially the plane is at a distance of 6.5 miles from the radar.
After the radar rotates through an angle of 115 , the plane is now at a distance of 3.2 miles from the radar.
What straight line distance, to the nearest tenth of a mile, has the plane flown between these two readings?
3.2 miles
6.5 miles
115
33. If a geometric sequence is defined by a first term of
first ten terms of this sequence.
2 then find the sum of the
6 and a common ratio of
34. A particularly virulent flu strain is spreading around a town such that the number of people infected doubles
every three days. When the health department first starts to track the disease, only five people were
d
infected. If the number of people infected, I, is given by the equation I 5 2 3 , where d is the number of
days since the first five were detected, then determine the number of days until 2560 people are infected.
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
35. A quadratic equation has roots that sum to 8 and have a product of 3 . Write a quadratic equation that fits
this description if its leading coefficient is equal to 2.
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the
necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all
questions in this part, a correct numerical answer with no work shown will receive only 1 credit. [12]
36. At a local PTA meeting, a sample of parents were surveyed to determine how many children they currently
had attending school. Their results are shown in the frequency table below:
Number
Number
of
of
Determine the mean, median, and standard deviation for this sample. Round
Children
Families
any non-integer answers to the nearest tenth.
Determine how many of the 55 families surveyed have a number of children
that was within one standard deviation of the mean.
37. Find all solutions, on the interval 0
x 360 , that solve 2sin 2 x sin x 1 0 .
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009
1
16
2
24
3
8
4
3
5
2
7
2
38. The following graph shows the function y
g x
h x
2 . Sketch a graph of y
h x .
A new function is defined by the formula
g x on the same axes and explain the transformations that have
occurred to the graph of h x to produce the graph of g x . Specify both the type and the order.
y
x
Part IV
Answer the question from this part. The correct answer will receive 6 credits. Clearly indicate the
necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct
numerical answer with no work shown will receive only 1 credit. [6]
39. Simplify the following expression.
x2
3x 2
4
9x2 1
7 x 2 x2 5x 6
2x x2
4 x 2 24 x
ALGEBRA 2 WITH TRIGONOMETRY, SAMPLE EXAMS
eMATHINSTRUCTION, RED HOOK, NY 12571, © 2009