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12/30/2015
Semester A Exam
Semester A Exam
Luigi Gjurashaj is taking this assessment.
1.
Suppose you went to a carnival. The price to get in was $8, and you
paid $0.50 to get on each ride. If you went to the carnival and rode 9
rides, how much did you spend?
(1 point)
$4.50
$17.50
$12.50
$13
2. Name the property of real numbers illustrated by the equation.
–3(x + 4) = –3x – 12
(1 point)
Distributive Property
Associative Property of Addition
Associative Property of Multiplication
Commutative Property of Addition
3. Solve the compound inequality. (1 point)
3x + 12 ≥ –9 and 9x – 3 ≤ 33
x ≥ –7 and x ≤ –4
x ≥ 7 and x ≤ 4
x ≥ 1 and x ≤ 4
x ≥ –7 and x ≤ 4
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4. Solve the absolute value equation. (1 point)
│4x + 3│= 3
x = 0 or x =
x = 0 or x =
x = 1 or x =
x = 1 or x =
5.
Given no other restrictions, what are the domain and range of the
following function?
f(x) = x2 – 2x + 1
(1 point)
D = all real numbers
R = all real numbers
D = all real numbers
R = {y | y ≥ –1}
D = all real numbers
R = {y | y ≥ 0}
D = {x | x ≥ 0}
R = {y | y ≤ 1}
6.
Write the equation in slope­intercept form. What are the slope and y­
intercept?
–12x + 11y = –8
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(1 point)
y=–
x+
slope:
; y­intercept:
y=–
x–
slope:
y=
; y­intercept:
x–
slope:
y=
; y­intercept: –
x+
slope:
; y­intercept:
7.
What is an equation of the line, in point­slope form, that passes through
the given point and has the given slope?
point: (11, 3); slope:
(1 point)
y–3=
(x + 11)
y–3=
(x – 11)
y–3=–
(x – 11)
y – 11 =
(x – 3)
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8.
Compare the function with the parent function. Without graphing, what
are the vertex, axis of symmetry, and transformations of the given
function?
y = │8x – 2│ – 7
(1 point)
(– , –7); x = – ; translated to the right
unit and up 7
units
(
, 7); x =
; translated to the right
unit and up 7 units
(– , 7); x = – ; translated to the left
unit and up 7 units
(
unit and down 7
, –7); x =
; translated to the right
units
9. Which graph best represents the following inequality? (1 point)
y ≥ 3x – 5?
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10.
Which graph best represents the feasibility region for the system
above?
(1 point)
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11.
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11.
Semester A Exam
Last night, Julie’s pet hamster Zoe kept Julie awake for at least an hour
running on her exercise wheel and scratching at the corner of her cage.
Zoe ran on the wheel at least twice as long as she scratched at the
corners of her cage, and she spent more than
hour running on her
wheel. Which system of inequalities represents the time Zoe kept Julie
awake last night if x is the number of hours Zoe spent running on her
wheel and y is the number of hours spent scratching her cage?
(1 point)
12. Which matrix represents the system of equations below? (1 point)
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13. Which graph represents y = 3(x –3)2 + 3? (1 point)
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14.
Every year in Delaware there is a contest where people create cannons
and catapults designed to launch pumpkins as far in the air as possible.
The equation y = 12 + 105x – 16×2 can be used to represent the height,
y, of a launched pumpkin, where x is the time in seconds that the
pumpkin has been in the air. What is the maximum height that the
pumpkin reaches? How many seconds have passed when the pumpkin
hits the ground? (Hint: If the pumpkin hits the ground, its height is 0
feet.)
(1 point)
The pumpkin’s maximum height is 184.27 feet and it hits
the ground after 3.28 seconds.
The pumpkin’s maximum height is 3.28 feet and it hits the
ground after 6.67 seconds.
The pumpkin’s maximum height is 184.27 feet and it hits
the ground after 6.67 seconds.
The pumpkin’s maximum height is 3.28 feet and it hits the
ground after 184.27 seconds.
15.
What is the equation, in standard form, of a parabola that models the
values in the table?
x
–2
0
4
f(x)
4
–6
70
(1 point)
y = 3x² + 4x – 6
y = 4x² + 3x – 6
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y = 6x² + 3x – 4
y = –4x² – 3x + 6
16. Use the quadratic formula to solve the equation. (1 point)
–x2 + 7x = 5
17. Simplify the expression. (1 point)
(–6i)(–4i)
–24
24i
–24i
24
18. What is the solution set to the following system? (1 point)
(0, –3), (3, 0)
(0, 3), (–3, 0)
(0, 3), (3, 0)
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(0, –3), (­3, 0)
19. Classify 4×5 + 2×4 – 5×3 + 12 by number of terms. (1 point)
binomial
trinomial
polynomial of 5 terms
polynomial of 4 terms
20. What are the zeroes of the function? (1 point)
y = (x – 2)(x – 3)(x + 3)
–2, 3, –3
2, 3, –3
2, –3, –3
–2, 3, 3
21.
Which of the functions graphed below could be defined by a cubic
equation?
(1 point)
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22. Find the rational roots of x4 + 5×3 + 7×2 – 3x – 10 = 0. (1 point)
–2, 1
2, 1
–2, –1
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2, –1
23. Find all the zeroes of the equation. (1 point)
3×2 – 4 = –x4
1, 2i
–1, –2i
1, –1, 2i, –2i, 0
1, –1, 2i, –2i
24. Use the binomial theorem to expand the binomial. (1 point)
(s + 3v)5
s5 + 45s4v + 270s3v2 + 810s2v3 + 1215sv4 + 729v5
s5 + 15s4v + 90s3v2 + 270s2v3 + 405sv4 + 243v5
s5 + 15s4v + 90s3 + 270s2 + 405s + 243
s5 – 5s4v + 10s3v2 – 10s2v3 + 5sv4 – v5
25.
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x
y
1
15
2
19
3
16
4
10
5
5
6
1
7
4
Semester A Exam
Which equation best represents the regression line for the data given in
the table above?
(1 point)
y = –3x + 22
y = –3x – 22
y = 3x + 22
y = 3x – 22
26.
An initial population of 293 quail increases at an annual rate of 6%.
Write an exponential function to model the quail population. What will
the approximate population be after 4 years?
(1 point)
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f(x) = (293 • 1.06)x; 930
f(x) = 293(0.06)x; 379
f(x) = 293(1.06)x; 370
f(x) = 293(6)x; 190
27.
The half­life of a certain radioactive material is 36 days. An initial
amount of the material has a mass of 487 kg. Write an exponential
function that models the decay of this material. Find how much
radioactive material remains after 5 days. Round your answer to the
nearest thousandth.
(1 point)
; 0.318 kg
; 0.847 kg
; 442.302 kg
; 0 kg
28. Evaluate the logarithm. (1 point)
log41024
5
–5
4
6
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29. Simplify the following expression completely. Show your work.
–3(–y – 1) + 5y
(1 point)
8y + 3
8y – 3
2y + 3
2y – 3
30. Estimate the value of the logarithm to the nearest tenth. (1 point)
log7 55
0.5
2.1
–2.6
6.0
31.
Solve ln 3 + ln (4x) = 4. Round your answer to the nearest hundredth.
(1 point)
0.01
0.91
4.55
12.90
32.
Solve the equation or formula for the indicated variable.
(2 points)
S = 6r³t, for t
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33.
Semester A Exam
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The function f(x) = x². The graph of g(x) is f(x) translated to the right 3 units and
What is the function rule for g(x)?
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34.
Semester A Exam
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Solve the system by substitution.
(2 points)
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35.
Semester A Exam
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Suppose x varies directly with y.
a. Use the fact that x = 39 when y = –117 to find the constant of variation and
equation of variation.
b. Find the value of x when y = –132.
(2 points)
36.
A factory can produce two products, x and y, with a profit approximated by
900. The production of y must exceed the production of x by at least 100 units. M
production levels are limited by the formula x + 2y ≤ 1400.
a. Identify the vertices of the feasible region.
b. What production levels yield the maximum profit, and what is the maximu
(2 points)
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37.
Semester A Exam
Explain how to solve the following system of equations. What is the solution to t
2x + 2y + z = –5
3x + 4y + 2z = 0
x + 3y + 2z = 1
(2 points)
38.
Factor the expression.
(2 points)
3×2 + 14x + 8
39.
What are the solutions of the quadratic equation?
(2 points)
4×2 – 9x – 9 = 0
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40.
41.
Semester A Exam
What is the result when 2×3 – 9×2 + 11x – 6 is divided by x – 3?
(2 points)
Explain the steps you would use to solve the equation. Find the solution.
82x = 4096
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© 2015 Connections Education LLC.
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