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Semester A Exam
18/12/15 16:33
Semester A Exam
Frank Gjurashaj is taking this assessment.
1. Suppose you went to a carnival. The price to get in was $4, and you paid $0.50 to get on each
ride. If you went to the carnival and rode 7 rides, how much did you spend?
(1 point)
$11.50
$7.50
$9
$3.50
2. Name the property of real numbers illustrated by the equation. (1 point)
–2(x + 4) = –2x – 8
Associative Property of Multiplication
Commutative Property of Addition
Distributive Property
Associative Property of Addition
3. Solve the compound inequality. (1 point)
5x + 11 ≥ –9 and 10x – 3 ≤ 27
x ≥ –4 and x ≤ 3
x ≥ –4 and x ≤ 2
x≥
or x ≤ 2
x≥
or x ≤ 3
4. Solve the absolute value equation. (1 point)
│3x + 1│ = 1
x = 1 or x =
x=
or x = 0
x = 1 or x = –2
x = 1 or x = 0
5. Given no other restrictions, what are the domain and range of the following function? (1 point)
f(x) = x2 – 2x + 3
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D = {x| x ≥ 2}
R = all real numbers
D = all real numbers
R = {y| y ≥ 2}
D= all real numbers
R = {y| y ≥ 3}
D = all real numbers
R = all real numbers
6. Write the equation in slope-intercept form. What are the slope and y-intercept? (1 point)
–12x + 11y = –8
y=–
slope:
y=–
slope:
y=
slope:
y=
slope:
x+
; y-intercept:
x–
; y-intercept:
x–
; y-intercept: –
x+
; y-intercept:
7. What is an equation of the line, in point-slope form, that passes through the given point and
has the given slope?
(1 point)
point: (7, 3); slope:
y–3=
(x – 7)
y–7=
(x – 3)
y–3=
(x + 7)
y – 3 = – (x – 7)
8. Compare the function with the parent function. Without graphing, what are the vertex, axis of
(1 point)
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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?
(1 point)
y = │8x – 2│ – 7
(–
(
(–
(
, –7); x = – ; translated to the right
, 7); x =
; translated to the right
, 7); x = – ; translated to the left
, –7); x =
; translated to the right
unit and up 7 units
unit and up 7 units
unit and up 7 units
unit and down 7 units
9. Which graph best represents the following inequality? (1 point)
y ≥ 3x – 5?
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10.
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(1 point)
Which graph best represents the feasibility region for the system above?
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11. Dolora spends at least 4 hours per week gardening. She spends more time on routine
(1 point)
maintenance such as weeding, pruning, and watering than on harvesting vegetables or flowers.
She spends at least 1 hour per week harvesting. Which system of inequalities represents
Dolora’s weekly gardening time if x represents the number of weekly hours spent on routine
garden maintenance, and y represents the number of weekly hours spent on harvesting?
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12. Which matrix represents the system of equations below? (1 point)
13. Which graph represents y = 2(x + 2)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 = 15 + 110x – 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 204.06 feet and it hits the ground after 7.01 seconds.
The pumpkin’s maximum height is 3.44 feet and it hits the ground after 7.01 seconds.
The pumpkin’s maximum height is 204.06 feet and it hits the ground after 3.44 seconds.
The pumpkin’s maximum height is 3.44 feet and it hits the ground after 204.06 seconds.
15. What is the equation, in standard form, of a parabola that models the values in the table?
x
–1
0
2
f(x)
12
5
15
(1 point)
y = –4×2 + 3x + 5
y = –4×2 – 3x + 5
y = 3×2 – 4x + 5
y = 4×2 – 3x + 5
16. Use the quadratic formula to solve the equation. (1 point)
–x2 + 7x = 8
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17. Simplify the expression. (1 point)
(–5i)( –3i)
15i
–15i
–15
15
18. What is the solution set to the following system? (1 point)
{(–4, 0), (0, 4)}
{(4, 0), (0, 4)}
{(4, 0), (0, –4)}
{(–4, 0), (0, –4)}
19. Classify 5×5 + 3×4 – 8×3 + 12 by number of terms. (1 point)
polynomial of 4 terms
binomial
trinomial
polynomial of 5 terms
20. What are the zeroes of the function? (1 point)
y = (x – 2)(x – 3)(x + 3)
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–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
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.
x
y
1
15
2
19
3
16
(1 point)
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Semester A Exam
4
10
5
5
6
1
7
4
18/12/15 16:33
Which equation best represents the regression line for the data given in the table above?
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
(1 point)
function to model the quail population. What will the approximate population be after 4 years?
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 half-life 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
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28. Evaluate the logarithm. (1 point)
log32187
5
6
7
–7
29. Simplify the following expression completely. Show your work. (1 point)
–2(–y – 3) + 4y
6y – 6
6y + 6
2y – 6
2y + 6
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 4 + ln (3x) = 2. Round your answer to the nearest hundredth. (1 point)
1.13
0.18
1.41
0.62
32. Solve the equation or formula for the indicated variable. (2 points)
S = 6r³t, for t
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33. The function f(x) = x². The graph of g(x) is f(x) translated to the right 3 units and down 3 units. (2 points)
What is the function rule for g(x)?
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34. Solve the system by substitution. (2 points)
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35. Suppose x varies directly with y.
a. Use the fact that x = 39 when y = –117 to find the constant of variation and to write the
equation of variation.
b. Find the value of x when y = –132.
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(2 points)
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36. A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y –
900. The production of y must exceed the production of x by at least 100 units. Moreover,
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 maximum profit?
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(2 points)
37. Explain how to solve the following system of equations. What is the solution to the system? (2 points)
2x + 2y + z = –5
3x + 4y + 2z = 0
x + 3y + 2z = 1
38. Factor the expression. (2 points)
3×2 + 14x + 8
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39. What are the solutions of the quadratic equation? (2 points)
4×2 – 9x – 9 = 0
40. What is the result when 2 3 – 9 2 + 11 – 6 is divided by – 3? (2 points)
x
x
x
x
41. Explain the steps you would use to solve the equation. Find the solution. (2 points)
82x = 4096
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