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StudentID: 21772952
Exam: 050357RR – QUADRATIC FUNCTIONS AND INEQUALITIES; MORE FUNCTIONS
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Questions 1 to 25: Select the best answer to each question. Note that a question and its answers may be split across a page
break, so be sure that you have seen the entire question and all the answers before choosing an answer.
1. Which of these statements is true about the graph of the equation y = x2 − x − 1?
A. It is a parabola with axis of symmetry .
B. It is a parabola with axis of symmetry .
C. It is a parabola with vertex at .
D.
It is a parabola with vertex at .
2. Which of the following choices are the solutions to 2×4 − 3×2 − 2 = 0?
A.
B.
C.
D.
3. Choose the one true statement about .
A. It is an odd function.
B. It has a vertical asymptote at x = 1.
C. It has no vertical asymptotes.
D. It has a horizontal asymptote at y = 0.
4. Which of these equations describes the same parabola as y = 6×2, except translated to place its vertex at
(–6, 1)?
A. y = 6(x + 6)2 − 1
B. y = 6(x + 6)2 + 1
C. y = 6(x − 6)2 − 1
D. y = 6(x − 6)2 + 1
5.
A.
B.
C.
D.
6. What is the result of performing partial fraction decomposition on the rational function ?
A.
B.
C.
D.
7. The square root property tells us that if (2x − 9)2 = 9 is true then which of the following must also be
true?
A. 2x − 9 = ±9
B. 2x − 9 = ±3
C. 2x = ±18
D. 2x = ±0
8. Choose the one true statement about .
A. It has a horizontal asymptote at .
B. It has a slant asymptote at .
C. It has one vertical asymptotes.
D. It is an even function.
9. The function f(x) = 6×3 − 6x has which symmetry or symmetries?
A. It is an even function.
B. It is both an even and an odd function.
C. It is neither an even function nor an odd function.
D. It is an odd function.
10. Solve kPt2 − Rt = 0 for t, assuming t > 0. Which of these describes your answer?
A. is the only solution.
B. is the only solution.
C. and 0 are both solutions.
D. t and kP − R are both solutions.
11. Which of these is true about 7×2 − 9x − 11 = 0?
A. The sum of its roots is .
B. The sum of its roots is .
C. The product of its roots is .
D. The product of its roots is .
12. Compute when f(x) = –2×2 + 4.
A.
B.
C.
D.
13. What is the inverse of .
A. f–1(x) = (x2 − 9)
B. f–1(x) = (x − 9)2
C. f–1(x) = (x2 + 9)
D. f–1(x) = (x + 9)2
14. What is the result of performing partial fraction decomposition on the rational function ?
A. It cannot be performed because the degree of the numerator is less than the degree of the denominator.
B.
C.
D.
15. Choose the one true statement about .
A. It has a slant asymptote at .
B. It is an even function.
C. It has a horizontal asymptote at .
D. It has vertical asymptotes at x = 2 and x = 1.
16. Which of these is the first step in solving x2 + 6x + 1 = 0 by completing the square?
A. x2 + 6x = –1
B. (x + 6)2 = –1
C. (x + 6)2 + 1 = 1
D. x2 + 6x + 9 − 9 + 1 = 0
17. The solution set for y > 6x − x2 is shown in which of these graphs?
A.
B.
C.
D.
18. Which of these is false about the quadratic function y = 12×2 + 12?
A. It is a parabola that opens upward.
B. It is a parabola whose axis of symmetry is they axis.
C. It is the parabola y = x2 shifted upward 12 units.
D. It is a parabola whose vertex is the point (0, 12).
19. Which of these is the equation of a parabola with vertex (–6, 2)?
A. y = x2 + 12x + 34
B. y = 4(x + 6)2 + 2
C. y = 4×2 + 6x − 2
D. y = (x + 6)2 + (–2)
20. If b2 − 4ac = 7 for some quadratic equation, then which of these is true about that equation?
A. None of its solutions are real numbers.
B. It has no discriminant.
C. All its solutions are real numbers.
D. All of its solutions are rational numbers.
21. Consider the functions f(x) = 2x + 13 and g(x) = x2 − 1. What is f/g and what is its domain?
A. with domain {–1, 1}
B. with domain (–∞, –1) ∪ (–1, 1) ∪ (1, ∞)
C. with domain all real numbers
D. You cannot compute f/g because g(x) ≠ 0.
22. Which are the solutions to 6×2 + 35x − 6 = 0?
A. It has no solutions.
B. and 6
C. –5.6565 and –0.1767
D. and –6
23. Which is a correct setup for the partial fraction decomposition of ?
A.
B.
C.
D.
End of exam
24. Which of the following functions satisfies f(2.1) = 6?
A.
B.
C.
D.
25. The solution set for 4×2 − 3x − 1 ≥ 0 is which of these?
A.
B.
C.
D.
Student ID: 21772952
Exam: 050358RR – EXPONENTIAL AND LOGARITHMIC FUNCTIONS;SOLVING
POLYNOMIALS
When you have completed your exam and reviewed your answers, click Submit Exam. Answers will not be recorded until you
hit Submit Exam. If you need to exit before completing the exam, click Cancel Exam.
Questions 1 to 25: Select the best answer to each question. Note that a question and its answers may be split across a page
break, so be sure that you have seen the entire question and all the answers before choosing an answer.
1. Find the point (x, y) on the parabola y = 9 − x2 such that the shaded rectangle in the figure below has
area 20 square units.
A.
B.
C.
D.
2. Which of the following is a correct description of the expression log
b
x?
A. It is the power to which x must be raised to yield b.
B. It is the bth power of x.
C. It is the xth power of b.
D. It is the power to which b must be raised to yield x.
3. Is it possible for a degree-4 polynomial P(x) to have only complex (no real) roots?
A. No, it is not possible.
B. Yes, but the coefficients of P(x) must have no sign changes, although the coefficients of P(–x) may have no sign changes.
C. Yes, but neither the coefficients of P(x) nor those of P(–x) can have any sign changes.
D. Yes, but the coefficients of P(x) must have 4 sign changes.
4. In 10 years, 25% of a radioactive substance decays. What is its half-life?
A. 20 years
B. 24 years
C. 29 years
D. 25 years
5. How long will it take a population with a 10% annual growth rate to double?
A. 9 years
B. 6.9 years
C. 14.4 years
D. 10 years
6. Solve for y.
A. y = –4
B. y = 0
C. y = 4
D. No solution
7. Which of the following is the conclusion you can draw using Descartes’ Rule of Signs applied to 2×4 −
6×3 + x2 + 7x − 4?
A. Zero is not a root.
There are either 1 or 3 positive real roots.
There is 1 negative real root.
No information is available about the number of complex roots.
B. Zero is not a root.
There are either 1 or 3 positive real roots.
There are 3 negative real roots.
No information is available about the number of complex roots.
C. Zero is not a root.
There are either 1 or 3 positive real roots.
There are 3 negative real roots.
There are either 0 or 2 complex roots.
D. Zero is not a root.
There are either 1 or 3 positive real roots.
There is 1 negative real root.
There are either 0 or 2 complex roots.
8. Which is better for the investor, an investment that pays 2% annual interest compounded monthly or an
investment that pays 2.1% interest annually?
A. The two plans are equal.
B. The 2.1% annually is better.
C. You cannot compare plans with different frequencies of compounding.
D. The 2% with monthly compounding is better.
9. An account with $300 in it has been earning 3% annual interest compounded continuously for 10 years
with no deposits or withdrawals in that time. How much was in the account 4 years ago?
A. $338.25
B. $222.25
C. $266.08
D. $77.75
10. On which interval does the Intermediate Value Theorem guarantee that the polynomial x4 + 7×2 − 9x −
1 has a root?
A.
B.
C.
D.
11. Why do we use the Intermediate Value and Bisection Theorems to find only the irrational roots of
polynomials?
A. No polynomial has rational roots.
B. Those theorems are unable to find rational roots.
C. The Rational Roots Theorem is better for finding the rational roots.
D. It is the only method available for finding irrational roots of any polynomial.
12. Solve for x.
A.
B. 54
C.
D.
13. Use the Rational Roots Theorem to list all possible rational roots of 24×3 + 2x − 7.
A.
B.
C.
D.
14. Find the negative root of x2 − 3 = 0 to the nearest tenth.
A. 1.7
B. –1.7
C. –1.4
D. 1.4
15. Which of these is a factor of 2×100 − x7 − 1?
A. x − 2
B. x + 1
C. x
D. x − 1
16. How many roots does x6 = 3×5 + 1 have?
A. 11
B. 1
C. 6
D. 5
17. What is the lowest-degree polynomial with integer coefficients and the roots 6, i, and –i?
A. x3 + 6×2 + x + 6
B. x3 + 6×2 − x − 6
C. x3 − 6×2 + x − 6
D. x3 − 6×2 − x + 6
18. Find all roots of x3 + 2×2 + 2x + 1. Hint: Find the rational one(s) first.
A.
B.
C.
D.
19. A falling object has velocity 37(1 − e–0.4t) meters per second after t seconds of free fall. Which of the
following statements is true?
A. Its initial velocity was 0 meters per second and its velocity after 10 seconds is 36.3 meters per second.
B. Its initial velocity was –1 meter per second and its velocity after 10 seconds is –36.3 meters per second.
C. Its initial velocity was 1 meter per second and its velocity after 10 seconds is 12.2 meters per second.
D. Its initial velocity was 0 meters per second and its velocity after 10 seconds is –12.2 meters per second.
20. If 2 − i is a root of 3×3 − 11×2 + 11x + 5, then what are its other roots?
A.
B.
C.
D.
21. If P(x) is a polynomial with P(–6) = –1.12 and P(–5) = 0.6 then which of the following must be true?
End of exam
A. There is a zero for P(x) between x = –6 and x = –5, but it may be a complex number.
B. There is a zero for P(x) between x = –1.12 and x = 0.6.
C. There is a zero for P(x) between x = –6 andx = –5.
D. There is a zero for P(x) between x = –1.12 and x = 0.6, but it may be a complex number.
22. Which of these is the remainder when 4×4 − 5×3 + 9 is divided by x − 3?
A.
B.
C.
D.
23. Which are upper and lower bounds for the real roots of 3×4 − 2×3 + x − 9 = 0?
A. –2 and –1, 1, and 2
B. –2 and 2
C. 0 and 3
D. –3 and –1, 1, and 3
24. If a cubic polynomial has roots –5 and 6 − 2i, what is its third root?
A. 6 + 2i
B. –30 + 10i
C. 1 − 2i
D. 5
25. A population of 2000 snakes is released into a marshland and grows according to the formula P =
2000 • 1.5t, where t is the number of months after the release. Find the population 10 months after the
release.
A. 115,330
B. 63,246
C. 5.9 x 1034
D. 30,000
