College Algebra Questions (for geniusy_2006)

Student ID: 21772952

Exam: 050358RR - EXPONENTIAL AND LOGARITHMIC FUNCTIONS;SOLVING POLYNOMIALS

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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. 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 2x4 −  6x3 + 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 + 7x2 − 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 24x3 + 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 2x100 − x7 − 1? A. x − 2

B. x + 1

C. x

D. x − 1

16. How many roots does x6 = 3x5 + 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 + 6x2 + x + 6

B. x3 + 6x2 − x − 6

C. x3 − 6x2 + x − 6

D. x3 − 6x2 − x + 6

18. Find all roots of x3 + 2x2 + 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 3x3 − 11x2 + 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 4x4 − 5x3 + 9 is divided by x − 3?

A.

B.

C.

D.

23. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + 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