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Math Practice Test
____ 1. For the following function, first find all values of x such that then find all x such that
____ 2. If one zero of the following function is 4, find the other two zeros.
____ 3. Use the remainder theorem to find
____ 4. Use the factor theorem to decide whether x-c is a factor of the polynomial.
a. x - c is a factor
b .x - c is not a factor
____ 5. Use synthetic division to decide whether c is a zero of .
a. x - c is a zero
b. x - c is not a zero
____ 6. Find a polynomial with leading coefficient of 1, degree 3, and zeros: -5,0,9.
____ 7. Use synthetic division to find the quotient and remainder if the first polynomial is divided by the second.
____ 8. Find a polynomial of degree that has the indicated zeros and satisfies the given condition.
____ 9. Find the fourth-degree polynomial function whose graph is shown in the figure.
____ 10. A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
____ 11. Find the oblique asymptote of
____ 12. Determine whether the function f is one-to-one
b. not one-to-one
____ 13. Use the theorem on inverse functions to determine whether f and g are inverse functions of each other.
a. f and g are inverse functions of each other.
b. f and g are not inverse functions of each other.
____ 14. Determine the range of
for the function without actually finding
Hint: First find the domain and range of f
____ 15. Find the inverse function of f
____ 16. Solve the equation:
____ 17. Sketch the graph of f if:
____ 18. Find an exponential function of the form f (x) = bax that has the given y-intercept and passes through the point P:
____ 19. The number of bacteria in a certain culture increased from 600 to 1,800 between 7:00 A.M. and 9:00 A.M. Assuming the growth is exponential, the number f (t) of bacteria t hours after 7:00 A.M. is given by:
Estimate the number of bacteria in the culture at 10:00 A.M.
____ 20. The radioactive bismuth isotope 210Bi has a half-life of 5 days. If there is 100 milligrams of 210Bi present at t = 0, then the amount f(t) remaining after t days is given by:
How much 210Bi remains after 25 days?
____ 21. In 1980, the population of blue whales in the southern hemisphere was thought to number 5,000. The population N(t) has been decreasing according to the formula
where t is in years and t = 0 corresponds to 1980. Predict the population in the year 2010 if this trend continues.
____ 22. Use the graph of y = ex to help sketch the graph of
____ 23. If $900 is deposited in a savings account that pays interest at a rate of per year compounded continuously, find the balance after 7 years.
____ 24. An investment of $835 increased to $16,771 in 20 years. If the interest was compounded continuously, find the interest rate.
____ 25. The 1980 population of the United States was approximately 227 million, and the population has been growing continuously at a rate of 0.7% per year. Predict the population in the year 2040 if this growth trend continues.
a.322 million people
b.229 million people
c.345 million people
d.382 million people
e.379 million people
____ 26. Change to exponential form.
____ 27. Solve the equation.
____ 28. Solve the equation.
____ 29. Express in terms of logarithms of x , y, z, or w.
____ 30. Write the expression as one logarithm.
____ 31. Solve the equation.
____ 33. Use the compound interest formula to determine how long it will take for a sum of money to double if it is invested at a rate of 6% per year compounded monthly.
Identify one or more choices that best complete the statement or answer the question.
____ 34. Find the zeros of , and state the multiplicity of each zero.
a.0 positive roots , 3 negative roots , 0 nonreal roots
b.2 positive roots, 1 negative root, 0 nonreal roots
c.1 positive root, 0 negative roots, 2 nonreal roots
d.1 positive root, 2 negative roots, 0 nonreal roots
e.3 positive roots, 0 negative roots, 0 nonreal roots
f.0 positive roots, 0 negative roots, 3 nonreal roots
5. ANS: A
9. ANS: E
10. ANS: B
11. ANS: D
14. ANS: E
15. ANS: C
16. ANS: E
17. ANS: B
18. ANS: C
19. ANS: D
20. ANS: D
21. ANS: B
22. ANS: C
23. ANS: C
24. ANS: D
25. ANS: C
26. ANS: C
27. ANS: E
28. ANS: B
29. ANS: A
30. ANS: C
31. ANS: B
32. ANS: A
33. ANS: A
34. ANS: B, D, F
35. ANS: C, E