Online Practice Test 2a for MATH 150.

This practice test covers material in Chapters 2 to 4 of the book: Precalculus, Mathematics for Calculus, 4th Edition.

This online test was created by Brent M. Dingle. You will notice if you select the wrong answer you are notified immediately (and perhaps given a hint). Assuming everything is working (i.e. your browser supports JavaScript and has it enabled) you should have been notified of a time limit to complete this test and you should see the words: "JavaScript Enabled" immediately below.

Test Questions:

1. Given that the function M(s) = -(1/28)s2 + 3s - 31 models the gas mileage for a car, when it is going at speed s, such that 15 <= s <= 70, at what speed is the best gas mileage attained?

    17 miles per hour
    32 miles per hour
    37 miles per hour
    42 miles per hour
    45 miles per hour

2. A theatrical play is being performed at a local civic center. The maximum capacity of the building is 15,000. It has been observed that the average attendance when tickets are priced at $14.00 is 9500 people. A recent study suggests that the average attendance will increase by 1000 people for every dollar the ticket price is reduced. What ticket price will maximize the REVENUE from ticket sales?

    $10.50
    $11.25
    $11.75
    $12.50
    $13.25

3. Find two numbers whose sum is -24 and whose product is a maximum.

    -14 and -18
    -6 and -18
    -50 and 26
    -8 and -16
    -12 and -12

4. Given f(x) = 3x - 5 and g(x) = 2 - x2 evaluate g(f(0)).

    1
    -10
    -23
    27
    -27

5. What is the inverse of f(x) = 3x - 2.

    (1/3)x - (1/2)
    -(1/3)x + (1/2)
    (2/3)x - (3/2)
    (1/3)x + (2/3)
    there is no inverse

6. What is the maximum number of local extrema that the following function may have?
        7x5 + 2x4 - 3x3 + 9x - 2

    1
    2
    3
    4
    5

7. Given: f(x) = 3x5 + 5x4 - 4x3 + 7x + 3
What is the remainder of f(x)/(x + 2) ?

    5
    4
    3
    2
    1

8. Given that 2i is a zero of: x4 - 16, find all REAL zeros, if any.

    2
    -4
    -4 and 4
    -2 and 2
    There are no real zeros.

9. Find all real roots of: 3x4 + 5x2 + 2 = 0.

    3/2
    2/3
    2
    -1
    There are no real roots.

10. Which of the following has a horizontal asymptote:
        r(x) = (2x - 1) / (x2 - x - 2)
        s(x) = (x3 + 27) / (x2 + 4)
        u(x) = (x2 + x - 6) / (x2 - 25)

    r(x) and s(x)
    r(x) and u(x)
    r(x)
    s(x)
    u(x)

Given loga 2 = 1.25, loga 3 = 2.5 and loga 7 = 4, to what does loga( (63*a3)/16 ) evaluate?

    12/5
    60
    7
    4
    a

12. If you invest $5000 at an intereste rate of 9% per year and the interest is compounded semiannually, how long will it take for your investment to double in value (to the nearest tenth of a year)?

    7.3 years
    7.7 years
    7.9 years
    8.4 years
    8.7 years

13. The spotted gapher was first placed on Mars about 8 years ago. The current population is known to be 4100, with a growth rate of 55% per year. Estimate what the population will be 7 years from now (to the nearest whole gapher).

    2350
    6355
    36,754
    191,381
    2,993,707

14. Solve the following equation for x:
        ( 3*x2*ex + x3*ex ) / x = 0

    -3
    -2
    0
    -3 and 0
    -2 and 0

15. Does the equation: y = (x2 - 4x - 5) / (x - 3) have a slant asymptote?

    yes
    no

16. Apply Descartes' rule of signs to determine the maximum number of real zeros that the following equation may have:
        P(x) = 3x6 + 4x5 + 3x3 - x - 3

    1
    2
    3
    4
    5

17. Find the real part of (7 - i)(4 + 2i), where i is square root of (-1).

    10
    18
    26
    28
    30

18. Given that a zero of multiplicity k is counted k times, how many zeros must the following equation have:
        3x5 + 7x3 - 4x2 + 2x - 1 ?

    1
    2
    3
    4
    5

19. Simplify (-16 + 4i)/(4 - i).

    -4 - i
    -4
    -1/4
    4i
    -4i

20.Simplify i45 * i347 * i123.

    i
    -i
    1
    -1
    0