Algebra II / Graham, Hansen, James

Name: _____________________________

Feb. 2000 Practice Test on Ch. 6 (40 minutes)

 

The purpose of this practice test is to help you review by showing you the wording and types of problems on the actual test. The actual test is slightly shorter (though not much) and contains different problems. Although most of these practice problems are similar to real ones, not all types of problems are represented here. See the review problems in §6-15 for additional examples. Mr. Hansen’s students are also required to know unit conversions and decibels.

No notes
You cannot use notes on the actual test. Ample room to write will be provided. In the unlikely event that you need extra space, scratch paper will be provided. Note, however, that this practice test has been written with the problems all scrunched together. For the practice test, write all answers on a separate sheet unless you write very small.

Calculator
You may use your calculator on all parts of the test. However, since your work is what will be graded, not your answer, in most cases you should use your calculator only to check your work. Decimal answers are acceptable only when the problem says "round to ____ places" or "round to the nearest _____ ."

Simplifying
The word "simplify" means to leave everything in simplest form (e.g., write 2Ö 2 instead of Ö 8 in your final answer), with no radicals in the denominator, and in a + bi format in the case of complex numbers.

Show all work
For full credit, show all work. Correct answers that could be obtained through mere button-pushing on the calculator will usually receive NO CREDIT. Reduce fractions to simplest form and rationalize all denominators. Give exact answers (no decimals) unless otherwise requested.

Units of measure
Show units of measure where appropriate. For example, if the answer is a number of people, you would round your answer and write it as "approx. _____ people." Because people come in integer quantities, this would be a case where rounding to the nearest integer is appropriate.

1.

Simplify without using a calculator (OK to use calculator to check):

(a)

log1/6 (1/216)

(b)

10log 17 + log 44

2.

Simplify to a single logarithm with a single argument. Do not give a decimal answer, but you probably will need to use your calculator for help in simplifying. For example, if the answer to part (a) simplifies to be log4 533, you would write log4 533, not the decimal approximation.

(a)

3 log4 7 – 1.5 log4 9 + 2 log4 541/2

(b)

log5005 7 + log5005 143 – log5005 5005 + log5005 5
3.

Solve for x. Express answer in exact form (no decimals) and use set notation.

(a)

logx 1/289 = –2

(b)

log3 2x + log3 (x + 3) = 2

(c)

4 · 150.25x = 38
4.
Suppose that "loggg" is a log function (we won’t say what the base is), and that loggg 2 = –4.9773, loggg 3 = –7.8888, and loggg 5 = –11.5569.

(a)
Use these facts to compute loggg 150. (You may use your calculator to assist you, but show all work. Give final answer correct to 4 decimal places.)

(b)
How can you tell that the base of "loggg" is between 0 and 1?

(c)
Compute the base of loggg.

5.
Use the change-of-base formula to convert the following expression to base-3 logarithms throughout, and then simplify to a rational number.
–3 log3 (1/3) + 2 log9 243

6.
Let f(x) = (2x + 4)1/2.

(a)
Find the inverse function.

(b)
Prove algebraically that f –1(f (x)) = x.

(c)
Plot both f and f –1 on the same set of axes.
7.
Morale of Algebra II students (measured in a special made-up unit called mors) has been found to decrease exponentially with time. If the class morale on day 0 is 150 mors and has dropped to 120 mors by midterm (day 126), will the morale level remain above 90 mors all the way to the end of the school year (day 265)? Justify your answer. Use units as appropriate.
8.
Decibels (dB) for a signal-to-noise ratio are defined as 10 times the base-10 logarithm of the ratio between the respective power levels. If signal strength is 45 watts and noise is 18 milliwatts, what is the signal-to-noise ratio to the nearest decibel?
9.
Compute 78994.