Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

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June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


19. To solve,

Ren multiplied both sides by the least common denominator. Which statement is true?
(1) 2 is an extraneous solution
(2) 7/2 is an extraneous solution
(3) 0 and 2 are extraneous solutions
(4) This equation does not contain any extraneous solutions.

Answer: (1) 2 is an extraneous solution.
The equation is undefined for 0 and 2 because of the terms in the denominator. When both sides are multiplied by x² - 2x, that restriction is lifted. If either 0 or 2 are solutions to the equation, then they are extraneous.
Look at the steps below:

At this point, you can check both 0 and 2 to see if they are solutions to the equation.
2(0)² - 11(0 - 2) = 0 - 11(-2) = 22, which is not equal to 8. Zero is not an extraneous solution.
2(2)² - 11(2 - 2) = 2(4) - 11(0) = 8 - 0 = 8. Two is an extraneous solution.
As for 7/2, if you finish working out the problem, you will see that it is a solution to the equation, but it is not an extraneous solution.

20. Given f(9) = -2, which function can be used to generate the sequence -8, -7.25, -6.5, -5.75,...?
(1) f(n) = -8 + 0.75n
(2) f(n) = -8 - 0.75(n - 1)
(3) f(n) = -8.75 + 0.75n
(4) f(n) = -0.75 = 8(n - 1)

Answer: (3) f(n) = -8.75 + 0.75n
The rate of change is +0.75, which eliminates (2) and (4).
Choice (1) is incorrect because it has an incorrect starting value. If you substitute n = 1, you get -7.25 instead of 8.
Choice (2) would have been correct if there had been addition instead of subtraction.
Choice (3) is the correct answer because adding 0.75 to -8.75 gives you the initial term of -8.

21. The function

represents a damped sound wave function. What is the average rate of change for this function on the interval [-7,7], to the nearest hundredth?
(1) -3.66
(2) -0.30
(3) -0.26
(4) 3.36

Answer: (3) -0.26
To find the average rate of change, calculate f(7) - f(-7) and divide it by (7 - -7). (Like the slope formula.)
This gives you the following equation:

When you plug this into a calculator -- use a lot of parentheses if you have an older operating system! -- you will get -0.261492..., which is -0.26 to the nearest hundredth.



Comments and questions welcome.

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