Algebra 2 Problems of the Day (Jan 2020)

Daily Algebra 2 questions and answers.

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January 2020, Part I

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


6. The expression (x + a)² + 5(x + a) + 4 is equivalent to

(1) (a + 1)(a + 4)
(2) (x + 1)(x + 4)
(3) (x + a + 1)(x + a + 4)
(4) x² + a² + 5x + 5a + 4

Answer: 3) (x + a + 1)(x + a + 4)
Replace (x + a) with y.
This gives you y² + 5y + 4, which factors into (y + 1)(y + 4).
Now replace y with x + a, and you get (x + a + 1)(x + a + 4)

7. Given x =/= -2, the expression (2x² + 5x + 8)/(x + 2) is equivalent to
After n months, which function represents Chet’s net worth, R(n)?

(1) 2x² + 9/(x + 2)
(2) 2x + 7/(x + 2)
(3) 2x + 1 + 6/(x + 2)
(4) 2x + 9 - 10/(x + 2)

Answer: 3) 2x + 1 + 6/(x + 2)
Set up the division as in the table below:

The divisor (x + 2) has a root of -2.
Bring down the first 2. Multiply -2 X 2 = -4. Write that down, and add 5 + -4 = 1.
Multiply -2 X 1 = -2. Write that down and add 8 + -2 = 6.
The result is 2x + 1 with a remainder of 6, which is written at 6/(x + 2).

8. Which situation best describes conditional probability?

(1) finding the probability of an event occurring two or more times
(2) finding the probability of an event occurring only once
(3) finding the probability of two independent events occurring at the same time
(4) finding the probability of an event occurring given another event had already occurred

Answer: 4) finding the probability of an event occurring given another event had already occurred
Choice (1) is incorrect because it doesn't have to be the same event re-occurring.
Choice (2) is simple probability.
Choice (3) is not conditional, if they are happening at the same time.

9. Which expression is not a solution to the equation 2^t = SQRT(10)?

(1) 1/2 log₂10
(2) log₂SQRT(10)
(3) log₄10
(4) log₁₀4

Answer: 4) log₁₀4
Choices (3) and (4) should pop out at you because there is no reason why they should be equal, so one of them should be the answer.

2^t = SQRT(10) means that log₂SQRT(10) = t (choice 2)
SQRT(10) = 10^1/2, which gives you: t = log₂(10)^1/2
The rules of logarithms say that log₂(10)^1/2 = 1/2 log₂(10) (choice 1)
If 2^t = SQRT(10),
then 2^2t = 10
and 4^t = 10
So t = log_{410. (Choice 3)}

10. What is the solution set of x = SQRT(3x + 40)?
(1) {-5, 8}
(2) {8}
(3) {-4, 10}
(4) { }

Answer: (2) {8}
First of all, you can work backward from the choices. Second, because there isn't a + symbol in front of the square root symbol, it is assumed to be the positive root. Since this is the case, choices (1) and (3) are not possible.

x = SQRT(3x + 40)
x² = 3x + 40
x² - 3x - 40 = 0
(x - 8)(x + 5) = 0
x = 8 or x = -5 (disgard)
Check: 8 = SQRT(3(8) + 40) = SQRT(64) = 8, check.

Comments and questions welcome.

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