This exam was adminstered in August 2022. These answers were not posted until they were unlocked on the NY Regents website or were posted elsewhere on the web.

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__Algebra 2 August 2022__

__Algebra 2 August 2022__

Part II: Each correct answer will receive 2 credits. Partial credit can be earned. One mistake (computational or conceptual) will lose 1 point. A second mistake will lose the other point. It is sometimes possible to get 1 point for a correct answer with no correct work shown.

*25. Determine the average rate of change, in mph, from 2 to 4 hours on the graph shown below.
*

**Answer: **

The average rate of change is the change is distance divided by the change in time. If you drew a line from (2,20) to (4,60), it would be the slope of that line. This is basically an Algebra 1 question. There isn't any twist to it.

(60 - 20) / (4 - 2) = 40/2 = 20 miles per hour.

*26. Factor the expression x ^{3} - 2x^{2} - 9x + 18 completely.
*

**Answer: **

The word "completely" usually means that there will be more than one step.

Start by factoring by grouping:

^{3}- 2x

^{2}- 9x + 18

x

^{2}(x - 2) - 9(x - 2)

(x

^{2}- 9)(x - 2)

Note that you have a Difference of Squares which can be factored

(x - 3)(x + 3)(x - 2)*27. Solve algebraically for all values of x:*√(4x + 1) = 11 - x

**Answer: **

Square both sides to eliminate the radical, and then solve the quadratic equation.

√(4x + 1) = 11 - x

4x + 1 = (11 - x)^{2}

4x + 1 = 121 - 22x + x^{2}

0 = 120 - 26x + x^{2}

x^{2} - 26x + 120 = 0

(x - 20)(x - 6) = 0

x - 20 = 0 or x - 6 = 0

x = 20 or x = 6

Discard x = 20 because 11 - 20 = -9 and a square root cannot be negative.

x = 6 is the only solution.

*28. Given that (y*

^{(17/8)}/ y^{(5/4)})^{-4}= y^{n}, where y > 0, determine the value of n.

**Answer: **

Basically, you need to simplify the expression on the left side. What will the exponent be?

Use the Laws of Exponents to simplify them.

(y^{(17/8)} / y^{(5/4)})^{-4}

= (y^{(17/8 - 5/4)})^{-4}

=
(y^{(17/8 - 10/8)})^{-4}

= (y^{(7/8)})^{-4}

= y^{(-7/2)}

n = -7/2

*29. Given cos A = 3/√(10) and cot A = -3, determine the value of sin A in radical form.
*

**Answer: **

Cotangent is cosine / sine. Substitute and solve for sine.

cot A = cos A / sin A

-3 = (3/√(10)) / sin A

sin A = (3/√(10)) / -3

sin A = -1/√(10)

sin A = -√(10) / 10

Either of the last two lines would be acceptable because the question didn't state "simplest radical form" or "rationalize the denominator" or anything to state that a radical in the denominator would not be acceptable.

*30. According to a study done at a hospital, the average weight of a newborn baby is 3.39 kg, with a standard deviation of 0.55 kg. The weights of all the newborns in this hospital closely follow a normal distribution. Last year, 9256 babies were born at this hospital. Determine, to the nearest integer, approximately how many babies weighed more than 4 kg.
*

**Answer: **

Use the normalcdf function on your calculator.

Enter the following command:

The 1000 is because you need a high number. You could've used 1,000,000 if you wanted.

You will get the result 0.13369....

Multiply 9256 * 0.13369 = 1237.43.. = 1237 babies weighing more than 4 pounds.

You must round because you can't have partial babies.

*31. The table below shows the results of gender and music preference. Based on these data, determine if the events “the person is female” and “the person prefers classic rock” are independent of each other. Justify your answer.
*

**Answer: **

Compare the probability that the respondent is female with the probability that a respondent who liked classic rock was female. If they are the same, they the are independent.

The total number of females in the survey is 165, and the total of male and female is 215. 165/215 = .488...

The likelihood that someone who liked Classic Rock was female is 36/(36+42) = 0.4615...

They are not independent.

*32. Algebraically determine the solution set for the system of equations below.
*

*y = 2x*

y = 11 - 2x

^{2}- 7x + 4y = 11 - 2x

**Answer: **

Solve using substitution.

y = 2x^{2} - 7x + 4

y = 11 - 2x

2x^{2} - 7x + 4 = 11 - 2x

2x^{2} - 5x - 7 = 0

(2x - 7)(x + 1) = 0

2x - 7 = 0 or x + 1 = 0

2x = 7 or x = -1

x = 7/2 or x = -1

Find y for each x:

y = 11 - 2(7/2) = 4, (7/2, 4)

y = 11 - 2(-1) = 13, (-1, 13)

End of Part II

How did you do?

More to come. Comments and questions welcome.

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