This exam was adminstered in August 2023.

More Regents problems.

__August 2023__

__August 2023__

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. Classify the expression (2 / SQRT(144)) + (SQRT(169)) / 3)
as rational or irrational. Explain your reasoning.
*

**Answer: **

The expression is rational because the sqaure root of 144 is 12 and the square root of 169 is 13. 2/12 and 13/3 are rational numbers and the sum of two rational numbers is always rational.

*26. Julia surveyed 150 of her classmates at City Middle School to determine their favorite animals.
Of the 150 students, 46% were male.
*

*Forty-two students said their favorite animal was a horse, and 1/3 of those students were female.
*

*Of the 60 students who said dolphins were their favorite animal, 30% were male.
*

*Using this information, complete the two-way frequency table below.
*

**Answer: **

Fill in the values that you know: 150, 42, 60. Calculate the fractions and decimals: 46% of 150 is 69, 1/3 of 42 is 14, 30% of 60 is 18.

Fill in the rest of the columns and rows based on the information you have been given or have calculated.

*27. Bryan said that the piecewise function graphed below has a domain of all real numbers.*

A friend tells her that the number of blocks in the pattern is increasing exponentially.

Is her friend correct?

State two reasons why Bryan is incorrect.

**Answer: **

Bryan is incorrect because the domain has a maximum at x = 4 and because the value x = 3 is not defined.

*28. The formula d = t(v*

_{i}+ v_{f}) / 2 is used to calculate the distance, d, covered by an object in a given period of time, t. Solve the formula for v_{f}, the final velocity, in terms of d, t, and v_{i}, the initial velocity.

**Answer: **

You don't need to understand what the formula means or where it is used. All you need to realize s that this is a Literal Equation and the variables can be manipulated. That is, they can be moved from one side to the other.

Use inverse operations. Divide both sides by t. Multiply both sides by 2. Then subtract the initial velocity, which will leave the final velocity by itself.

d = t(v_{i} + v_{f}) / 2

2d = t(v_{i} + v_{f})

2d / t = v_{i} + v_{f}

(2d / t) - v_{i} = v_{f}

*29.Solve x ^{2} - 9x = 36 algebraically for all values of x.
*

**Answer: **

Subtract 36 from both sides of the equation and then factor.

x^{2} - 9x = 36

x^{2} - 9x -36 = 0

(x - 12)(x + 3) = 9

x - 12 = 0 or x + 3 = 0

x = 12 or x = -3

*30. Determine the common difference of the arithmetic sequence in which a _{1} = 5 and a_{5} = 17.
*

*Determine the 21st term of this sequence.
*

**Answer: **

The common difference is similar to the slope between the points (1,5) and (5,17).

d = (17 - 5) / (5 - 1) = 12/4 = 3. The common difference is 3.

The 21st term can be found by multiplying the difference, 3, by 1 less than the term, n - 1, or 20, and then add the initial term, 5.

That is a_{21} = 5 + 3(21 - 1) = 65.

*31. Factor 18x ^{2} - 2 completely.
*

**Answer: **

"Factor completely" almost always means multiple steps. Remove the Common Factor (2) from each term and then factor the binomial using the Difference of Squares Rule.

18x^{2} - 2 = 2(9x^{2} - 1) = 2(3x + 1)(3x - 1)

*32. Solve x ^{2} + 3x - 9 = 0 algebraically for all values of x. Round your answer to the nearest hundredth.
*

**Answer: **

The polynomial can't be factored in the easy way. The "round your answer" is a hint that you will get irrational numbers for solutions. Use the quadratic formula.

Look at the image below.

Rounded, the solutions are x = 1.85 and x = -4.85.

End of Part II

How did you do?

More to come. Comments and questions welcome.

More Regents problems.

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