Thursday, August 04, 2022

June 2022 Algebra 1 Regents, Part I (multiple choice)



This exam was adminstered in June 2022.

More Regents problems.

June 2022

Part I

Each correct answer will receive 2 credits. No partial credit.


9. Which expression is not equivalent to (52x)3?

(1) (5x)6
(2) (53x)2
(3) (55)x
(4) (52)3x

Answer: (3) (55)x


Even if you forgot, this is one time where you can use "One of these things is not like the others."

The expression (52x)3 is equivalent to 56x because when a power is raised to another power, you multiply the exponents.

The products of the exponents is Choices (1), (2) and (4) are each 6x. The product of the exponents is Choice (3) is 5x. This is the answer.





10. Which relation is a function?

Answer: (3) [See Image]


A graph is a function if it passes the vertical line test. A table or a set of elements can represented a function if each input has only one output -- that is, no x value is repeated. No choice shows a mapping diagram, but in those, no input can have more than one arrow pointing to an output.

The y values are allowed to repeat in a function.

Choice (1), the input 1 has two different outputs. Eliminate Choice (1).

Choice (2), the input 2 is included in each condition. (One of them should say < instead of <.) Eliminate Choice (2).

Choice (3) passes the vertical line test. No x has more than one y. Choice (3) is the answer.

Choice (4), the input 3 has two different outputs. Eliminate Choice (4).





11. The formula Ax + By = C represents the equation of a line in standard form. Which expression represents y in terms of A, B, C, and x?


(1) (C - Ax) / B
(2) (C - A) / (Bx)
(3) (C - A) / (x + B)
(4) (C - B) / (Ax)

Answer: (1) (C - Ax) / B


The variable y is multiplied by B and then Ax is added to get C. To isolate y, you have to do inverse operations in the opposite order. That means subtract Ax first and then divide by B.

That is:

Ax + By = C
By = C - Ax
y = (C - Ax) / B

This is Choice (1).





12. What are the zeros of f(x) = (2x - 4)(3x + 4)?

(1) {-4/3,2}
(2) {-4,4}
(3) {-2,4/3}
(4) {-4,2}

Answer: (1) {-4/3,2}


Solve 2x - 4 = 0 and 3x + 4 = 0.

2x - 4 = 0
2x = 4
x = 2

Eliminate Choices (2) and (3).

3x + 4 = 0
3x = -4
x = -4/3

The correct choice is (1).

If you plugged if x = 2 and x = -4, you could have eliminated three of the four choices.

You could also have put y = (2x - 4)(3x + 4) into your graphing calculator and checked the Table of Values.





13. Joe has dimes and nickels in his piggy bank totaling $1.45. The number of nickels he has is 5 more than twice the number of dimes, d. Which equation could be used to find the number of dimes he has?

(1) 0.10d + 0.05(2d + 5) = 1.45
(2) 0.10(2d + 5) + 0.05d = 1.45
(3) d + (2d + 5) = 1.45
(4) (d - 5) + 2d = 1.45

Answer: (1) 0.10d + 0.05(2d + 5) = 1.45


When you evaluate your coins, you count up the dimes and multiply that number by 0.10, and you count up the nickels and multiply that by 0.05.

Given this rule, Choices (3) and (4) make absolutely no sense. They appear to be totalling the number of coins but not their value. Eliminate them.

The second sentence says "n = 5 + 2d" if read algebraically.

If 0.10d + 0.05n = 1.45 then 0.10d + 0.05(2d + 5) = 1.45, which is Choice (1).





14. Donna and Andrew compared their math final exam scores from grade 8 through grade 12. Their scores are shown below.

Which statement about their final exam scores is correct?

(1) Andrew has a higher mean than Donna.
(2) Donna and Andrew have the same median.
(3) Andrew has a larger interquartile range than Donna.
(4) The 3rd quartile for Donna is greater than the 3rd quartile for Andrew

Answer: (3) Andrew has a larger interquartile range than Donna.


Put the numbers in order. Donna's scores are 87, 90, 92, 94, 95. Andrew's scores are 78, 87, 93, 94, 96.

By inspection, you can see that Donna's average (mean) is higher than Andrew's. You can find the average in your calculator to verfiy this, if you wish. Eliminate Choice (1).

When put in order, the middle numbers are different, so they don't have the same median. Eliminate Choice (2).

The IQR is the different between the first and third quartile, which is this instance would be the 2nd and 4th pieces of data. Donna's IQR is 94 - 90 = 4. Andrew's IQR is 94 - 87 = 7. Andrew's is larger. Choice (3) is the answer.

Q3 is 94 for both Donna and Andrew, so Choice (4) can be eliminated.





15. The first term in a sequence is 5 and the fifth term is 17. What is the common difference?

(1) 2.4
(2) 12
(3) 3
(4) 4

Answer: (3) 3


The common difference would be the same as the slope of the linear equation between the points (1,5) and (5,17).

17 - 5 = 12, 5 - 1 = 4, and 12/4 = 3. The common difference is 3.





16. A quadratic function and a linear function are graphed on the same set of axes. Which situation is not possible?

(1) The graphs do not intersect.
(2) The graphs intersect in one point.
(3) The graphs intersect in two points.
(4) The graphs intersect in three points.

Answer: (4) The graphs intersect in three points.


A straight line can be drawn that intersects a parabola in two places, in a single place (a tangent line), or it could miss it completely. It is impossible for a line to cut through a parabola three times.

The quadratric graph can cross the straight line and then curve back, but it cannot curve again.






More to come. Comments and questions welcome.

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