While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.
More Regents problems.
Administered June 2013
Part I: Each correct answer will receive 2 credits.
21. Carol plans to sell twice as many magazine subscriptions as Jennifer.
If Carol and Jennifer need to sell at least 90 subscriptions in all, which
inequality could be used to determine how many subscriptions, x,
Jennifer needs to sell?
(1) x > 45
(2) 2x > 90
(3) 2x - x > 90
(4) 2x + x > 90
Answer: (4) 2x + x > 90
If Jennifer needs to sell at least x, and Carol plans to sell twice as many as Jennifer, which would be 2x, and together they needed to sell more than 90, then the total could be written as 2x + x > 90.
Hopefully you noticed that Choices (1) and (2) are equivalent so neither could be the answer. Jennifer isn't selling half of the 90 subscriptions if Carol is selling twice as many. She's only selling one third.
22. When 2x2 - 3x + 2 is subtracted from 4x2 - 5x + 2, the result is
(1) 2x2 - 2x
(2) -2x2 + 2x
(3) -2x2 - 8x + 4
(4) 2x2 - 8x + 4
Answer: (1) 2x2 - 2x
If 2x2 - 3x + 2 is subtracted from 4x2 - 5x + 2, then you need to calculate
(4x2 - 5x + 2) - (2x2 - 3x + 2) which is
(4x2 - 2x2) + (-5x - (-3x)) + (2 - 2) which is
2x2 + (-2x)) + 0
If you didn't put the "from" expression first (I took three dollars from the fifteen in my pocket), you would have gotten the addition inverse, Choice (2), which is incorrect. Choices (3) and (4) happen when you add the 2nd and 3rd terms instead of subtract.
23. Which expression represents the number of hours in w weeks and d days?
(1) 7w + 12d
(2) 84w + 24d
(3) 168w + 24d
(4) 168w + 60d
Answer: (3) 168w + 24d
The number of hours in d days is 24d. The number of hours in w weeks is the same as in 7w days. Since there are 24 hours in one day, that becomes 7(24)w hours, which is 168w.
24. Given:
R = {1, 2, 3, 4}
A = {0, 2, 4, 6}
P = {1, 3, 5, 7}
(1) {0, 1, 2, 3, 4, 5, 6, 7}
(2) {1, 2, 3, 4, 5, 7}
(3) {1, 3}
(4) {2, 4}
Answer: (3) {1, 3}
The Intersection consists of all the elements of R that are also elements of P. Only 1 and 3 are present in both sets.
Thankfully, this is no longer on the Algebra 1 regents exam, not until they change the curriculum again.
Choice (1) is the Union of all three sets R ∪ A ∪ P.
Choice (2) is the Union of R ∪ P.
Choice (4) is the Intersection of R ∩ A.
25. Which equation could be used to find the measure of angle D in the right triangle shown in the diagram below?
(1) cos D = 12 / 13
(2) cos D = 13 / 12
(3) sin D = 5 / 13
(4) sin D = 12 / 13
Answer: (4) y < x - 1
This isn't in Algebra 1 any more, but it is in Geometry.
The sine (sin) ratio is the length of the side opposite the angle divided by the length of the hypotenuse. The cosine (cos) ratio is the length of the side adjacent to the angle divided by the length of the hypotenuse.
The side adjacent to angle D has a length of 5, so cos D = 5 / 13, but this is not one of the choices. The side opposite of angle D has a length of 12, so sin D = 12 / 13, which is Choice (4).
Note that the sine and cosine ratios can never be greater than 1 (or equal to 1 for that matter). Therefore, Choice (2) can be quickly eliminated because 13/12 is greater than 1.
More to come. Comments and questions welcome.
More STAAR problems.
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