This exam was adminstered in January 2025.
More Regents problems.
January 2025 Algebra Regents
Part I
Each correct answer will receive 2 credits. No partial credit.
The domain of the function is
17. A function is graphed on the set of axes below.
(1) {x | x > -2}
(2) {x | x > -2}
(3) {x | x > -4}
(4) {x | x > -4}
Answer: (1) {x | x > -2}
The open circle indicates greater than but not equal to. Eliminate Choices (2) and (4).
The domain is the x value and the lowest possible x value is -2. The correct answer is Choice (1).
Choices (3) and (4) confuse the domain with the range, except they use x instead of y. The range is {y | y > -4}.
18. Which ordered pair is a solution to the equation y − 1 = 2(x + 1/4)?
(1) (0.75,0)
(2) (1.25,4)
(3) (2.5,-6.5)
(4) (4,-9.5)
Answer: (2) (1.25,4)
Add 1 to both sides of the equation and check y = 2(x + .25) + 1 for each of the four choices.
Choice (1), y = 2(.75 + .25) + 1 = 3, not 0. Eliminate Choice (1).
Choice (2), y = 2(1.25 + .25) + 1 = 4. Choice (2) is the correct answer.
In Choices (3) and (4), it should be obvious that the value of y for the given x will be positive and not negative, so both Choices (3) and (4) could be eliminated. However, if you didn't notice that, we can continue.
Choice (3), y = 2(2.5 + .25) + 1 = 6.5, not -6.5. Eliminate Choice (3).
Choice (43), y = 2(4 + .25) + 1 = 9.5, not -9.5. Eliminate Choice (4).
19. Elena’s fastest time for the 50-meter dash is 7 seconds. She wants to know how fast this is in inches per minute.
Which expression can Elena use for a correct conversion?
Answer: (4) [See Image]
If you are changing meters per second into inches per minute than inches needs to appear once on top and minutes need to appear once on the bottom. The starting fraction needs to be meters/second, and both of those units need to be cancelled.
Choices (1) and (2) start with seconds per meter. Eliminate both of them.
Choice (3) has meters twice in the numerator, so neither one cancels. The end result will be meters2 per min-in. Eliminate Choice (3).
Choice (4) has meters once in the numerator and once in the denominator, which cancel. It has seconds once in the numerator and once in the denominator, which cancel. The final result is in/meter. Choice (4) is the correct answer.
The interquartile range of these data is
20. The table below shows the highest temperatures recorded in August for several years in one town.
(1) 7
(2) 10
(3) 11
(4) 18
Answer: (3) 11
You can put the temperatures (not the years) into a list in your calculator and get a Five-Number Summary by doing 1-Var Stats.
Or you could arrange the data in order and do it yourself:
There are 8 pieces of data, so the average of the fourth and fifth is the median, which is 85, but not important to this problem.
The median of the first four numbers is 79.5, which is Q1. The median of the last four numbers is 90.5, which is Q3. The IQR is Q3 - Q1, which is 90.5 - 79.5, which is 11. This is Choice (3).
21. The function f(x) = x2 is multiplied by k, where k < −1. Which graph could represent g(x) = kf(x)?
Answer: (4) [See Image]
Multiplying a quadratic function by a factor greater than 1 will make it skinnier. Multiplying a quadratic function by a factor less than -1 will make it skinnier AND flip the direction of the parabola.
The given function, f(x) = x2, opens upward. The new function, g(x), will open downward and be thinner than the original. This is Choice (4).
If 0 < k *lt 1, then Choice (1) would've been the correct answer.
If -1 < k < 0, then Choice (2) would've been the correct answer.
If k > 1, then Choice (3) would've been the correct answer.
22. Which graph is the solution to the inequality 6.4 − 4x ≥ −2.8?
Answer: (2) [See Image]
Since greater than or equal to is specified, the answer will have a closed circle. Eliminate Choices (1) and (3).
Next, you can check to see if x = 0 is in the solution set or not.
6.4 ≥ −2.8 (check)
Since 0 is in the solution set, the correct choice must be Choice (4) and not Choice (2).
Algebraically,
-4x ≥ −9.2
x < 2.3
Remember that when you divide (or multiply) an inequality by a negative number, you have to flip the direction of the inequality symbol.
The correct answer is Choice (2).
23. The number of fish in a pond is eight more than the number of frogs. The total number of fish and frogs in the
pond is at least 20. If x represents the number of frogs, which inequality can be used to represent this situation?
(1) x + 8x ≥ 20
(2) 2x + 8 ≥ 20
(3) x + 8x ≤ 20
(4) 2x + 8 ≤ 20
Answer: (2) 2x + 8 ≥ 20
The term 8x refers to 8 times as many fish as frogs, not 8 more than the number of frogs. Eliminate Choices (1) and (3).
The pond has at least 20 fish and frogs meaning that the combined number is greater than 20. The correct choice is Choice (2).
24. Which graph below represents a function that is always decreasing over the entire interval −3 < x < 3?
Answer: (4) [See image]
Always decreasing means as x gets bigger, y gets smaller. The graph is always going down and to the right.
Choice (1) is increasing in the interval −3 < x < 3. Eliminate Choice (1).
Choice (2) is increasing in the interval −3 < 0 and then starts decreasing. Eliminate Choice (2).
Choice (3) is increasing in the interval −3 < x < 3. Eliminate Choice (3).
Choice (4) is the correct answer.
End of Part I. Comments and questions welcome.
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