This exam was adminstered in June 2025.
More Regents problems.
June 2025 Algebra 2 Regents
Part I
Each correct answer will receive 2 credits. No partial credit.
9. The probabilities that a randomly selected teenager uses social media
websites F and I are shown below.
P(I) = 0.52
P(F or I) = 0.77
(1) 0.06
(2) 0.19
(3) 0.46
(4) 0.96
Answer: (3) 0.46
The union (OR) of two probabilities is the equal to the sum of the independent probabilities minus their intersection (AND).
P(F or I) = P(F) + P(I) - P(F and I)
P(F) + P(I) - P(F or I) = P(F and I)
0.71 + 0.52 - 0.77 = P(F and I)
0.46 = P(F and I)
This is Choice (3).
10. Consider f(x) = (x - 2)2(x + 3), and g(x) as strictly defined in the
table below.
Which statement or statements must be true, based on the
information given?
I. Both f(x) and g(x) have the same x-intercepts.
II. Both f(x) and g(x) have a y-intercept at y = -6
(1) I, only
(2) II, only
(3) I and II
(4) neither I or II
Answer: (1) I, only
The x-intercepts of f(x) are 2 and -3. The x-intercepts of g(x) are -3 and 2. These are the same.
The y-intercept of f(x) = (-2)2(3) = 12. The y-intercept of g(x) is -6. These are not the same.
The correct answer is Choice (1).
11. Josie examines the graphs of f(x) = 3x - 8 and g(x) = 1 / (x2 - 4). The
number of solutions to f(x) = g(x) is
(1) 1
(2) 2
(3) 3
(4) 0
Answer: (3) 3
Just graph them. The answer is 3.
Choice (3) is the correct answer.
12. Which binomial is a factor of g3 + 6g2 + g - 14?
(1) g - 1
(2) g - 2
(3) g + 1
(4) g + 2
Answer: (4) g + 2
Once again: graph it. Check the zeroes. The roots are x = -2, or x = -2 + √(11).
If g - 1 is a factor, then the polynomial will eqaul zero when g = 1. However, it is -6. Eliminate Choice (1).
If g - 2 is a factor, then the polynomial will eqaul zero when g = 2. However, it is 20. Eliminate Choice (2).
If g + 1 is a factor, then the polynomial will eqaul zero when g = -1. However, it is -10. Eliminate Choice (3).
If g + 2 is a factor, then the polynomial will eqaul zero when g = -2. And it is 0. Choice (4) is the correct answer.
13. Consider the recursively defined sequence below.
an = 2an-1
(1) an = 2n
(2) an = 2(4n)
(3) an = 2(n+2)
(4) an = 8n
Answer: (3) an = 2(n+2)
If the answer doesn't jump out at you, write out the first few terms of the sequence. Then check each one.
The recursive formula is doubling, starting with 8: 8, 16, 32, 64, ...
Choice (1) is 2, 4, 8, ... Eliminate Choice (1).
Choice (2) is 8, 32, 128, ... Eliminate Choice (2).
Choice (3) is 8, 16, 32, 64. ... Choice (3) is the correct answer.
Choice (4) is 8, 64 ... Eliminate Choice (4).
14. What is the exact value of tan(-5π/6)?
(1) 1 / √(3)
(2) -1 / √(3)
(3) √(3)
(4) -√(3)
Answer: (1) 1 / √(3)
Tangent is positive in Quadrants I and III and this is Quadrant III. Eliminate Choices (2) and (4).
The coordinates for that point on the unit circle are (-√(3)/2, -1/2).
Tangent is sin/cos = (-1/2) / (-√(3)/2) = 1 / √(3)
This is Choice (1).
15. Given m ≠ 0 and (171/m)n = 172, what is n in terms of m?
(1) 2m
(2) 2/m
(3) m/2
(4) 2m
Answer: (1) 2m
Multiplying the exponents give you 17n/m = 172. This means n/m = 2.
Therefore, n = 2m.
This is Choice (1).
16. In order to qualify for a college tennis scholarship, Joe needs to win
90% of the matches he plays during his senior year of high school. If
he has won 8 of the 10 matches that he has played, which equation
can be used to determine how many more consecutive matches, x, Joe
must win in order for his winning percentage to equal 90%?
(1) (8 + x) / x = 0.90
(2) 8 / (10 + x) = 0.90
(3) 8/10 + x = 0.90
(4) (8 + x) / (10 + x) = 0.90
Answer: (4) (8 + x) / (10 + x) = 0.90
The number of games won divided by the number of games played must equal 0.90.
Currently, Joe is at 8/10 = .80. If he keeps winning, his average will be 9/11, 10/12, 11/13, etc.
Both the numerator and the denominator will increase.
This means that x games will be added to both the 8 and the 10, so Choice (4) is the correct answer.
More to come. Comments and questions welcome.
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