Algebra Problems of the Day (Algebra Regents, August 2025 Part I)
The Problems of the Day are BACK! Let’s see for how long. Life, y’know?
This exam was adminstered in August 2025.
More Regents problems.
August 2025 Algebra Regents
*Part I *
Each correct answer will receive 2 credits. No partial credit.
*17. The formula for the area of a trapezoid is A = (1/2)h(b1 + b2). The height, h, of the trapezoid may be expressed as
(1) 2A / (b1 + b2) (2) (1/2)A(b1 + b2) (3) (b1 + b2) / (2A) (4) (1/2)A - (b1 + b2)
**Answer: (1) 2A / (b1 + b2) **
Inverse operations to isolate h in terms of the other variables.
A = (1/2)h(b1 + b2) 2A = h(b1 + b2) 2A / (b1 + b2) = h
Choice (1) is the correct answer.
*10. Three functions are given below. *
**
- Which functions have the same y-intercept?
(1) f(x) and g(x) (2) g(x) and h(x (3) f(x) and h(x) (4) The functions all have different y-intercepts.
**Answer: (1) f(x) and g(x) **
The y-intercept of h(x) is in the table – when x = 0, h(x) = -3. Now calculate f(0) and g(0), or graph them.
f(0) = -|0 + 2| + 7 = -2 + 7 = 5, so f(x) and h(x) have different y-intercepts.
g(0) = (0 - 3)2 - 4 = 9 - 4 = 5, which is the same as f(0).
Therefore, the correct answer is Choice (1).
*19. The sum of (x + 7)2 and (x - 3)2 is
(1) 2x2 + 58 (2) 2x4 + 58 (3) 2x2 + 8x + 58 (4) 2x4 + 8x2 + 58
**Answer: (2) -3.75 **
The sum of two quadratics is also a quadratic (unless the x2 terms cancel out for some reason, in which case the order of lower, but it’ll never be higher.) Eliminate Choices (2) and (4).
It should also be obvious that Choice (1) is incorrect because there is no reason why the middle term should be missing.
(x + 7)2 + (x - 3)2
x2 + 14x + 49 + x2 - 6x + 9
2x2 + 8x + 58
Choice (3) is the correct answer.
*20. The product of 2√(10) and 3√(2) is
(1) 12√(5) (2) 5√(20) (3) 24√(5) (4) 5√(12)
**Answer: (1) 12√(5) **
Multiply the coefficients and multiply the radicands.
So (2√(10)) * (3√(2)) = 6√(20), which is not one of the choices. However, the radical can be simplified.
6√(20) = 6√( (4)(5) ) = 6√(4)&sqrt;(5) = 12√(5)
This is Choice (1).
This problem could’ve been solved by putting all four choices and the original question into a calculator.
*21. When 6x3 - 2x + 8 is subtracted from 5x3 + 3x - 4, the result is
(1) x3 - 5x + 12 (2) x3 + x + 4 (3) -x3 + 5x - 12 (4) -x3 + x + 4
**Answer: (3) -x3 + 5x - 12 **