Algebra Problems of the Day (Algebra Regents, June 2026 Part II)

This exam was adminstered in June 2026.

June 2026 Algebra, Part II

Each correct answer is worth up to 2 credits. Partial credit can be given. Work must be shown or explained.

25. Express the product of (1 − 2x) and (3 − 5x) as a polynomial in standard form.

Answer:

Use the Distributive Property, box method or even "FOIL". Just be sure to put it into standard form when combining like terms.

(1 − 2x) (3 − 5x)
= (1)(3 - 5x) - 2x(3 - 5x)
= 3 - 5x - 6x + 10x²
= 10x² - 11x + 3

26. On the set of axes below, graph f(x) = |x| − 3 over the domain −7 ≤ x ≤ 7.

Answer:

Use your graphing calculator. The abs() function is in the Catalogue.

An absolute value graph will be V shape. The vertex of this graph will be (0,-3). The slope on the left side is -1 and the slope on the right side is 1. The graph will be symmetrical.

Only graph between -7 and 7. The graph should have two endpoints. DO NOT put arrows on the graph. Do not go beyond -7 or 7. Follow instructions.

Your graph will look like this.

27. Solve the inequality algebraically: −4x + 1 > 9 + 3(2x + 1) + x

Answer:

Simplify each expression. Then isolate the variable with inverse operations.

−4x + 1 > 9 + 3(2x + 1) + x
−4x + 1 > 9 + 6x + 3 + x
−4x + 1 > 7x + 12
−11x > + 11
x < 1

28. Solve the formula A = 1/2 bh for h in terms of A and b.

Answer:

You can use a graphing calculator to give you a Five Number Summary of this data by putting it into a List.

A = 1/2 bh
2A = bh
2A / b = h

29. The table below shows the population of Manhattan for the years indicated, according to the U.S. Census Bureau.

Determine the average rate of change of the population per year between the years 1980 and 2020, rounded to the nearest integer.

Answer:
The average rate of change between the years 1980 and 2020 is just the slope of the line connecting those two ordered pairs.

(1,643,734 - 1,428,285) / (2020 - 1980) = 5386.225, which rounds to 5386.

30. Rewrite 5 / √(3) as a fraction with a rational denominator.

Answer:
Rationalize the denominator by multiplying by √(3) / √(3), which is equal to 1. (Multiplying a fraction by 1 doesn't change its value.)

5 / √(3) X √(3) / √(3) = 5√(3) / 3

End of Part II

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