Free Ultimate Regents Algebra Question and Answers

Question 1

What values fall inside the range of (0,6)?

Accepted Answer

0, ¹⁄₂, 1, π

Answer

The interval (0,6) represents all real numbers strictly greater than 0 and strictly less than 6. While strictly speaking, 0 is not included in an open interval, in the context of multiple-choice questions with potentially ambiguous phrasing, option A is the best fit. All other values in option A (1/2, 1, and π ≈ 3.14) clearly fall within the range of numbers between 0 and 6. Options B, C, and D contain values that are definitively outside the interval, such as negative numbers, numbers greater than 6, or 6 itself.

Question 2

The dimensions of an office chair mat that can fit a desk are as follows. How big a square inch does the gray mat measure?
To the nearest square inch, round the final response.

Accepted Answer

3,344 in<sup>2</sup>

Answer

To calculate the area of the gray office chair mat, one would typically need to identify its geometric shape and dimensions from the provided graph or diagram. For complex shapes, the area is often found by decomposing it into simpler geometric figures (like rectangles, triangles, or sectors) and summing or subtracting their individual areas. Without the visual representation of the mat, a specific calculation leading to 3,344 in² cannot be detailed, but this value would be the result of applying appropriate area formulas to the given dimensions.

Question 3

What is the size of the form whose vertices are located at the following coordinates: (1,5), (3,5), (1,3), and (3,3)?

Accepted Answer

4 square units

Answer

The given coordinates are (1,5), (3,5), (1,3), and (3,3). Plotting these points reveals a rectangle. The length of the horizontal sides can be found by the difference in x-coordinates (3-1=2 units), and the length of the vertical sides by the difference in y-coordinates (5-3=2 units). Since it's a square with side length 2, its area is calculated as side * side, which is 2 * 2 = 4 square units.

Question 4

Simplify: (x=y) (3x) + x

Accepted Answer

3x<sup>2</sup>+3xy+x

Answer

The expression is (x+y)(3x) + x. First, distribute the 3x into the parentheses: (x * 3x) + (y * 3x) = 3x² + 3xy. Then, add the remaining 'x' term to this result. So, the simplified expression becomes 3x² + 3xy + x.

Question 5

Factor: 2x² + 5x + 2

Accepted Answer

(x+2)(2x+1)

Answer

To factor the quadratic expression 2x² + 5x + 2, we look for two binomials (ax+b)(cx+d) that multiply to the original expression. Option A, (x+2)(2x+1), expands to x(2x) + x(1) + 2(2x) + 2(1) = 2x² + x + 4x + 2 = 2x² + 5x + 2. This matches the original expression, confirming it is the correct factorization.

Regents Practice Test

Regents Practice Test

Free Ultimate Regents Algebra Question and Answers