Algebra Problems of the Day (Integrated Algebra Regents, June 2011)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones. The Integrated Algebra Regents covered most of the same material as the current Algebra Regents, with a few differences.

More Regents problems.

Integrated Algebra Regents, June 2011

Part II: Each correct answer will receive 2 credits. Partial credit is available.


31. The area of a rectangle is represented by x² − 5x − 24. If the width of the rectangle is represented by x − 8, express the length of the rectangle as a binomial.

Answer:

You are being asked to factor the polynomial and they gave you one of the factors. What is the other one?

Divide -24 by -8 and you get +3, and -8 + 3 = -5, so the binomial you want is (x + 3).

Make sure you show some kind of work in arriving at that answer, even if you can do it in your head.

32. A method for solving 5(x − 2) − 2(x − 5) = 9 is shown below. Identify the property used to obtain each of the two indicated steps.

Answer:

In Step (1), the Distributive Property was used to get rid of the parentheses by multiplying everything inside the parentheses by what is outside the parentheses.

In Step (2), the -10 and the -2x have switched places, which is allowed using the Commutative Property.

33. State the equation of the axis of symmetry and the coordinates of the vertex of the parabola graphed below.

Answer:

The axis of symmetry is an imaginary vertical line that goes through the vertex and the center of the parabola. It has an equation of x = a.

The Axis of Symmetry is x = 1, and the vertex is the point (1, -5). Label these, and do NOT forget the "x = ".

If you write "The Axis of Symmetry is 1", you will not get credit. That is not an equation.

End of Part II.

More to come. Comments and questions welcome.

More Regents problems.

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