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 I: Each correct answer will receive 2 credits.


11. Which type of function is represented by the graph shown below?

1) absolute value
2) exponential
3) linear
4) quadratic

Answer: 4) quadratic

The graph is a "U-shaped" parabola, which is the result of graphing a quadratic function.

Absolute-value functions have a "V-shaped" graph. Linear functions are straight lines, not curves. Exponential functions go to close to vertical on one end and close to horizontal on the other.

12. Which equation represents a line parallel to the y-axis?

1) y = x
2) y = 3
3) x = -y
4) x = -4

Answer: 4) x = -4

Parallel to the y-axis means that it is a vertical line, which will have a formula of x = a, where a is a constant. The line will have an undefined slope.

Choice (1) is a diagonal line with a slope of 1 which intercepts the y-axis at the origin.

Choice (2) is a horizontal line with a slope of 0 that is parallel to the x-axis which intercepts the y-axis at the point (0,3).

Choice (3) is a diagonal line with a slope of -1 which intercepts the y-axis at the origin.

13. Melissa graphed the equation y = x² and Dave graphed the equation y = −3x² on the same coordinate grid. What is the relationship between the graphs that Melissa and Dave drew?

1) Dave’s graph is wider and opens in the opposite direction from Melissa’s graph.
2) Dave’s graph is narrower and opens in the opposite direction from Melissa’s graph.
3) Dave’s graph is wider and is three units below Melissa’s graph.
4) Dave’s graph is narrower and is three units to the left of Melissa’s graph.

Answer: 2) Dave’s graph is narrower and opens in the opposite direction from Melissa’s graph.

The equation y = x² is the parent function for quadratics. It is a parabola that opens upward with a vertex at the origin.

The graph of y = -3x² is a transformation of the parent function. It will open down because of the negative sign and will be narrower because of the coefficent having a magnitude greater than 1. The multiplier will cause the y values to move away from the x-axis at a much faster rate.

The coefficient of the x² term does NOT move the vertex up, down, left nor right.

14. In right triangle ABC shown below, AB = 18.3 and BC = 11.2.

What is the measure of ∠A, to the nearest tenth of a degree?

1) 31.5
2) 37.7
3) 52.3
4) 58.5

Answer: 1) 31.5

You are given the opposite and the adjacent sides. You do not have the hypotenuse, nor are you asked to find it.

You need to use the tangent ratio to answer the problem.

tan A = opp/adj = 11.2/18.3

A = tan^-1(11.2/18.3) = 31.46...

You would get Choices (2) and (3) if you did either sine or cosine.

15. The maximum height and speed of various roller coasters in North America are shown in the table below.

Answer: 2) [see image]

Scatter plots do NOT have the points connected. Eliminate choices (3) and (4).

The table specifically says that Speed is the x variable and Height is the y variable. Choice (1) has that reversed. Eliminate it.

The correct choice is (2).

More to come. Comments and questions welcome.

More Regents problems.

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