January 2018 Common Core Algebra I Regents, Part 2

The following are some of the open-ended questions from the recent January 2018 New York State Common Core Algebra I Regents exam.

January 2018 Algebra I, Part II

Each correct answer is worth up to 2 credits. Work must be shown.

25. On the set of axes below, graph f(x) = |x - 3| + 2.

Answer: See below. You could use a graphing calculator to find a table of values, or you could realize that the parent functions has been translated 3 units to the right and 2 up. (In other words, the vertex is at the point (3, 2).) The slope on the left is -1 and the slope on the right is 1, so finding the other points on the line is simple.

26. Determine all the zeros of m(x) = x² - 4x + 3, algebraically.

Answer: Pretty straight forward. Set the expression equal to zero and factor it. The factors of +3 that add up to -4 are +3 and +1.
If you didn't see that, you can always use the Quadratic Formula. It's longer, but it will give you the answer.

x² - 4x + 3 = 0
(x - 3)(x - 1) = 0
x - 3 = 0 or x - 1 = 0
x = 3 or x = 1

27. The distance traveled is equal to the rate of speed multiplied by the time traveled. If the distance is measured in feet and the time is measured in minutes, then the rate of speed is expressed in which units? Explain how you arrived at your answer.

Answer: The rate of time is measured in feet per minute.
Because distance = rate * time,
Then rate = distance / time, which gives you feet / min.

28. Determine if the point (0,4) is a solution to the system of inequalities graphed below. Justify your answer.

Answer: (0, 4) is NOT a solution to the system. It is the point on the y-axis where the two boundary lines intersect. However, one of those lines is broken, which means that those points are NOT point of the solution to the system. (0, 4) is on the broken line.

Note that each box in the scale is 2 units. If you put a point on the fourth line, which would be (0, 8), you would probably have lost a point.

29. If the zeros of a quadratic function, F, are -3 and 5, what is the equation of the axis of symmetry of F? Justify your answer.

Answer: If the zeroes are at -3 and 5, then the axis of symmetry has to be right in the middle of them. Average the two numbers:
x = (-3 + 5) / 2 = 2 / 2 = 1. x = 1 (Note: "equation" means you MUST include "x = ")

One longer way would be to find the equation of the function and then the axis of symmetry:
f(x) = (x + 3)(x - 5) = x² - 2x - 15.
Formula for Axis of Symmetry is x = -b / (2a)
x = -(-2) / ((2)(1)) = 2 / 2 = 1. x = 1.

30. The formula F_g = (GM₁M₂)/r² calculates the gravitational force between two objects where G is the gravitational constant, M1 is the mass of one object, M2 is the mass of the other object, and r is the distance between them. Solve for the positive value of r in terms of F_g, G, M₁, and M₂.

Answer:

F_g = (GM₁M₂)/r²
F_g r² = (GM₁M₂)
r² = (GM₁M₂) / F_g
r = SQRT ( (GM₁M₂) / F_g )

31. At Mountain Lakes High School, the mathematics and physics scores of nine students were compared as shown in the table below.

State the correlation coefficient, to the nearest hundredth, for the line of best fit for these data.
Explain what the correlation coefficient means with regard to the context of this situation.

Answer: Put all the values into a list and then do a linear regression.
You will see that the correlation coefficient r = .92.
In this example, it means that there is a strong positive correlation between math and physics scores.

32. The graph of the function f(x) = ax² + bx + c is given below.

Could the factors of f(x) be (x + 2) and (x - 3)? Based on the graph, explain why or why not.

Answer: Yes. Those are the factors because (x + 2) means that there is a zero at -2 and (x - 3) means that there is a zero at +3, which is what the graph shows.

End of Part II

How did you do?
Questions, comments and corrections welcome. Typos happen.