Monday, June 26, 2017

June 2017: Common Core Algebra Regents, Part 1

The following are the questions and answers (and commentary) for part of the New York State Algebra Regents exam. If you have any questions or comments (or corrections), please add them in the Comments section.

My apologies for typos, particularly if they are in the questions, because then the answers are subject to change.

Answers to Part II can be found here.

Answers to Part III can be found here.

Answers to Part IV can be found here.

June 2017, Algebra I (Common Core), Part I

1.To keep track of his profits, the owner of a carnival booth decided to model his ticket sales on a graph. He found that his profits only declined when he sol between 10 and 40 tickets. Which graph could represent his profits?

(3) (image omitted). If his profits declined, then the y values will decrease in that interval -- in other words, the graph will go down, but only between x = 10 and x = 40. In choice (1), his profits are flat; that is, the remain the same. In choice (4), there is a decline, but it is in the wrong place.

2.The formula for the surface area of a right rectanguar prism is A = 2lw + 2hw + 2lh, where l, w, and h represent the length, width, and height, respectively. Which term of this formula is not dependent on the height?

(3) 2lw. There is no height, h, in the term.

3.Which graph represents y = SQRT(x - 2)?

(4) image omitted. Hopefully, this was an easy one. Besides the fact that you had a graphing calculator available to you, only one of the four graphs was a square root graph. The "- 2" under the radical shifts the graph two units to the right away from the origin.

You should make a note of this. Shifting functions is a common theme and may show up again

4.A student plotted the data from a sleep study as shown in the graph below. (image omitted)
The student used the equation of the line y = -0.09x + 9.24 to model the data. What does the rate of change represent in terms of these data?

(2) The average number of hours of sleep per day increases 0.09 hour per year of age.
Negative correlation. Sleep goes down as age goes up.

5. Lynn, Jude, and Anne were given the function f(x) = -2x2 + 32, and they were asked to find f(3). Lynn's answer was 14, Jude's answer was 4, and Anne's answer was +4. Who is correct?

(1) Lynn, only. Calculate (-2)(3)2 + 32 = (-2)(9) + 32 = -18 + 32 = 14.
The other two tried to solve for the zeroes of the function instead substitution 3 into the function.

6.Which expression is equivalent to 16x4 - 64?

(3) (4x2 + 8)(4x2 - 8). Difference of Squares rule.
If you multiply the choices, choice (1) will have a middle term of -64x2. Choice (2) doesn't even produce the terms in the original expression, plus it will have an x2 term. Choice (4) also yields incorrect coefficients, but no middle term.

7.Vinny collects population data, P(h), about a specific strain of bacteria over time in hours, h, as shown in the graph below. (image omitted)
Which equation represents the graph of P(h)?

(1) P(h) = 4(2)h. If you look at the graph, you'll notice that the y-values are doubling. It's exponential with a base of 2.
If you look at the choices, there is only one exponential function. The others are linear, quadratic and cubic (3rd power).
If you weren't sure if the graph was a parabola, then you could have looked at the y-intercept. In Choice (3), if you substitute 0 for h, then P(h) = 3(0)2 + 0.2(0) + 4.2 = 4.2. However, the graph shows a point at (0, 4), so choice (3) is incorrect.

8.What is the solution to the system of equations below?

y = 2x + 8
3(-2x + y) = 12

(1) no solution. Since "no solutions" and "infinite solutions" are options, it might make sense to rewrite the second equation in slope-intercept form first.

3(-2x + y) = 12
-2x + y = 4
y = 2x + 4

The first equation has a slope of 2 and y-intercept of 8. The second has the same slope but a different y-intercept.
That makes them parallel, and there will be no solutions.

9.A mapping is shown in the diagram below. (image omitted)
This mapping is

(3) not a function, because Feb has two outputs, 28 and 29. Each element in the domain (input) can map to only one element of the range (output). It is okay for Jan and Mar to both map to 31.

10. Which polynomial function has zeroes at -3, 0 and 4?

(3) f(x) = x(x + 3)(x - 4). Flip the signs. Which of the choices will give you a result of 0 when you enter each of those values?
Choices (1) and (2) don't work for 0 (you can stop checking). In choice (4), -3 - 3 =/= 0, nor is 4 + 4.

11.Jordan works for a landscape company during his summer vacation. He is paid $12 per hour for mowing lawns and $14 per hour for planting gardens. He can work a maximum of 40 hours per week, and would like to earn at least $250 this week. if m represents the number of hours mowing lawns and g represents the number of hours planting gardens, which system of inequalities could be used to represent the given conditions?

(1) m + g < 40, 12m + 14g > 250.
The hours must be less then or equal to 40. The amount he makes is the sum of the number of hours times the pay for those hours for each of these jobs, and that should be greater than or equal to 250.

12.Anne invested $1000 in an account with a 1.3% annual interest rate. She made no deposits or withdrawals on the account for 2 years. If interest was compounded annually, which equation represents the balance in the account after the 2 years?

(2) A = 1000(1 + 0.013)2. Interest increases your value, so choices (1) and (3) are right out. The percent 1.3% must be converted to a decimal, which is 0.013. The correct answer is (2).

13. Which value would be a solution for x in the inequality 47 - 4x < 7?

(4) 11. You could solve the inequality, or you can plug in the choices to see what works. Note that 47 - 4(10) = 7, it is not less than 7. Don't let them catch you on that.

47 - 4x < 7
-4x < -40
x > 10
11 is greater than 10.

14.Bella recorded data and used her graphing calculator to find the equation for the line of best fit. She then used the correlation coefficient to determine the strength of the linear fit.
Which correlation coefficient represents the strongest linear relationship?

(1) 0.9. The closer to 1 or -1, the stronger the correlation, the closer to a straight line you get.

15.The height, in inches, of 12 students are listed below
61, 67, 72, 62, 65, 59, 60, 79, 60, 61, 64, 63
Which statement best describes the spread of these data?

(4) 79 is an outlier, which would affect the standard deviation of these data.

16.The graph of a quadratic function is shown below. (image omitted)
An equation that represents the function could be

(4) q(x) = -1/2 (x - 15)2 + 25. The four choices are written in vertex form. The vertex is (15, 25).
Vertex form is y = a(x - h)2 + k. h = 15 and k = 25. (Note that the minus is part of the form.)

17.Which statement is true about the quadratic function g(x), shown in the table below, and f(x) = (x - 3)2 + 2?

(3) They have the same axis of symmetry. The vertex of the equation is (3, 2). The vertex of the table is (3, -5). These points are different but they both lie on the axis of symmetry x = 3.

18.Given the function f(n) defined by the following:

f(1) = 2
f(n) = -5f(n - 1) + 2
Which set could represent the range of this function?

(2) {2, -8, 42, -208, ...}. Frankly, the other choices make no sense. The first number has to be 2, so choices (3) and (4) are right out. Choice (1) is all positive, but the negative multiplier. Substitute 2, 3, and 4, and you'll get the rest of the numbers in the list.

19.An equation is given below.

4(x - 7) = 0.3(x + 2) + 2.11
The solution to the equation is

(1) 8.3

4(x - 7) = 0.3(x + 2) + 2.11
4x - 28 = 0.3x + 0.6 + 2.11
3.7x = 2.71 + 28
3.7x = 30.71
x = 8.3

20.A construction worker needs to move 120 ft3 of dirt by using a wheelbarrow. One wheelbarrow load holds 8 ft3 of dirt and each load takes him 10 minutes to complete. One correct way to figure out the number of hours he would need to complete his job is

(4) (image omitted)
Choice (4) is the only one where all the units cancel out, except for hours.

21.One characteristic of all linear functions is that they change by

(3) equal differences over equal intervals. In other words, a constant rate of change.

22.What are the solutions to the equation x2 - 8x = 10

(2) 4 + SQRT(26)

x2 - 8x = 10
x2 - 8x + 16 = 10 + 16
(x - 4)2 = 26
x - 4 = SQRT(26)
x = 4 + SQRT(26)

23.The formula for blood flow rate is given by F = (P1 - P2) / r, where F is the flow rate, P1 the initial pressure, P2 the final pressure, and r the resistance created by blood vessel size. Which formula can not be derived from the the given formula?

(3) r = F(p2 - p1). To solve for r, you would have to multiply the original equation by r, but then you would have to divide by F, which would put it in the denominator of a fraction.

24.Morgan throws a ball up into the air. The height of the ball above the ground, in feet, is modeled by the function h(t) = -16t2 + 24t, where t represent the time, in seconds, since the ball was thrown. What is the appropriate domain for this situation?

(1) 0 < t < 1.5. The domain is the t axis, so choices (3) and (4) are no good.
If you substitute t = 1.5, then h(1.5) = 0, which is the ground. Everything after that would yield a negative number meaning that the ball went below the ground.

End of Part I

How did you do?
Comments, questions, corrections and concerns are all welcome.
Typos happen.

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