Thursday, September 23, 2021

Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2013)



Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Algebra 2/Trigonometry Regents, January 2013

Part I: Each correct answer will receive 2 credits.


1. What is the equation of the graph shown below?



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

Answer: 2) y = 2-x


The graph shows exponential decay, which is given by the formula y = ax, where 0 < a < 1.

The base in this graph cannot be 2, but it could be 1/2, which is 2-1.

Checking the graph you can see that 2-(-1) = 2, 2-(-2) = 4, and 2-(-3) = 8.





2. Which ordered pair is a solution of the system of equations shown below?

x + y = 5
(x + 3)2 + (y - 3)2 = 53


1) (2,3)
2) (5,0)
3) (-5,10)
4) (-4,9)

Answer: 3) (-5,10)


A quick check will tell you that all four points are solutions for x + y = 5, so we can ignore that one and focus on the other equation.

(2 + 3)2 + (3 - 3)2 = 52 + 02 = 25

(5 + 3)2 + (0 - 3)2 = 82 + (-3)2 = 73

(-5 + 3)2 + (10 - 3)2 = (-2)2 + 72 = 53

(-4 + 3)2 + (9 - 3)2 = (-1)2 + 62 = 37





3. The relationship between t, a student’s test scores, and d, the student’s success in college, is modeled by the equation d = 0.48t + 75.2. Based on this linear regression model, the correlation coefficient could be

1) between -1 and 0
2) between 0 and 1
3) equal to -1
4) equal to 0

Answer: 2) between 0 and 1


It is a positive correlation, so the correlation coefficient must be a positive number between 0 and 1.

It wouldn't be negative, so choices (1) and (3) are eliminated. A coefficient of 0 means that there is no correlation at all, so there would be no equation that could model it.





4. What is the common ratio of the geometric sequence shown below?

-2, 4, -8, 16, …


1) -1/2
2) 2
3) -2
4) -6

Answer: 3) -2


To find the common ratio divide any term by the term before it.

4/(-2) = -8/2 = 16/(-8) = -2

Sn = a1(1 - rn) / (1 - r)
= 3(1 - (-4)8) / (1 - (-3))
= -39321





5. Given the relation {(8,2), (3,6), (7,5), (k,4)}, which value of k will result in the relation not being a function?

1) 1
2) 2
3) 3
4) 4

Answer: 3) 3


In a function, each input can have one and only one output. If k = 3, then the relation would contain (3,6) and (3,4), and would fail the vertical line test.

When you enter 3 into a function, it can't sometimes have 6 as its output and sometimes have 4 as its output.




More to come. Comments and questions welcome.

More Regents problems.

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