This exam was adminstered in June 2022.
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June 2022 Algebra 2 Regents
Part I
Each correct answer will receive 2 credits. No partial credit.
9. Monthly mortgage payments can be found using the formula below,
where M is the monthly payment, P is the amount borrowed, r is the
annual interest rate, and n is the total number of monthly payments.
If Adam takes out a 15-year mortgage, borrowing $240,000 at an
annual interest rate of 4.5%, his monthly payment will be
(1) $1379.09
(2) $1604.80
(3) $1835.98
(4) $9011.94
Answer: (3) $1835.98
Depending upon the operation system of the calculator that you are using, you may what to evaluate this in parts. PARENTHESES ARE IMPORTANT if you're calculator doesn't handle fractions graphically. Look at the image below:
P = 240,000, the amount that was borrowed. r = 0.045, the rate expressed as a decimal. n is the number of MONTHS, which is 15 years times 12 months per year. You could use 180 instead of 15 * 12 in your calculator.
Working out the above problem gives you M = 1835.983..., which is approximately $1835.98, which is Choice (3).
Lucky for me, my incorrect answer wasn't there. I forgot to multiply 15 by 12 and got an answer that wasn't there on my first try.
If you used 4.5 instead of 0.045, you would've gotten $9000.00, which isn't quite Choice (4) but very close.
10. For all real values of x, if f(x) = (x - 3)2 and g(x) = (x + 3)2, what is
f(x) - g(x)?
(1) -18
(2) 0
(3) -12x
(4) 2x2 - 12x - 18
Answer: (3) -12x
Expand the binomials and subtract.
f(x) - g(x)
= (x - 3)2 - (x + 3)2
= x 2 - 6x + 9 - (x2 + 6x + 9)
= -12x
This is Choice (3).
11. If f(t) = 50(.5)(t/5715) represents a mass, in grams, of carbon-14 remaining
after t years, which statement(s) must be true?
II. The mass of the original sample is 50 g.
(1) I, only
(2) II, only
(3) I and II
(4) neither I nor II
Answer: (2) II, only
The initial sample is given as 50. Statement II is true.
If the mass was decreasing by 50% every year, then the exponent would be t not t/5715. The mass is actually decreasing by 50% every 5,715 years.
The correct answer is Choice (2).
12. Consider the graph of g and the table representing t below.
Over the interval [2, 4], which statement regarding the average rate
of change for g and t is true?
(1) g has a greater average rate of change.
(2) The average rates of change are equal.
(3) The average rate of change for g is twice the average rate of change for t.
(4) The average rate of change for g is half the average rate of change for t.
Answer: (4) The average rate of change for g is half the average rate of change for t.
The rate of change of g(x) over the interval [2,4] is (10 - 6)/(4 - 2) = 4/2 = 2.
The rate of change of t(x) over the interval [2,4] is (3 - -5)/(4 - 2) = 8/2 = 4.
The rate of change of t is twice that of g, which means that the rate of change of g is half the change of t.
This means that Choice (4) is correct.
Note: Choice (3) could not be correct because it would imply that Choice (1) was correct as well.
13. A parabola has a directrix of y = 3 and a vertex at (2,1). Which ordered pair is the focus of the parabola?
(1) (2,-1)
(2) (2,0)
(3) (2,2)
(4) (2,5)
Answer: (1) (2,-1)
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix.
The directrix is 3 - 1 = 2 units away from the vertex. So the y-coordinate for the focus is 1 - 2 = -1. This is Choice (1).
All of the values of h(x) have been multiplied by -1, which is Choice (3).
14. The heights of the 3300 students at Oceanview High School are approximately normally distributed with a mean of 65.5 inches and a standard deviation of 2.9 inches. The number of students at Oceanview who are between 64 and 68 inches tall is closest to
(1) 1660
(2) 1070
(3) 2244
(4) 1640
Answer: (1) 1660
If the standard deviation is 2.9, then 65.5 - 64 = 1.5, which is about 1/2 of one standard deviation. Also, 68 - 65.5 = 2.5, which is a little less than one standard deviation above the mean.
This means that we want approximately 19.1 + 19.1 + 15.0 = 53.2%
This is a little more than half. Choice (1) is a little more than one-half.
Choices (2) and (4) are less than one-half of the population. Choice (3) is closer to the 2/3 of the population, which is too much.
15. Which statement below about the graph of f(x) = −log(x + 4) + 2 is true?
(1) f(x) has a y-intercept at (0,2).
(2) −f(x) has a y-intercept at (0,2).
(3) As x → ∞, f(x) → ∞.
(4) x → −4, f(x) → ∞.
Answer: (4) x → −4, f(x) → ∞.
Put the function into your calculator and take a look. You will see that the y-intercept is neither 2 nor -2.
When x = 0, f(0) = -log(0 + 4) + 2 = -log(4) + 2, which is approximate -1.4 + 2 = 0.6. That means that -f(0) = -0.6. Eliminate Choice (1) and (2).
The graph will show you that function approaches infinity when x approaches -4. The function approaches negative infinity when x approaches infinity.
Choice (4) is the correct answer.
16. A researcher wants to determine if room-darkening shades cause people to sleep longer. Which method of data collection is most appropriate?
(1) census
(2) survey
(3) observation study
(4) controlled experiment
Answer: (4) controlled experiment
A controlled experiment will give the best results.
More to come.
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