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 2014
Part I: Each correct answer will receive 2 credits.
6. A school cafeteria has five different lunch periods. The cafeteria staff wants to find out which items on the menu are most popular, so they give every student in the first lunch period a list of questions to
answer in order to collect data to represent the school. Which type of study does this represent?
1) observation
2) controlled experiment
3) population survey
4) sample survey
Answer: 4) sample survey
The list of questions is a survey. Since it is only given out in the first lunch period, it isn't a population survery. It's only a sample.
7. Which relation is both one-to-one and onto?
Answer: 2)
One-to-one means that each input has one output and it is a distinct output from the other inputs. If it was graphed, it would pass a horizontal-line test. Onto means that every element in the domain maps to an element in the range and vice versa. That is, there are any leftover elements.
Choice (1) is not one-to-one. Both h amd m map to 2. Eliminate it.
Choice (2) is both one-to-one and onto. This is the answer.
Choice (3) is not one-to-one. Both h and m map to 2, and r has 2 outputs. Eliminate it.
Choice (4) is not onto. Nothing maps to the number 1. Eliminate it.
3. Max solves a quadratic equation by completing the square. He shows
a correct step:
What are the solutions to his equation?
1) 2 + 3i
2) -2 + 3i
3) 3 + 2i
4) -3 + 2i
Answer: 2) -2 + 3i
Two-step equation with imaginary numbers. Take the square root and subtract. It's similar to solving quadratics with irrational numbers in Algebra. (Imagine that the -9 was +8. Solve it in a similar manner.)
x + 2 = +3i
x = -2 +3i
Once you realize that the square root of -9 is 3i, you should have eliminated Choices (3) and (4).
9. Which expression represents the total number of different 11-letter arrangements that can be made using the letters in the word “MATHEMATICS”?
1) 11!/3!
2) 11!/8!
3) 11!/(2! + 2! + 2!)
4) 11!/(2! * 2! * 2!)
Answer: 3) 11!/(2! * 2! * 2!)
The number of ways to rearrange ABCDEFGHIJK is 11! However, the word MATHEMATICS has repeated letters, two Ms, two As, two Ts, which means that some of the rearrangements will be duplicates, and we must eliminate those.
We do that by dividing by (number of times letter is repeated)! And we have to do that for each distinct letter that is repeated. In other words, don't divide by 6!, which isn't an option, by instead we divide by 2! * 2! * 2!.
10. If $5000 is invested at a rate of 3% interest compounded quarterly,
what is the value of the investment in 5 years? (Use the formula
A = P(1 + r/n)nt, where A is the amount accrued, P is the principal,
r is the interest rate, n is the number of times per year the money is
compounded, and t is the length of time, in years.)
1) $5190.33
2) $5796.37
3) $5805.92
4) $5808.08
Answer: 3) $5805.92
The formula is given. Substitute all the values and put the expression in your calculator. Note that quarterly means 4 times per year, so n = 4.
Evalute this: 5000(1 + .03/4)^(4*5) = 5805.920...
More to come. Comments and questions welcome.
More Regents problems.
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