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, June 2013
Part I: Each correct answer will receive 2 credits.
16. Which value of r represents data with a strong positive linear
correlation between two variables?
1) 0.89
2) 0.34
3) 1.04
4) 0.01
Answer: 1) 0.89
A strong positive correlation means that the value of r will be close to 1 WITHOUT GOING OVER 1. This is because the number 1 represents a 100% correlation, which would be the data is perfectly linear.
Choice (1) is Strong. Choice (2) is weak. Choice (3) is impossible. Choice (4) would suggest that there is no correlation between the two variables at all.
Which problem involves evaluating 6P4?
1) How many different four-digit ID numbers can be formed using
1, 2, 3, 4, 5, and 6 without repetition?
2) How many different subcommittees of four can be chosen from
a committee having six members?
3) How many different outfits can be made using six shirts and four
pairs of pants?
4) How many different ways can one boy and one girl be selected
from a group of four boys and six girls?
Answer: 1) How many different four-digit ID numbers can be formed using 1, 2, 3, 4, 5, and 6 without repetition?
The permuation 6P4 refers to selecting four objects from a group of six when the order they are selected is important.
Choice (1) matches that description. This is the answer.
Choice (2) is a Combination problem because the order the members are selected is not important. (If the first person were, say, head of the committee, and the second one the assitant, etc, then it would be different.)
Choice (3) is an example of the Counting Principle, where 6 * 4 = 24 outfits can be made.
Choice (4) is an example of the Counting Principle, where 4 * 6 = 24 pairs of one boy and one girl can be selected.
18. Which equation is represented by the graph below?
1) (x - 3)2 + (y + 1)2 = 5
2) (x + 3)2 + (y - 1)2 = 5
3) (x - 1)2 + (y + 3)2 = 13
4) (x + 3)2 + (y - 1)2 = 13
Answer: 4) (x + 3)2 + (y - 1)2 = 13
The equation of a circle is given by the formula: (x - 2)2 + (y - 5)2 = r2, where (h, k) is the center and r is the radius. Notice that there are MINUS signs in the formula for (h, k).
The radius isn't obvious, and you could figure it out using Distance formula or Pythagorean Theorem. Or you could see that it is somewhere between 3 and 4, so r2 must be between 9 and 16. It could be 13, but it couldn't be 5.
Aside from this, the four choices each show a different center, so you only need to know the center to find the correct equation. The center is at (-3, 1). When you flip the signs you get (x + 3)2 + (y - 1)2.
19. If x = 3i, y = 2i, and z = m + i, the expression xy2z equals
1) -12 - 12mi
2) -6 - 6mi
3) 12 - 12mi
4) 6 - 6mi
Answer: 3) 12 - 12mi
Multiply the expressions, use the Distributive Property, and don't forget that i2 = -1.
xy2z
= (3i)(2i)2(m + i)
= (3i)(4i2)(m + i)
= (3i)(-4)(m + i)
= -12i(m + i)
= -12mi - 12i2
= -12mi + 12
= 12 - 12mi
20. An angle, P, drawn in standard position, terminates in
Quadrant II if
1) cos P < 0 and csc P < 0
2) sin P > 0 and cos P > 0
3) csc P > 0 and cot P < 0
4) tan P < 0 and sec P > 0
Answer: 3) csc P > 0 and cot P < 0
In Quadrant II, x is negative (x < 0) and y is positive (y > 0).
Remember that cos is x, so it should be negative, and sin is y, so it should be positive. Also, sec, is 1/cos, so it is negative, csc is 1/sin so it should be positive, tan is sin/cos, so it is negative, and cot is cos/sin, so it is negative.
You might want to make a little chart next to the question that you can refer to.
Choice (1) has the first part right and the second part wrong.
Choice (2) has the first part right and the second part wrong.
Choice (3) has both parts correct.
Choice (4) has the first part right and the second part wrong.
More to come. Comments and questions welcome.
More Regents problems.
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