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.
16. For y = 3 / ( SQRT(x - 4) ), what are the domain and range?
1) {x | x > 4} and {y|y > 0}
2) {x | x > 4} and {y|y > 0}
3) {x | x > 4} and {y|y > 0}
4) {x | x > 4} and {y|y > 0}
Answer: 1) {x | x > 4} and {y|y > 0}
The domain cannot less than 4 because the radical would be undefined. The domain cannot contain 0 because the fracton would be undefined.
The range will go to infinity as x decreases close to 4. As x increases, the demonimator increases, so the fraction will approach zero, but it can never hit the x-axis.
17. A math club has 30 boys and 20 girls. Which expression represents
the total number of different 5-member teams, consisting of 3 boys and 2 girls, that can be formed?
1) 30P3•20P2
2) 30C3•20C2
3) 30P3+20P2
4) 30C3+20C2
Answer: 2) 30C3•20C2
If a combination problem, not a permutation problem. The order the students are chosen does not matter.
The Counting Principle tells you that the number of ways to choose 3 boys and 2 girls is equal to the number of ways to choose 3 boys TIMES the number of ways to choose 2 girls.
18. 8 What is the product of the roots of x2 - 4x + k = 0 if one of the roots is 7?
1) 21
2) -11
3) -21
4) -77
Answer: 3) -21
If one of the roots is 7, the factors are (x - 7)(x - n). This means that (-7)(-n) = 7n = k. Also the sum (-7) + (-n) = -4.
So -n = 3, and n = -3
The factors are (x - 7)(x + 3). The product of the roots is (7)(-3) = -21.
19. In DEF, d = 5, e = 8, and m∠D = 32. How many distinct triangles can be drawn given these measurements?
1) 1
2) 2
3) 3
4) 0
Answer: 2) 2
Three is not possible. It's one, two, or zero.
If you have a 32 degree angle and a point 8 units away, you can draw an arc from that point that is 5 units long. It will the other line, f, in two places, so two triangles can be formed.
See the image below:
20. Liz has applied to a college that requires students to score in the top 6.7% on the mathematics portion of an aptitude test. The scores on the test are approximately normally distributed with a mean score of 576 and a standard deviation of 104. What is the minimum score Liz must earn to meet this requirement?
1) 680
2) 732
3) 740
4) 784
Answer: 2) 732
If you look at the chart of the normal distribution curve, you will see that the top 6.7% of the data will be 1.5 standard deviations away from the mean.
The mean is 576, and the standard deviation is 104.
Calculate 576 + 1.5(104) = 732
Note that Choice (1) is 576 + 1.0(104) and Choice (4) is 576 + 2.0(104), if you misread the chart.
More to come. Comments and questions welcome.
More Regents problems.
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