Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
June 2012
Part I: Each correct answer will receive 2 credits.
1. In a baseball game, the ball traveled 350.7 feet in 4.2 seconds. What was the average speed of the ball, in feet per second?
1) 83.5
2) 177.5
3) 354.9
4) 1,472.9
Answer: 1) 83.5
To find the unit rate of speed in feet per second divide the number of feet by the amount of seconds:
350.7 / 4.2 = 83.5
Common sense should tell you that if something travels a little over 350 feet in a little over 4 seconds, then in just ONE second, it should go about 1/4 of the distance. Choices (3) and (4) are just ridiculous. Choice (2) isn't much better, but at least it's smaller.
2. A survey is being conducted to determine if a cable company should
add another sports channel to their schedule. Which random survey
would be the least biased?
1) surveying 30 men at a gym
2) surveying 45 people at a mall
3) surveying 50 fans at a football game
4) surveying 20 members of a high school soccer team
Answer: 2) surveying 45 people at a mall
Bias means that you are more likely to find people who are predeisposed to give one particular answer over another. It also comes from focusing too much on one particular subgroup of people.
In Choice (1), the survey would only be asking men of their opinion, and in particular, men who are most likely athletic.
In Choice (3), the survey is specifically asking fans if they want more sports while they are attending a sporting event.
In Choice (4), the survey is again asking people involved with sports, but this time they are all of high school age, and there aren't even that many of them.
The only problem with Choice (2) is that 45 people may not seem like very many, but you will find a more random collection of people to ask.
3. The quotient of (8x5 - 2x4 + 4x3 - 6x2) / (2x2) is
1) 16x7 - 4x4 + 8x5 - 12x4
2) 4x7 - x6 + 2x5 - 3x5
3) 4x3 - x2 + 2x - 3x
4) 4x3 - x2 + 2x - 3
Answer: 4) 4x3 - x2 + 2x - 3
Divide each coefficient by 2 and reduce each exponent by 2. An exponent of 1 can be left out because it means one factor of x, which is just x. An exponent of 0 means that there are NO factors of the variable, so leave the variable off.
If should be obvious that Choice (1) is silly. It's the only one that even looks like that. Despite the word "quotient" and the fraction in the problem, Choice (1) shows the product of the two expressions.
Choice (2) is similarly wrong because it divided the coefficients but it added the expoents, instead of reducing them.
Choice (3) is incorrect because it ends with "2x - 3x", which you should wonder, why weren't those like terms combined? Because they weren't supposed to be like terms. If the original exponents were 5, 4, 3, 2, and each is reduced by 2, then you should have 3, 2, 1, 0 in your answer. But -3x has an exponent of 1.
Choice (4) is correct because -3x0 is -3.
4. Marcy determined that her father’s age is four less than three times her age. If x represents Marcy’s age, which expression represents her father’s age?
1) 3x - 4
2) 3(x - 4)
3) 4x - 3
4) 4 - 3x
Answer: 1) 3x - 4
Three times her age, x, is 3x. Four less than that means take four away from that or subtract 4 from that amount. That is 3x - 4.
4 - 3x is "obviously" wrong because her father would be less than 4 years old. In fact, if Marcy was over the age of 1, her father's age would be a negative number.
5. A set of data is graphed on the scatter plot below.
This scatter plots shows
1) no correlation
2) positive correlation
3) negative correlation
4) undefined correlation
Answer: 2) positive correlation
As the x values get bigger, the y values generally get bigger. If you were to draw a line of best fit through the data, it would have a positive slope.
More to come. Comments and questions welcome.
More Regents problems.
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