Can someone explain why both answers A and B are not valid on the metacarpal problem? If the line indicates a linear relationship between these two values, and the choice of axis is arbitrary, it seems to me you could just as well predict one from the other as vice versa.
You're right that the graph contains the data for both A and B (and for that matter C and D as well) but the question refers to what the slope means. Here we have a Y = MX + B graph. M indicates how much Y changes for every 1 unit change in X.
The SAT is a money-making machine created by College Board - they are a business first and foremost. Yes, they measure basic academic aptitude, but past a certain level they are not very useful in ascertaining real academic potential.
Can someone explain why both answers A and B are not valid on the metacarpal problem? If the line indicates a linear relationship between these two values, and the choice of axis is arbitrary, it seems to me you could just as well predict one from the other as vice versa.
Sure, you could just as well predict one from the other. But the question asks "What is the following is the best interpretation of the _slope_ of the line of best fit in the context of this problem?", and you are expected to interpret "slope" in the usual jargon sense (as the the ratio of vertical change to horizontal change, rather than vice versa). (By "vertical" and "horizontal" here, I mean with respect to the g…
This then seems like less of a test of math ability and more of a test of whether or not you have effectively absorbed the jargon and conventions around certain math concepts. Maybe that's what they want, but it doesn't really seem like problem solving at all.
> It is fine—good, even—to ask students to carry out these tasks, but in many cases these are skills that students unfortunately haven’t yet mastered. If they aren’t being taught to think about graphs that way, let alone articulate their reasoning in that matter, chances are only the smartest (or well-prepared) teens will be able to arrive at the correct answer under the time and emotional pressure of the test. But i…
The original point of the SAT was to measure "aptitude" in order to identify students might perform well in college, but did not have good opportunities to demonstrate that in high school. This was before things like "aptitude" and "intelligence" became dirty words.
Steven Pinker argues for admissions based on standardized tests, in part because he contends that the current Ivy League admissions process suffers from "eye-of-newt-wing-of-bat mysticism that jerks teenagers and their moms around and conceals unknown mischief.":
In the 3rd question, if the fee were 6%, would the right answer be 7075 or 7076? I don't know the high school rules of rounding. Are you allowed to round to a number that doesn't satisfy the question? Fortunately they picked values where it is not ambiguous, but that question could be really nasty.
7075.471698 technically rounds to 7075. Less than 0.5, round down. 0.5 or greater, round up.[1] But saying "what's the least" and then "round your answer" at the same time is silly. If you ask a student "each bus holds 10 people; how many buses do you need to move 32 people?" the answer is 4. I would hate to be asked to "round" that answer. 7075 rupees is too few; 7076 is the first whole number that is "enough." The…
I'm glad you pointed this out to your teacher. It is worth noting, though, that if it weren't for the arbitrary "If it's exactly halfway inbetween, you should just round it up" rule taught as received wisdom in school, your teacher would've been on stronger ground. And it is reasonable that they were attempting, in their way, to convey (or even fully come to terms with themself) the understanding that the nearest integers to a value are always also among the nearest integers to the nearest multiples of 0.1 to that value (and all the generalizations of this); it's just that sometimes there are other nearest integers to nearest multiples of 0.1 as well.
Sure, you could just as well predict one from the other. But the question asks "What is the following is the best interpretation of the _slope_ of the line of best fit in the context of this problem?", and you are expected to interpret "slope" in the usual jargon sense (as the the ratio of vertical change to horizontal change, rather than vice versa). (By "vertical" and "horizontal" here, I mean with respect to the g…
This then seems like less of a test of math ability and more of a test of whether or not you have effectively absorbed the jargon and conventions around certain math concepts. Maybe that's what they want, but it doesn't really seem like problem solving at all.
See my other response, but I don't think you're giving the question enough credit. The other responses don't mention the fact that the line would likely be different if we swapped the variables. The question tests both whether you know what a line of best fit represents, and also whether you know that the correlation in one direction is not necessarily equal to the correlation in the other direction. This is something that could be covered in an algebra class with a unit on linear regression. I remember seeing a demonstration and explanation of this in mine.
Seems like the math portion is becoming less about math and more like an MBA reading comprehension test.
It's actually become less about wrote manipulation of symbols and more about a deeper understanding of actual math concepts. The latter is, indeed, harder.
One thing rote learning is good for is how to spell in languages whose pronunciation and spelling are inconsistent, like English.
I know what that graph-line question is trying to ask, but I can't figure out those possible answers.
The answers are so ungrammatical and mystifying that it almost seems like the designers were trying to kill the test on purpose. The "correct" answer is this: The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone ...as far as I can tell, the answer written for sentient humans would be something like: As the length of the metacarpal bone increases, so does height. But my…
I think their answer is perfectly sensible and perfectly grammatical. It's also clearly correct according to even the most basic notion of slope as rise over run. I honestly don't see the issue with this question. Not only does your answer not fit grammatically, but it's also less precise.
Sure, you could just as well predict one from the other. But the question asks "What is the following is the best interpretation of the _slope_ of the line of best fit in the context of this problem?", and you are expected to interpret "slope" in the usual jargon sense (as the the ratio of vertical change to horizontal change, rather than vice versa). (By "vertical" and "horizontal" here, I mean with respect to the g…
This then seems like less of a test of math ability and more of a test of whether or not you have effectively absorbed the jargon and conventions around certain math concepts. Maybe that's what they want, but it doesn't really seem like problem solving at all.
The definition of slope is an extremely basic fact from middle school math. This isn't exactly crazy trivia.