College Board released a bunch of sample questions this week for the new PSAT and SAT, which will make their debuts in October 2015 and March 2016, respectively. Over the next few days, I’ll be making posts working through each question, a few at a time, and commenting on them when I feel like I have something insightful to say.

In this post, I’ll deal with questions 1 through 5 in the “calculator permitted” section. See questions 6 through 11 here, 12 through 15 here, 16 through 20 here, 21 through 26 here, and 27 through 30 here.

Question 1 (link)

On the one hand, this is as easy as it gets. On the other hand, it already feels like a departure from what you see on the current SAT. This kind of question, where a scenario is explained in English and then the tester has to identify the right equation (or, in this case, inequality) in the answer choices, feels much more ACT-ish. But whatever. Stuff like this is what you can expect from “Heart of Algebra” questions.

The main thing this question is testing is whether you, the tester, can read that the “recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg),” and recognize that you want your answer to say, “≥ 1000,” not just “> 1000.” That’s because if a 20-year-old has exactly 1,000 mg of calcium in a day, he meets the recommended daily intake. He doesn’t need any more.

I doubt many folks reading this would be fooled by C or D, but it’s not hard to see why they’re in there as traps.

Question 2 (link)

Oh for crying out loud. There are 107 words in that question. 107! Ugh.

This is a question that doesn’t require you to be able to calculate anything. It just requires you to know, on a very superficial level, how a margin of error works.

Basically, you need to know that if you want to figure out the mean hours spent reading for the population of psych students at this university, you can ask a small sample of that population and arrive at a pretty good estimate of the actual mean of the whole population, within some margin of error. If you want to be more sure, you ask more people from the same population. The more people you ask, the smaller your margin of error. This makes sense if you think about it: say I wanted to know the average height of 100 people. I could feel pretty OK about my estimate if I only measure, say, 20 of them. I’d feel even better if I measured 60 of them. If I measured 99 of them, I’d be super confident that my mean is close tot he actual mean—even if the 100th person is a 7-foot giant, he can’t bring the average up very much! The larger the sample, the more sure you can be that the sample mean is close to the actual population mean.

So C is the answer because it increases the number of people in the experiment without changing the population from psych students to students from all across the university.

Question 3 (link)

More superficial statistics knowledge being tested here. We’re three questions into the “calculator allowed” section and we haven’t had to calculate anything yet. Given that this graph will be the basis of the next three questions, that means we’ll be through 5 out of 30 questions in this exercise without so much as needing to turn our calculators on. Make a mental note of that.

What the question is saying is that there’s a correlation between the length of a person’s metacarpal bone and that person’s height. It’s not a perfect correlation, which is why all the dots aren’t right on the line of best fit, but it’s a correlation. All the question’s asking you to do is count the dots that are more than 3 inches from the line in either direction. There are 4 dots that are at least 3 cm off the line of best fit, so the answer is B.

Things to watch out for on a question like this:

  • Axis scale. Every horizontal line represents 1 cm on this graph, like you’d expect it would, and that’s the axis you need to pay attention to for this question since it asks about outlier heights. The vertical lines represent 0.1 cm, though, and I bet a future question will test that somehow…Math_Sample_Question__5___SAT_Suite_of_Assessments
  • Dots they hope you miss. In this case, there’s that one all the way on the bottom left. Did you see that one? Not everyone will. The answer choice you’d expect to be there to catch the people who miss that dot, 3, isn’t there, but I don’t think we can take that as a sign that the new test won’t do that kind of thing with regularity.

Question 4 (link)

More on the same graph. Here, they’re asking about slope. Ah, slope! Our old friend! I hope we’ll be seeing more of you!

Slope, as you know, is a measure of rise over run. Here, given the axes, it’s a measure of height increase over metacarpal length increase. That’s precisely what choice A describes. If you’re having trouble distinguishing between choices A and B (choices C and D aren’t very tempting) pay attention to units. The metacarpal length axis only increases by 1 cm, total. From this graph, it’s easy enough to say that height would be expected to increase about 18cm with a 1cm increase in metacarpal bone length. It would not be easy to predict from this data how much longer someone’s metacarpal bone would be if they were 1 cm taller.

Question 5 (link)

Still on this silly graph. I was expecting these questions to get harder as they go, but this might be the easiest of the bunch! All you need to do is trace the graph. 4.45 cm metacarpal is going to be in the middle of 4.4 and 4.5—trace that up to the line of best fit, then look left to the height axis and see where you are. You’re right on 170!

Math_Sample_Question__5___SAT_Suite_of_Assessments 2

The danger here, of course, is that you misread the scale on the bottom axis, and there is the 169 there in the answer choices to make you feel good about your mistake if you trace the 4.4 line up by mistake. Still, if you can read a graph, you’ll have no problem nailing this question.


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