kitchen table math, the sequel: PSAT Math

Sunday, June 19, 2011


Since my son gets to take the PSAT test as a sophomore in October, I thought that it would be a good place to start. Taking into account the warnings of "imposter" questions, I decided to get some real tests. Unfortunately, they are not offered by the College Board anymore, so I had to get them through Amazon. I got them the other day, and I thought I would share my initial impressions.

First, the real questions are so enlightening compared to a 3rd party PSAT test book I bought. The questions on the test are simple, ... but speed and accuracy are very critical. In the first section, you have 20 questions to answer in 25 minutes. Even though some questions are trivial, it still takes you time to read the question, check to make sure you are not jumping to conclusions (that it really is that simple), and then fill in the bubble. It's one thing to do this informally, but if you try to simulate a real test situation, the seconds slip by very quickly, and the pressure to rush increases.

Second, some of the questions go out of their way to try and trick you into the wrong answer. In one question, you find x+y, but they ask for the average of the two numbers. One answer is x+y and another is (x+y)/2. Clearly, the test is not just about your knowledge of math. I think there were 3 out of 20 questions where they went out of their way to mislead you.

Third, there are certain things you need to know very quickly, like the ratios of the sides of a 45-45-90 triangle and a 30-60-90 triangle. It's not good enough to know the Pythagorean Formula or to find the answer with trig. The formula is too slow and trig gives you the result in decimal, when the answer is in radical form.

One test example was to find the height of a equilateral triangle with a side length of 8. Right now. Fast. With trig, you get 8*sin(60) = 6.928, but the answer is in radical form. With the formula, you get sqrt(64 - 16) = sqrt(48). Quick, what is the reduced radical form? Your brain might start to freeze before you find 4*sqrt(3).

You really need to be able to immediately write down any other side of these common triangles given any one of the sides. One would like to use simple concepts and mathematical understanding to solve many things, but that's not what the test is all about. The test is all about saving seconds. I only finished it with about 3 minutes to spare.

I know this is nothing new to SAT wonks, but I hope to share some of the math shortcuts I find.


pckeller said...

Two quick notes:

If you can get the answer with trig, you can then change the answer choices to decimals and pick the ones that match. Often (but not always) the decimal approximations are provided next each answer choice.

Also, since your son is a sophomore, he has plenty of time to get comfortable with a TI89. and on a TI89, (64-16)^(1/2) does report back as 4root3.

But more importantly, now you see what I mean about using real materials to calibrate yourself!

debbie stier said...

Is the PSAT test any different than the actual SAT (besides the fact that it's shorter and does not have an Essay)?

I'd always heard they were the same, so I never went out of my way to get special PSAT materials (though I do have a few of the PSAT tests, including the one that my son took in 10th grade (he's going into 11th next year).

Should I be spending any time on College Board PSAT materials versus the SAT materials?

SteveH said...

As pckeller says, I think the real test is important to calibrate yourself. It seems to be all about speed. You need to save up time for the few strange questions they always throw at you.

I think it's important to know the 45-45-90 and 30-60-90 triangle ratios automatically. Anything that saves you time, but only costs a little in memorization, is important. I'm trying to figure out whether the PSAT expects you to know the ratios or whether they always give you the lengths of two sides of the triangles. They can't expect you to know trig.

A sample question in a non-official PSAT publication showed an equilateral triangle with an inscribed circle with a diameter of 2. You had to find the area of the triangle minus the area of the circle. It seems that you have to know the ratios.

There are issues of knowing the math, but there is also a big issue of getting the test done in time without getting what I will call time-brain-freeze. My son got it doing the triangle-circle area problem knowing that he only had 75 seconds to do the problem.

Jen said...

45-45-90 and 30-60-90 side ratios are part of the information given on the SAT (and PSAT).

I agree thought that kids need to be taught to recognize and use them quickly, so as to not waste their time.

Catherine Johnson said...

In one question, you find x+y, but they ask for the average of the two numbers.

I blew a question like that JUST THIS WEEKEND.

I was aghast.

Catherine Johnson said...

P Keller and/or PWN may feel differently, but having read C's test, I think they're the same.

As I understand it, the PSAT is made up of items from SAT tests.

I went over all of the math questions on C's PSAT a couple of weeks ago & was shocked at how difficult some of them were. I was assuming that the PSAT would include only the easy & medium questions from the SAT, but it had several 'hards.'

Catherine Johnson said...

A couple of years ago, Ed did one of the critical reading passages, which was on the subject of historiography. (For passers-by, Ed is a historian.)

He got everything right, but he didn't finish early, and he didn't find it simple.

Catherine Johnson said...


I'm going to start using that.

In fact, I think I'm going to invent a whole new ktm SUBJECT CATEGORY called time-brain-freeze.

There's another category, too, which maybe you can name for us....something along the lines of time-brain-stupid-freeze.

I'll have times, tearing through an SAT math test, where I simply do fantastically stupid things I wouldn't do if I weren't tearing through a test.

I don't 'freeze'; I suddenly lose about 30 years of math knowledge and a matching 30 points of IQ.

Stacey HL said...

:-) I think there's at least three different levels of performance on the SAT.
1. Knowledge - Do I know how to answer slope questions?
2. Reliability - Can I recognize and answer all the different flavors of slope questions that show up?
3. Speed - Can I answer these questions under time pressure?
All three are really different animals. I have my students work on them independently to build confidence. Then add two together. Then finally add all three.
I wish students would treat it like any other athletic skill. You need tons of PRACTICE to increase your skills. Alot of my top scoring students have taken at least 5 full practice tests and worked through about 5 more before they take the SAT.

SteveH said...

My reaction to almost any problem in math or computer programming is to slow down and be methodical. One of my first interviews after college was an all-day one at Ford. One of the interviewers, in a fancy office behind a big desk, asked me if I was a fast programmer or a slow programmer. I said I was a slow programmer. That's the right answer, of course.

I hate (!) being rushed. There may be some correlation between speed and ability, but not if the speed is due to remembering special cases. Right now, I'm making a list of all variations of circles and triangles. If you are given a 45-45-90 triangle with an inscribed circle, can you quickly find the height of the triangle given the radius of the circle? What if the triangle is inscribed in the circle?

Beyond some point, speed is not indicative of anything except practice. This is good because I can make a list of key shortcuts for my son to memorize.

Speaking of slopes, I asked my son if he remembered how to find the slope of a perpendicular line. It took him way too long. Another one was to find the X,Y midpoint between any two coordinate points. Just add the two values for X or Y and divide by two. I've seen some who will first find the difference, divide by 2, and then add that number to the first number. If there are negative numbers, some don't believe that adding and dividing by two works.

Catherine Johnson said...

Alot of my top scoring students have taken at least 5 full practice tests and worked through about 5 more before they take the SAT.


The other day, I was looking at what we've done and I was shocked at how much it adds up to.

We've done all the math sections in the Blue Book once; we've done some of the math sections in the Blue book twice; we've done all the math sections in Online Tests 1-5 once; we've done all 3 of PWN's diagnostic tests; we've done all 3 math sections in a friend of mine's SAT test; we've done all 3 math sections in the 2006 test....and we've done some of Chung....and the chapters on geometry and functions in Keller's book....and I learned how to set up absolute value inequality word problems from Elizabeth King's book....and lately I've taken to doing the math tests in Kaplan's SAT Math Workbook (which I find quite useful, fyi).

We've both jumped at least 70 points and are both, now, hovering around the 700 mark (at least in practice tests).

We've only done a few reading tests because C. is incredibly good at those. This morning I told him we should probably start doing some of them just **because** least, we ought to do the vocabulary sections.

Now we'll probably work our way through all the writing tests in BB & in the Online Tests -- or at least we'll keep going until C. is getting 100% correct, which may happen before we come to the end of the tests.

This has all taken place in very short time 'slots' over the course of one year. We did quite a lot of SAT work last summer; then we did virtually nothing all fall & not much in the winter. We've started up again in earnest this summer.

Although we didn't do much During the school year, we did keep our hand C. and I were getting **some** distributed practice over one year's time.

If I had it to do over again, I'd start my child doing a bit of SAT/ACT math, reading, and writing in middle school.

I wouldn't put tons of time into it in absolute terms. Instead I would put small amounts of time over a long stretch of time into SAT/ACT prep.

Catherine Johnson said...

This morning C probably broke 700 on the writing section (compared to the 660 he got on the real thing).

It looks like he's seeing parallelism pretty well; he also sees misplaced modifiers. He's good on verb tense.

He still doesn't see comma splices in the answer choices!

Catherine Johnson said...

My reaction to almost any problem in math or computer programming is to slow down and be methodical.


C loves to go as fast as possible, and it usually just means he's blowing the whole thing off.

When he takes a real test, he stays for the whole hour & doesn't rush. If he does finish early, he checks his work.

Catherine Johnson said...

I'm thinking...."hovering around 700" isn't quite right.

We've both, more than once, completed a math section with only one error, which puts you at 700.

But we also continue to end up with two errors in a section, which would be 6 errors overall.

It's probably more accurate to say that we both now have 'floors' at around 650.