Better Math Solutions (than what the College Board will give you)

The College Board would like you to believe that they are on your side. To help convince you of this, they have provided many resources to help you prepare for the SAT. One essential resource: actual practice SATS. You can get them here. Taking real practice tests is certainly the key element in an effective prep plan. So it is nice of the College Board to provide you with them. And they even give you answers and solutions. How kind of them!

But one way to tell that they are not sincerely trying to helping you is by examining those math solutions. Yes, the solutions are scrupulously correct. A bit dry maybe. Sometimes stark and intimidating, but nevertheless, quite correct.

But there is an omission so glaring, so disingenuous, that the only explanation is that they want to claim the appearance of being helpful while still maintaining their own agenda. (World domination? Eventually. But for now, they would like to be the official end-of-high-school test in every state.)

If they were honest, the solutions would open with something like this:

Every SAT problem can be solved by a formal application of the mathematical concepts and procedures you have been learning in high school. We believe that this knowledge is important for success in many fields of study in college. So we are presenting solutions that exercise those skills in that formal way you have seen. If you learn to solve these problems in this particular way, your score on the SAT will certainly improve.

I believe the College Board would not object to that last paragraph. But here is what I wish they would say next:

But we also recognize that many of the problems on the SAT can be solved in alternative ways, using less formal (but more creative) mathematical approaches. We present those solutions here as well. Learning to solve problems in this manner will also help your score to improve. While these methods occasionally seem to circumvent some of the required math knowledge, they also promote a flexibility and creativity that will serve you well in your future studies.

I am emphatically not “anti-math” in any way. I like algebra! But if we want to help people to improve their SAT scores, we should not be holding back this information. And if you happen to be a little shaky in the formal methods of algebra, that is hard to fix in a shorter (say a few months) time frame. Learning another way to play can really open some doors for you. There is no way that the College Board does not know about these methods. But you see no evidence of that in their solutions. I guess they want to help you improve but only if you are willing to do it their way.

To illustrate what I am talking about, I am going to provide a few examples from the most recent practice test, #10. (I have a longer set of these for tests 1 – 8 here and I will try to update the collection soon.)

I hope that is a large enough sample to convince you that these approaches are potentially useful. I have seen them work a substantial number of times on every SAT that has ever been released. Also, it is good to have more than one way to approach a question. That gives you a way to stay in the game even when you don’t feel you know the “right” way to do a problem.

From Test #10, Section 3:

Again, I am not saying that these are the fastest solutions. Please don’t feel that you have to email or tweet at me with your algebra. These are ALTERNATIVE solutions! (And not every question has one…that I have found yet!)

1.You could try each answer, plugging in until you find one that works.

2. Ignore the algebra and just play around until you find how many weeks it will take: You after the initial $60 payment, you still owe $240. At $30 per week, it will take 8 weeks. Aha! Now plug in w=8 into each answer choice…

3. From the table, we can get a sample value. For example, when x = 10, the answer is supposed to come out to $21.89 . So try x = 10 in each answer choice. If you don’t get $21.89, it’s wrong.

5. Make up a number for x…like x=4. You get the square root of 144 which is 12. Now put x=4 into each answer choice….

6. Seriously, carefully trying each answer is quicker and easier than doing the algebra…

9. Go to the graph and find a point that is on the line. I used (-2,-2). That means that we can put x=-2 and y=-2 into the equation and it should work. Only one does! (If more than one worked, I would try another point.)

11. Draw a neat diagram of a circle centered at (5,7) with a radius of 2. Find any point on that circle. For example, 2 units to the right is (7,7). Then, see which equation works when you use x=7, y=7…

14. Again, trying their answers is a lot easier than doing the algebra. But this question is obnoxious. It targets the students who do not know that the square root symbol means the POSITIVE number that squares to give you what you want.

20. I cannot believe that they did not mention this solution: you could solve for u and t. That seems to require algebra, but you can also do it by playing with numbers. We need numbers whose sum is 5 and difference is 2. Let’s see: 4+1=5 but 4-1=3…too big. 2+2=4 but 2-2=0…too small. Uh oh. Fractions? 3.5 + 1.5 = 5. 3.5-1.5 = 2. Nice. You still have to do the arithmetic though…

OK that’s all for now. I will eventually post more of these for Section 4 and for Test #9. And I am pondering a way to turn this into a group project. I know a good number of fellow SAT nerds. So here is a heads-up to them: I may be reaching out soon to see if you want to help build a collection of these in some free, publicly available format. Stay tuned…