How to Crush a Standardized Math Test: SAT/ACT, AP/IB, GRE/GMAT, JEE, etc.

by Justin Skycak on

First, you need extensive and solid content knowledge. Then, you need to work through tons of practice exams for the specific exam you're taking. This might sound simple, but every year, countless people manage to screw it up.

I used to tutor SAT/ACT math prep and AP Calculus BC prep.

One thing that initially shocked me was the number of students & parents who thought there were some “secrets” or “tricks” I could quickly teach them to make up for a lack of foundational math content knowledge.

The #1 rule in test prep is that if you want to get a high exam score, then you must have extensive and solid knowledge of the underlying content.

Yes, many standardized exams include nonstandard problem types that go beyond typical course content.

But to have any chance of solving a nonstandard problem type, you need to be able to solve standard problems that are “sort of, kind of” similar, or that at least exercise the component skills you’ll be piecing together in the nonstandard problem.

Yes, the nonstandard problem is going to require some sort of mental leap.

But the longer of a mental bridge you’ve built outwards in that direction, the shorter the distance you have to leap, and the higher the chance that you’ll make the rest of the way across.

And the way you build this mental bridge is by having a complete knowledge base of all the standard types of problems.

∗     ∗     ∗

…Okay, now it’s time for a change-up.

The truth is that there is a grain of truth behind all the “secrets” and “tricks” nonsense.

The #2 rule in test prep is that extensive and solid knowledge of the underlying content does not automatically guarantee a high test score.

Suppose you’re solid on all your standard course content knowledge. That’s great, but that’s not sufficient to crush a test full of nonstandard problems.

What you need to do next is take tons of practice exams for the specific exam you’re planning to take.

It’s best if the practice exams are real exams from the past, or at least come directly from the organization who puts out the exam.

This is where lots of people screw up by trying to improve their general problem-solving skills without reference to the particular exam they’re going to be taking.

To go back to the mental leaps / bridge analogy, lots of people think they have to improve their jumping ability. But the problem is that there’s a lack of empirical evidence that you can even train the jumping ability.

So the failure mode that people fall into is they just try to solve a bunch of really hard problems thinking that it will somehow carry over and increase their mental jumping ability.

It’s not a bad idea on surface level, and I would love if things actually worked out like that, but that sort of approach just turns out not to be supported by cognitive science research.

I’ll quote, for instance, Sweller, Clark, and Kirschner (2010):

• "the research suggests that we can teach aspiring mathematicians to be effective problem solvers only by providing them with a large store of domain-specific schemas. Mathematical problem-solving skill is acquired through a large number of specific mathematical problem-solving strategies relevant to particular problems. There are no separate, general problem-solving strategies that can be learned."

So, what you need to do instead is just continue building bridges as best you can in the specific direction of the nonstandard problem types that you might expect to see on the exam.

∗     ∗     ∗

I know, I know, you can’t predict exactly what’s going to be on the test.

But what you can do is train yourself on the same statistical distribution that the test problems are going to come from.

You do that by going through as many practice exams as you can – ideally real exams from the past, or at least practice exams that come directly from the organization who creates the exam.

(If, for whatever reason, those resources aren’t available, you should try to find practice exams from some other organization that has a good reputation for matching its problem types up really well with the real exam.)

Whenever you miss a question on a practice exam (or answer the question with a low degree of confidence), you should refer to the solution, identify your mistake, and immediately work it out again correctly, and then the next day you try working out the same problem unassisted – and you keep repeating this process until you’re able to work it out unassisted. And then you try again after a delay of several days or a week.

Basically, you’re using the practice exams to do spaced repetition on the problems that you missed. And once you get through all the practice exams, you go through another round. You keep this process going until the actual exam.

At this same time, though, you also need to be doing active problem-solving reviews on your standard course content to make sure that you don’t get rusty on any of it.

At the time you take the exam, you want to be 100% solid and 100% fresh on all your standard course content AND all the nonstandard problem types covered in the practice exams.

∗     ∗     ∗

Scheduling

If you’ve read this far, then you’re probably interested in more specifics.

As a rule of thumb, I would recommend that at a minimum, students finish learning all their standard course content knowledge at 6 weeks prior to their exam, and go through at least 6 practice tests leading up to the exam.

About 1.5 hours of prep per day: 30-45 minutes of review problems in their course, and 45-60 minutes taking / grading / re-attempting practice tests.

The practice tests need to be timed, but they can be broken up into smaller increments (e.g. if the whole test is 2 hours long, you could construct a 30-minute segment by doing every problem number that’s a multiple of 4).

In the week before the exam I would probably up that to 2 hours of prep per day, spending extra time on practice tests.

∗     ∗     ∗

Another thing to note:

When a student is solid on their course content knowledge and starts taking actual practice exams, they will probably be surprised at how low their score is initially.

This is normal and it just takes a bit of exposure to get used to the time limit, question types, and phrasing of the exam questions.

I’ve prepped numerous students for the AP Calculus BC exam, which is graded on a 1-5 scale (5 being the best), and typically, even students who end up getting a 5 start out getting a 2 or maybe a 3 on their first practice exam.

By their second exam, they’d typically get a 3 or 4, and then a solid 4 or maybe just barely a 5 on their third exam, and then a more solid 5 on their fourth exam, and then they’d get deeper and deeper into 5 territory on their fifth and sixth practice exams.

∗     ∗     ∗

Related article: What To Do Leading Up to a Standardized Exam Like AP Calculus BC

Tags: