Know What You Have to Learn
The new SAT Math can be overwhelming with all the different concepts tested. However, the range of concepts tested on the SAT is nowhere what you’d encounter in the high school textbooks you use. Really speaking, the SAT features the highlights: algebra, basic trig, basic geometry (no proofs!) and lots and lots of word problems (many with graphs).
For a good sense for the range and depth of what you will need to know to score well on the new SAT, check out the SAT Test Prep App, which includes over 20 of the top math lessons. It includes math lessons for the new Algebra, Problem Solving and Data Analysis sections as well as Geometry, Trigonometry and Complex Equations. The app is available for both iPhone and Android.
Identify Your Weaknesses
Amongst the concepts I listed above you are likely to be more familiar with some than others. You’ll want to make sure to budget your time so that you address these weaknesses. For instance, if you really hate the whole visual element that’s inherent to most geometry questions, practicing geometry is a great place to start. You might even notice that within this subject, you have a certain weaknesses. So if circles really got your goat, start drilling these so that you can become stronger. Then, pick off some other weak areas in geometry before moving on to another topic altogether.
Let Concepts Incubate
It’s a good idea to flit around from concept to concept, sort of like a bumblebee daubing flowers. The idea is that you don’t want to focus only on one concept and let the other concepts wilt (to continue the flower metaphor). By coming back to, say, circles, a few days after initially studying them, you’ll find that you’ll get a little bit better. Take five days off circles. Then, when you come back, you’ll feel even more comfortable with the concepts you learned. That’s because the brain has had time to let them sink in.
In the meantime, of course, you’ll be able to study other concepts from math and other sections, concepts you’ll be able to return to after a few days. Once you’ve revisited a concept several times, you can space out the intervals much more. Remember, you’ll be doing lots of drilling of question sets containing a random mixture of problems (see “Mixed practice sets” below). This way you are reinforcing these concepts.
Don’t Dive too Deeply
This is similar to the concept above. Many think that they have to become really good at one thing; I will be the master of the polynomial! However, on a standardized test, which tests many different concepts, such intense preoccupation with one concept, will hurt you. It’s like a bee sitting on one flower all day long. You might get one humongous flower, but the rest of the garden will be anything but luxuriant.
You also should remember that the SAT typically tests these concepts at a high-level. Usually having a decent grasp of the concept means that you will likely have a fair shot of getting question right. It is better to prep from range of concepts, then to overly focus on a few.
Identify the Different Kinds of Errors You Make
I have a bad habit of moving through a math section too quickly and either misreading what the question is asking or bubbling in the wrong answer (I know: silly me). When I take a deep breath at the beginning of a section and say to myself, “Don’t rush; read carefully”, I’m anticipating this kind of mistake.
Likewise, you should do the same. Be as specific as possible when figuring out the kind of careless errors you make. That way you can best avoid them. Of course, not all errors are careless. You might commonly fall into a trap or be prone to misinterpreting a certain question. If so, go back and look at such questions. Again, the more specific you can be (“hmm…it seems that on long word problems I spend too much time reading the unimportant stuff and not the part that actually helps me answer the question”), the sooner you’ll improve.
Learn the Language of the SAT Math
Speaking of word problems, the SAT has a certain way of framing and asking questions. Call it “math lingo”. Phrases such as “find y in terms of x” or “the polynomials f(x) and g(x) are defined above”. Learning which kind of verbiage causes you to stumble and learning what these phrases mean will make you able to work through questions more efficiently (often, you’ll see that what might seem like a convoluted or vague phrase is actually describing something pretty straightforward once you look at the explanations).
Build up Your Endurance
You might follow all of the above, but find that when you take an SAT practice test your focus wanes far before the end of the section. Don’t worry! This is an issue for many and it is also an issue you can work on. How? Doing practice drills that push your endurance.
Think of it like a marathon, it is also about pacing yourself. Experiment with taking 10 to 15-second breathing breaks. Do they help you recharge your batteries? Taking these breaks every two to three questions and they might help and don’t worry. If they are working, then the time they do cost is easily redressed by the fact that you are less likely to hit a wall, where you are reading and re-reading the same line of text because your brain is fried.
Do Mixed Practice Sets
This tip goes back to the idea of not diving into one concept too deeply. Remember, the SAT doesn’t test concepts at a very deep level. It is more an overview of important concepts. The test writers are determining whether you remember the basic gist of a math concept (trigonometry is a good example of this).
By doing mixed practice sets, you are always exposing yourself to the same range of concepts you see test day. This is important because on the real test you’ll be jumping around from one concept to another, in no particular order. Just as importantly, by doing mixed practice sets, you’ll be able to reinforce concepts and ideas that you’ll likely have encountered earlier in your prep. At first, of course, much will seem new. You might want to do fewer mixed practice sets. But as you drill and get more concepts under your belt, you should move increasingly to mixed practice sets.
Take Practice Tests Each Week
Taking an entire test will reveal a lot about your abilities that you might not have noticed by just doing numbers 1- 8 above. You’ll become aware of how well you pace, how well you are able to focus and countless other insights. It’ll also give you a good idea of concept areas you might want to revisit.
For instance, you might have not really bothered with imaginary numbers, but there on the test, on the third question, you saw an imaginary number. You froze and that reaction affected you performance on the rest of the section.
Become a Mental Math Whiz
Recently, we asked Magoosh students who took the March 2016 test about their experience. One theme that emerged was that quite a few said that they wished they were more used to doing mental math when working out questions.
If you’ve forgotten, one section does not allow for a calculator. While you can work out 14 x 7 on scratch paper, knowing how to do this quickly in your head will save you a lot of time, and you won’t get easily distracted from the problem at hand. With more difficult sums, 11/9 + 5/2, you should be adept with pencil and paper.
To become a whiz is not easy. But doing something as simple as adding a number to itself till you get past 200 is a fun little exercise when you are waiting for the bus, or for your twitter feed to load. For example, counting to 200 by 14s will give me 14, 28, 42, 56, 70, 84, 98 (14 x 7), 112, 126, 140, 154, 168, 182, 196, 210. Check your calculator by diving the final number by 14. If it equals an integer, you did it successfully. If not, you’ll want to try again. This will help you with adding and it will also help you recognize patterns (oh, I see, 14 x 7 = 98).
Another fun game to see which digits between 1 and 100 you can arrive at by using just 1, 2, 3, and 4 only once and by using any or all of the following: +, -, multiplication, division, exponents, square roots, and factorials. (Factorials, which likely won’t show up on the test but are nonetheless good for mental math work the following way: whatever number is next to the factorial, “countdown” by multiplying each number next to each, e.g., 3! = 3 x 2 x 1, 4! = 4 x 3 x 2 x 1 = 24.)
Can you end up with 99 using this method? What about 100? (see answer below). Here are some other numbers between 1 and 100 to show you how it works. By the way, these are just solutions I came up with. See if you can come up with your own. Remember: no calculator!