Test-Taking Strategies
The Math Section
The Math section tests various concepts in numbers and operations, algebra, geometry, data analysis, statistics, and probability. The first thing you need to do to succeed on the Math section is study up on the concepts that are tested.
Once you’ve got the basic math down, you’ll need a plan to get you through test day. We’re going to highlight seven strategies that will help achieve your target score on the Math section.
Plugging in Numbers for Variables
This is a very valuable strategy you can use on the Math section, especially on long, hard-to-follow word problems. Essentially, it turns an algebra item into a simple numbers and operations item by using numbers instead of variables.
We’ll use an algebra item to show you how this strategy works:
5. Fred had 3b bicycles for sale at a price of d dollars each. If x is the number of bicycles he did NOT sell, which of the following represents the total dollar amount he received in sales from the bicycles?
(A) (3bx)d
(B) (x + 3b)d
(C) (3b x)d
(D) (3dx)b
(E) 3 + bxd
Let’s assume you can’t translate the word problem into a mathematical expression. Choose some numbers for the variables, as follows:
b = 2
d = 4
x = 3
The numbers don’t have to be realistic. They just need to be easy to calculate.
Now substitute those numerical values for the variables in the stem—change this item from algebra to a very logical arithmetic problem:
1. Fred has 3(2) bicycles = 6 bicycles total.
2. Each costs $4.
3. He did NOT sell 3 of them.
4. Therefore, he sold 6 – 3 = 3 of them for $4 each.
5. 3 bicycles$4 per bicycle = $12 received in sales from the bicycles.
Okay, fine, you say. Now what? How does that help me? You know the correct answer choice is going to be the one that spits out 12 when you use b = 2, d = 4, and x = 3. Let’s see how it goes. Start with A:
A: (3bx)d = (323)4 = 72
Incorrect; eliminate.
B:(x + 3b)d = (3 + 32)4 = 36
Incorrect; eliminate.
C:(3b x)d (32 – 3)4 = 12
D:(3dx)b = (34 – 3)2 = 18
Incorrect; eliminate.
E: 3 + bxd = 3 + (234) = 27
Incorrect; eliminate.
If you are running out of time, after you eliminated A and B, you can guess from among the other three choices and beat the wrong-answer penalty.
Plugging Numbers from the Answer Choices Back into the Stem
Here’s another powerful way to turn algebra into basic math:
2. If x + 2x = 5xx + 20, then x =
(A) –20
(B) –10
(C) 5
(D) 10
(E) 20
Let’s say you can’t do the algebra. No worries. With this method, start with C’s value and plug it into the stem’s equation. Why start with C? Because SAT answer choices are always listed in numerical order, from largest to smallest or smallest to largest. You’re starting with the middle value. If it doesn’t work, you often (but not always) know whether you need a bigger or smaller number—that is, you know whether to go to B or to D next. Sit tight: this will become clear as we run through the example.
Okay, now we’re ready to go:
Choice C says x = 5. So x + 2x = 5xx + 20 becomes:
5 + (25) = (55) – 5 + 20
5 + 10 = (25) – 5 + 20
15 = 40
Well, that’s not true. Eliminate C.
In this example, it’s not easy to tell whether you need a bigger or smaller number, so let’s try B. Don’t worry about knowing whether to go up or down with this method. Sometimes it’ll be obvious to you. Other times, just choose one or the other. Remember, you can always bail after eliminating even one choice.
Choice B says x = –10. So x + 2x = 5xx + 20 becomes:
–10 + (2–10) = (5–10) – (–10) + 20
–10 + (–20) = (–50) + 10 + 20
-–30 = –20
Well, that’s not true, either, so eliminate B.
Note that if you are running out of time, you can guess from among the three remaining choices and beat that wrong-answer penalty.
But let’s try choice A.
Choice A says x = –20. So x + 2x = 5xx + 20 becomes:
–20 + (2–20) = (5–20) – (–20) + 20
–20 + (–40) = (–100) + 20 + 20
–60 = –100 + 40
–60 = –60
Bingo. That’s a true statement. Choice A is correct.
When in Doubt, Draw It Out
Many geometry items will ask you to imagine a figure. Whenever a figure is described but not shown, you should use information in the stem to draw a picture to orient yourself.
When in Doubt, Write It Out
A related point is that you should write out your math work as much as possible. Don’t sacrifice accuracy for speed. Particularly on algebra items, writing out each step helps to prevent careless errors.
What Do I Know? Where Do I Need to Go?
In general, when confronted with a Math item, ask yourself these two questions. Let’s look at the bicycle item again. What do we know? Where do we need to go?
5. Fred had 3b bicycles for sale at a price of d dollars each. If x is the number of bicycles he did NOT sell, which of the following represents the total dollar amount he received in sales from the bicycles?
What do we know?
  • Fred had a certain number of bikes he was selling.
  • He was selling them at a certain price in dollars.
  • He didn’t sell all of his bikes.
Where do we need to go?
  • Some algebraic expression that tells us how much he made, in dollars, from the bikes he did sell.
Asking these two questions separates the known from the unknown, which is, after all, a large part of mathematical reasoning, especially in algebra. It focuses your attention on what steps you’ll need to take to get from the known to the unknown, which is especially helpful for multistep, complex items.
The best advice is: use your calculator rarely. If you could answer every item on the SAT by just plugging numbers into your calculator, you wouldn’t be allowed to have a calculator during testing. The fact that you’re allowed to have a calculator on the test day tells you two things:
  1. This is not a test that’s designed to assess your ability to calculate directly—especially because anyone can buy a calculator or use a computer in the real world.
  2. If you see a way to solve an item that requires heavy calculations, you’re probably missing the point. Don’t run to your calculator just because you have a little machine to lean on. Think before you start hitting buttons.
Usually, your calculator will come in handy to solve a step in your solution to an item. But overall, you’ll have to use your brain to do most of the reasoning.
Because grid-ins don’t include answer choices, you won’t be able to plug in numbers as easily. Furthermore, you won’t be able to make an educated guess because there are no answers to eliminate. The good news is that there is no wrong-answer penalty on grid-ins. Always put something down, even if you’re not certain it is the correct answer. If worse comes to worst, you will get zero points for that item.
If you follow a few simple rules with grid-ins, you’ll never mess up on this section. Grid-ins:
  • Can’t have negative answers. If you get a negative answer, you made a mistake.
  • Can have more than one correct answer. If you find two or more answers for the item, pick one and move on.
  • Cannot accommodate mixed numbers. The scanning machine reads as , so change your mixed numbers into either proper fractions or decimals.
  • Cannot accommodate a zero before a decimal point, so instead of gridding in 0.34, grid in .34.
With decimals—especially repeating decimals—don’t round up. Just start with the leftmost bubble and fill in all four spaces. You’ll never be penalized for not rounding up but you might be penalized for rounding up inappropriately.
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