Some strategies to maximize your new SAT math score

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Ballparking

One way to eliminate answers on the Math Test is by looking for ones that are the wrong size, or that are not "in the ballpark." Although you can use your calculator on the following question, you can eliminate without doing any calculations.

25. Joy plants three rows of corn in her garden. The row on the south edge of the garden receives more sunlight than the row on the north edge of the garden. Therefore, the corn on the north edge of the garden is 30% shorter than that on the south. If the corn on the south edge of the garden is 50 inches tall, how tall is the corn on the north edge of the garden, in inches?

A) 30

B) 33

C) 35

D) 65

Here's How to Crack It

The question states that the corn on the north edge is shorter than the corn on the south edge, which is 50 inches tall. You are asked to find the height of the corn on the north edge, so the correct answer must be less than 50. Eliminate (D), which is too large. Often, one or more of the bad answers on these questions is the result you would get if you applied the percentage to the wrong value. To find the right answer, take 30% of 50 by multiplying 0.3 by 50 to get 15, then subtract that from 50. The corn on the north edge would be 35 inches tall, which is (C).

Read the Full Question

You never know what College Board is going to decide to ask for, so make sure to always read the full question before solving. Underline what you are actually solving for and any key words you think you might forget about as you solve the question. Then, try to Ballpark before you solve.

7. If 16x ? 2 = 30, what is the value of 8x ? 4 ?

A) 12

B) 15

C) 16

D) 28

Here's How to Crack It

First, see if you can eliminate answers by ballparking, which can also work on algebra questions. To go from 16x to 8x, you would just divide by 2. Dividing 30 by 2 gives you 15, so 28 is way too big. Eliminate it. The correct answer is not likely to be 15, either, because that ignores the ?2 and the ?4 in the question.

To solve this one, add 2 to each side of the equation to get 16x = 32. Divide both sides by 2, which gives you 8x = 16. But don't stop there! The full question asks for 8x ? 4, so (C) is a trap answer. You have to take the last step and subtract 4 from both sides to find that 8x ? 4 = 12, which is (A).

One Piece at a Time

When dealing with complicated math problems, make sure to take it one little piece at a time. If you try to do more than one step at a time, especially if you do it in your head, you are likely to make mistakes or fall for trap answers. After each step, see if you can eliminate any answer choices.

Let's give it a try.

9. A paper airplane is thrown from the top of a hill and travels horizontally at 9 feet per second. If the plane descends 1 foot for every 3 feet travelled horizontally, how many feet has the plane descended after 5 seconds of travel?

A) 3

B) 10

C) 15

D) 20

Here's How to Crack It

There are a few things going on here. The plane is traveling horizontally, and it is also descending. Start by figuring out how far it travels horizontally. It moves in that direction at 9 feet per second for 5 seconds, so it moves horizontally 9 × 5 = 45 feet. It descends 1 foot for every 3 traveled horizontally. If it goes 45 feet horizontally, it will descend more than 3 feet, so eliminate (A). Now see how many "3 feet" are in 45 feet—for each one of them, the plane will descend 1 foot. 45 ÷ 3 = 15, so the plane descends 15 feet, (C).

You may also have noticed that all the numbers in the question are odd. This makes it unlikely that the answer would be 10 or 20, which are even. If you see things like that, use them as opportunities to eliminate.

Here's another example.

6. (5jk2 + 5j2 - 2j2k) - (jk2 + 2j2k + 5j2)

 

Which of the following is equivalent to the expression above?

A) 4jk2
B) 4jk2 - 4j2k
C) 5j2k4 - 10j4k
D) 8j2k3 + 7j2k - 5j2

Here's How to Crack It

Start with one tiny piece of this ugly looking question. The first set of parentheses starts with a term containing jk2. Check in the second set of parentheses for the same combination of variables and exponents. The first term there matches, so the first tiny step to take is 5jk2 - jk2 = 4jk2. There are no other terms with jk2, so the correct answer must contain 4jk2. Eliminate (C) and (D). Now you have a fifty-fifty chance of getting it right, so you could guess and go. Or you could do one more step to determine if the answer is (A) or (B). The difference between the two answers is the - 4j2k term, so focus on the terms in the expression that contain j2k. In the first set of parentheses, you have -2j2k, and then you subtract the 2j2k term in the second set of parentheses. -2j2k - 2j2k = -4j2k, so the correct answer is (B).

Write Stuff Down

As you solve questions in small pieces, write down the steps. Don't keep track of things in your head—your test booklet is there for your notes. If a figure is given, write the information from the question right on it.

Here's an example.

Lines l and m extend from two sides of the regular hexagon as shown above. If A = 120, what is the value of B, in degrees?

A) 30

B) 60

C) 90

D) 140

Here's How to Crack It

Sometimes, Ballparking can even help on geometry questions. Not all pictures are drawn to scale, so don't assume the figure is exact. You can, however, use what the question tells you about the figure to estimate angles, line lengths, areas, and points on graphs in the xy-plane.

If this picture is drawn to scale, the angle with measurement B looks to be acute, making (A) or (B) a good bet. The question says the hexagon is "regular," which means that all the interior angles have the same measure, and the drawing looks like this is the case. Start by marking the angle that is A° as 120° on the figure. This angle looks like 120°, so B can't possibly equal 90° or 140°. Eliminate (C) and (D). To find the exact value of B, you need to find the measure of the angle opposite it, which is one of the angles from the triangle. The angle of the upper left corner of the triangle is formed by drawing a straight line from the angle that is A°, or 120°. There are 180° in a straight line, so the upper left corner of the triangle measures 180 - 120 = 60°. Label that on the figure as well. The fact that the hexagon is a regular one means that all the interior angles are 120°, so label the one next to the bottom corner of the triangle. Since this corner of the triangle is formed in the same way as the upper left corner, the bottom corner also measures 60°. Label that. There are 180° in a triangle, so the upper right angle is also 60°. The angle measuring B° is opposite this, so B is 60° and (B) is correct.

By the time you're done, your figure should look like this:

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