Avoid the Pitfalls

Common Math Mistakes

Watch the operations. Read the problems carefully and pay attention to what the test writer wants you to do. Be sure you don’t divide when you should be multiplying. Make sure you are converting word problems to the appropriate math operation.

Forgetting PEMDAS. Remember PEMDAS. The order of operations is very important on the SAT. We wouldn’t want Aunt Sally to have to say, “Please excuse my dear niece/nephew!”

Percents of percents. When the question asks you to calculate a final percent by doing two percentages (either two increasing, or two decreasing, or one of each) from an initial unspecified value, be sure the second calculation is based on the result of the first calculation. For example, if a price went up 10% and then another 20%, the final price is not 130% of the original price. It is 132%. (100 times 1.10 times 1.20=1.32 or 132%)

Weighted averages. When calculating averages of unequally sized groups or rates, be sure you “weight” the information you are given. Do not treat the two groups equally. If a group of 5 has an average of 82 and a group of 15 has an average of 90, the average for all 20 is NOT 86. It is 88.

Proportions and Ratios: Be careful to read the question and answers to compare the right groups (parts and whole). Some questions compare parts to parts. Others compare a part to the sum of other parts. Others compare a part to the whole.  Be sure when you set up the proportion to cross-multiply that you put the corresponding units on each side of the equals sign.

Interval Counting. Remember the number of values between two values on the number line is the difference of the two values PLUS one. For example, how many interstate mile markers are there between Orlando (mile marker 272) and Ft. Lauderdale (mile marker 58)? Remember this question doesn’t ask how many miles it is. Think about a number line. If you start at 0 and stop at 5, how many integers are there? 6. Now subtract 0 from 5. Why is there a difference? In the first case, you are determining the number of values. In the second case, you are calculating the difference. If I print pages 17 through 20, how many pages did I print? It isn’t the difference, 3. It’s 4. Count them to prove it to yourself.

Assuming the Sequence. Sometimes on line questions the order of the points is not indicated and there is no diagram provided. Be sure to draw ALL POSSIBLE sequences before you answer the question. For example, draw the possibilities of “X, Y, and Z are points on a line. X is 1 unit from Y and Y is 2 units from Z. How many can you find? There are 4 possibilities: XYZ, ZYX, ZXY AND YXZ.

Length’s Effect on Area. For squares and circles doubling the length of a side or radius DOES NOT double the area. For example, a square with a side of one has one-fourth the area of a square with a side of two. The same is true for a radius of one versus a radius of two. You can do the whole calculation, when confronted with these problems. You can also do something very clever–square the ratio of the lengths. For example, if you triple the side of a square the area becomes nine times as large!

Forgetting the “Reference Information.” Remember that at the beginning of every math section there is a box full of VERY useful formulas. You will find that there are very few formulas or constants that you’ll need for the test that aren’t either in that box or included in the question. If you get stumped on a geometry problem, look at the information in the box to see if there is a formula or diagram that has pieces in common with the question. Oftentimes, that technique will get you started in the right direction.  The Wizard refers to “Reference Information” to the “Cheat Sheet” for a reason.

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