# 5 Common Pitfalls to Avoid on SAT Math

Sure, multiple choice questions on the SAT are easy, right? Did you ever notice when practicing SAT multiple choice questions that even when you get an answer that you think is correct (but is wrong), your incorrect answer is a choice! Repeat – your wrong answer is one of the choices! Aarrgghh. This instills unfounded confidence in your math ability and you move along thinking you aced that question.

Here, we’ll help you avoid some common math mistakes.

Mistake 1 – Incorrectly distributing a negative sign through parentheses.

$(x^2-3)-(-3x^2+5)$

Which of the following expressions is equivalent to the one above?

The common mistake students make looks like this:

Many students correctly distribute the negative sign to the $-3x^{2}$, but forget to distribute the negative to the 5. The SAT people know this and your answer, once simplified, will look like $4x^2+2.$  There it is! Choice (B). Wrong! To avoid making this mistake, a good rule of thumb is to quickly double check your math anytime you distribute a negative sign through an expression in parentheses. This hardly takes any time at all and will help you avoid this error.

The correct answer is Choice (A).

Mistake 2 – Incorrectly dealing with undefined values.

Which of the following is a value of $x$ for which the expression  $\frac{-3}{x^2+3x-10}$  is undefined?

A)     -3

B)     -2

C)     0

D)    2

For this one, the common mistake the hasty student makes is assuming, “Hey, I can’t have a zero in the denominator so the answer must be Choice (C). Done.” Not so fast. True, you can’t have a zero in the denominator. But, if you substitute 0 into $x^2+3x-10$ the result is -10, not 0. So, we can eliminate Choice (C).  This question is basically a factoring question. The correct answer should look like this:

The correct answer is Choice (D).

Mistake 3 – Incorrectly squaring a binomial.

Which of the following is equivalent to  $(a+\frac{b}{2})^{2}$  ?

This problem should be a fast and relatively easy one to solve. But once again, the hasty student makes a common mistake that looks like this:

$(a+\frac{b}{2})^{2}&space;=&space;a^{2}+\frac{b^{2}}{4}$

A quick glance at the answer choices and the student bubbles in Choice (B). Here again, that choice is wrong. What happened? The key fact to remember when squaring a binomial is that you will get a middle term. The correct way to approach this problem is by the FOIL method – multiply First terms, Outer terms, Inner terms, and Last terms, then combine like terms.

$(a+\frac{b}{2})^{2}&space;=&space;(a+\frac{b}{2})(a+\frac{b}{2})$$=&space;a^{2}+\frac{ab}{2}+\frac{ab}{2}+\frac{b^{2}}{4}$$=&space;a^{2}+ab+\frac{b^{2}}{4}$The correct answer is Choice (D).

Mistake 4 – Using the wrong total in a proportion/probability problem.

The table above shows the results of a research study that investigated the therapeutic value of vitamin C in preventing colds. A random sample of 300 adults received either a vitamin C pill or a sugar pill each day during a 2-week period, and the adults reported whether they contracted a cold during that time period. What proportion of adults who received a sugar pill reported contracting a cold?

The common mistake students make is using the wrong total for the proportion. The number of people who received the sugar pill who reported contracting a cold is 33. This number corresponds to the numerator of the proportion. Many students incorrectly will write the proportion as $\tfrac{33}{300}$, using the grand total 300 as the denominator. This fraction reduces to $\tfrac{11}{100}$, giving the incorrect answer as Choice (D).

For a problem of this type we need to use the idea of conditional probability. We are trying to find the proportion of adults who received a sugar pill that reported contracting a cold. As soon as we see that the group of people we’re interested in is those who received a sugar pill (the condition) we should immediately highlight the row for Sugar Pill. The numbers in this row are the only numbers we’ll use to solve this problem. Of this group, the number of people who reported contracting a cold is 33, but the total of this group is the row total 150. Thus, the correct proportion is $\tfrac{33}{150}$ which reduces to $\tfrac{11}{50}$.

The correct answer is Choice (B).

Mistake 5 – Calculating the Wrong Decay Factor.

A radioactive substance decays at an annual rate of 13 percent. If the initial amount of the substance is 325 grams, which of the following functions f models the remaining amount of the substance, in grams, t years later?

In an exponential decay problem of the form $y=ab^{x}$, the common mistake is to incorrectly calculate the decay factor $b$. Many students see that the rate of decay is 13%  and assume that the base is 0.13 leading to the incorrect answer Choice (B).

For exponential decay, the main thing to remember is the exponential decay equation gives the amount left after a certain amount of time. In order to calculate the correct decay factor we need to subtract the annual decay rate from 1, so the correct value of $b$ is $1-.13=.87$.

The correct answer is Choice (A).

Hopefully, you will now be on high alert for these common pitfalls! Happy studying!