SAT Math Prep II: Exponents, Ratios And Percentages

In the first part of our SAT Math Prep series, we went over some tips for tackling the math portion of the SAT, as well as a practice problem for the Heart of Algebra section. But that's only one of three major concepts covered on the math SAT, and if you want to get a top grade, there are two more concepts you'll have to master: Passport to Advanced Math and Problem Solving and Data Analysis. This article will lead you through a practice problem for each section.

The Passport to Advanced Math section involves working with equations that include powers or exponents, whether solving them, interpreting them or graphing their solutions.

A practice problem involves the function:

\(g(x) = ax^2 + 24\)

Where a is a constant. The value of g(4) = 8. So what is the value of g(−4)?

a) 8
b) 0
c) −1
d) −8

Try to solve this problem yourself before reading on for the solution. The key here is thinking about what information you've been given and what you haven't been given. You can't work out the whole equation explicitly because you don't know what constant a is. So how can you solve the problem?

The solution involves following what happens when you insert the given value for x into the equation. You know that when this is done with x = 4, the result is 8. But the x value in this equation is squared. Everything in the equation is the same as the result you know, except the value that is squared is −4 instead of 4. However, −4² = 4² = 16. So the result of the x part of the equation is the same, and the rest of the equation is the same.

So g (−4) = 8 and the answer is a).

The final (and less interestingly-named) major section of the SAT math exam involves proportions, ratios and percentages, as well as many topics involving working with data in tables or graphs.

A practice problem in this area involves both reading data from tables and calculating percentages. Questions like this – which use skills from more than one area – are very common on the SAT. This problem involves the data:

\(\def\arraystretch{1.5}
\begin{array}{c:c:c:c:c}
& Algebra \;1 & Geometry & Algebra \; 2 & Total \ \hline
Female & 35 & 53 & 62 & 150\
\hdashline
Male & 44 & 59 & 57 & 160 \
\hdashline
Total & 79 & 112 & 119 & 310
\end{array}\)

These are the results of a survey which asked male and female students which math classes they were enrolled in. Which category accounts for approximately 19 percent of the survey respondents?

a) Females taking geometry
b) Females taking algebra II
c) Males taking geometry
d) Males taking algebra I

Try to find the answer by yourself before reading on for the solution. Here the key is working out what information you actually need to answer the question. Re-read the question and look at what the question is asking you for.

The solution comes after you note that what you really need to know is which group is about 19 percent of the total 310 participants. You could work out the percentages individually (e.g. what percent of the total group are females taking geometry and so on), but it's easier to find what proportion of the total you're looking for. You need to find 19 percent of 310.

This is easy to do. Convert 19 percent into a decimal: 19 % / 100 = 0.19. Then simply multiply this by the total to get:

\(0.19 × 310 = 58.9\)

All you have to do to finish the problem is find this number on the table. There are 59 males taking geometry. Even though this isn't exactly 19 percent, the question says "approximately." So you can be confident that the answer is c).

In math, the best way to learn is often by doing. The best advice is to use practice papers, and if you make a mistake on any questions, work out exactly where you went wrong and what you should have done instead, rather than simply looking up the answer.

It also helps to work out what your main issue is: Do you struggle with the content, or do you know the math but struggle to answer the questions in time? You can do a practice SAT and give yourself extra time if needed to work this out.

If you get the answers right but only with extra time, focus your revision on practicing solving problems quickly. If you struggle with getting answers right, identify areas where you're struggling and go over the material again.