Key concepts to master for the SAT

Apr 16, 2019 | Sharyland

The following 6 concepts are about 30% of the Math Content portion of the SAT

Ratios

A ratio is a numerical comparison that depicts the relationship between two or more values. When sitting and studying for the SAT, students should think of ratios in terms of their individual parts. This allows you to convert values into easy-to-manage fractions.

For instance, consider this recipe for instant soup: Each serving calls for two parts (or 2/3) water and one part (1/3) noodles, but you would like to make 15 servings of soup. How much water must you add? All you need to do is multiply 15 by 2/3, which yields a total of 10 cups. Recipes thus provide a simple way to practice with ratios.

To perform ratio calculations, students should be comfortable with multiplying and dividing fractions. Also note that ratios may be expressed in any of the following formats on the SAT: X to Y, X:Y, X/Y or X (when Y is equal to 1).

2. Percentages

First and foremost, students should remember that percentages are always relative to the number 100. This is true even for percentages that exceed 100 – 150 percent, for example, is 1.5 times 100.

To calculate any value related to percentages, students can memorize the following formula: IS/OF = %/100. “Is” represents a partial amount, such as 60 blue marbles, while “of” represents the total amount, such as 100 colored marbles. In this case, blue marbles represent 60 percent of all the marbles.

Students must also be comfortable with cross-multiplying to find missing values in the formula. Food nutrition labels are a practical outlet for familiarizing yourself with percent

3. Unit conversion and unit rate

Unit rate expresses one quantity as compared to another. Common examples include “miles per hour” or “dollars per year." Words like “per,” “each,” and “every” indicate unit rate. Unit rate problems often require you to convert from one unit, such as feet, to another unit, such as inches.

The SAT is known to draw on both the English system of feet and inches and the metric system of kilometers and meters. Therefore, students should be familiar with common units for both.

4. Lines of best fit

A line of best fit represents the relationship between variables as a linear function. It is generally a straight line on a scatterplot that is expressed as y = mx+b

It is crucial for SAT test-takers to know the best fit formula. Furthermore, students should understand the concept of best fit as a prediction of values. Practice specifically with scatterplot questions to gain familiarity with lines of best fit.

5. Relationships between variables

Relationships between variables are frequently expressed as equations or functions, which may be exponential, linear, or quadratic. You should also be aware that charts and tables are more simplistic representations of relationships between variables.

SAT test-takers should be extremely knowledgeable about basic equations and their components – namely those for lines (y = mx + b), quadratic equations (ax² + bx + c = 0), and exponential equations – as well as what they look like. A helpful way to practice this skill is by matching graphs with their equations.

6. Statistics

To start, students should be familiar with the more basic concepts in statistics: mean, or average; median, the number precisely in the middle when values are placed in order; mode, the value that appears most often; and range, the difference between the highest value and the lowest. Once these concepts are understood, students can make sense of the more complicated concepts in statistics. These include terms like population parameter, a characteristic of a population as described by a value, and standard deviation, or how far away points in the data set are from the mean.

Students can gain confidence in statistics by first analyzing relatively straightforward data sets, such as the distribution of test grades in a class. Once the student feels comfortable calculating statistical values for such a set, he or she can move on to looking at more complex data sets, such as those found in scientific studies.

For success on the SAT Math section, deeply familiarize yourself with the six concepts listed above. These are key areas in the Problem Solving and Data Analysis subsection, which amounts to nearly one-third of SAT Math.