Jump to a New ChapterIntroductionThe Discipline of DisciplineSAT StrategiesThe SAT Personal TrainerMeet the Writing SectionBeat the EssayBeat Improving SentencesBeat Identifying Sentence ErrorsBeat Improving ParagraphsMeet the Critical Reading sectionBeat Sentence CompletionsReading Passages: The Long and Short of ItThe Long of ItThe Short of ItSAT VocabularyMeet the Math SectionBeat Multiple-Choice and Grid-InsNumbers and OperationsAlgebraGeometryData, Statistics, and Probability
 19.1 To Algebra or Not to Algebra? 19.2 A Very Short Algebra Glossary 19.3 Substitution Questions 19.4 Solving Equations 19.5 Algebra, ABSOLUTE Value, and Exponents 19.6 Beat the System (of Equations) 19.7 Inequalities 19.8 Binomials and Quadratic Equations

 19.9 Variation 19.10 How Do Functions Function? 19.11 Evaluating Functions 19.12 Compound Functions 19.13 Domain and Range 19.14 Functions As Models 19.15 Defeating Word Problems 19.16 The Most Common Word Problems
Variation
One way that the new SAT tests whether you understand an equation is to ask questions about the relationship between certain variables. For example,
 If z triples while x doubles, what happens to y?

The easiest way to solve such problems is to just plug in:
So the value of y will be 2/3 of what it was.
Essentially, these sorts of problems are testing to see if you understand how an equation works and how different variables interact. While in a simple equation like the first example, this is easy to see, it becomes a little more complicated as the equations get more complex:
 If z triples while x doubles, what happens to y?

Once again, you can still find the answer by plugging in 2x for x and 3z for z. You just have to do some additional math:
The value of y will be 8/3 of what it was. Since the original expression was y = x3/2z, we must figure out what fraction times 1 /2 is equal to 4/3:
It’s also possible that you’ll have to know some variation jargon for the new SAT. There are two terms you need to know: direct and inverse. A direct relationship between two variables exists when, if one variable increases, the other variable increases. In the equation
y and x share a direct relationship, since if x increases, so does y.
An inverse relationship is just the opposite. In the same example, y and z have an inverse relationship, because if z were to increase, y would decrease.
 Jump to a New ChapterIntroductionThe Discipline of DisciplineSAT StrategiesThe SAT Personal TrainerMeet the Writing SectionBeat the EssayBeat Improving SentencesBeat Identifying Sentence ErrorsBeat Improving ParagraphsMeet the Critical Reading sectionBeat Sentence CompletionsReading Passages: The Long and Short of ItThe Long of ItThe Short of ItSAT VocabularyMeet the Math SectionBeat Multiple-Choice and Grid-InsNumbers and OperationsAlgebraGeometryData, Statistics, and Probability
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