Math Symbols

The SAT likes to include a math few problems with unusual symbols, such as ◊, or ♠. For some exam takers, this is a signal to panic, since they have no idea what ◊ or ♠ mean, but really, these are simple replacement questions, similar to the f(x) questions I addressed in an earlier post.

Really, no one knows what what ◊ or ♠ mean.  The College Board (the writers of the exam) make up a meaning for the symbols as they write the question.  In each case they give you the definition of the symbol, then ask you to apply that definition.

For example:

a ♣ b = a + (b x 2)

3 ♣ 7 = ?

The first line defines the symbol ♣.  We'll use that definition as a template for answering the question on the second line.

Note that in the definition, a appears before the ♣. And in the question, 3 appears before the ♣. The test makers have replaced a with 3 in the left half of the equation; we just need to make the same replacements in the right side of the equation:

a ♣ b = a + (b x 2)

3 ♣ 7 = 3 + (b x 2)

We still have to account for b, though. In the left side of the equation, the test maker replaced b with 7, so now we need to make the same replacement on the right:

a ♣ b = a + (b x 2)

3 ♣ 7 = 3 + (7 x 2)

At this point, we have an equation that we can easily solve. Following the usual order of operations (PEMDAS), we get:

3 ♣ 7 = 3 + (7 x 2)
= 3 + 14
= 17