Select Page In a typical first session with a high school junior studying for the SAT we discuss math.

At some point we touch on linear equations, and most students remember the topic from class. They can tell me the equation of a line – in one form – and say something about the slope: e.g. “It’s the rate of change”, which is correct. But many of those same students who know that the slope is the rate of change cannot answer the following question:

“What happens to the quantity measured on the y axis, if what’s measured on the x axis changes by 1?”

The answer to that question is not important. What is important is that the answer is the direct logical implication of the fact they just recited.

Facts and their Logical Implications (and Direct Consequences)

Time and again the SAT asks similar questions. They essentially assume that students at a certain level know certain facts, so they ask them to do something with those facts: i.e. draw a conclusion.

In the math sections, a hierarchy exists. The first third or half of each section will ask easier questions, where students will be asked for “just the facts”. But in the later portions of the sections, they’ll be asked for the logical implication of those facts. A frequently repeated example of this involves the factors and roots of quadratic equations: given the factors, what are the roots (and the reverse).

My students are generally “college ready” when they begin working with me. They’re scoring at least 520-590 of 800, putting them in the third quartile (the 50-75th percentile range – the lower half of the top 50%). So they’re fine on the first third of a math test section, but they may start struggling in the middle third or the second half.