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Course details

SAT Math — The Method Behind the Questions

SAT Math — The Method Behind the Questions

About the course

The SAT is not a mathematics exam. It is a test of whether you can recognise about twenty recurring question shapes and execute each one quickly, and it re-uses those shapes with remarkable consistency. That is good news, and it is the entire premise of this course.

I spent three years writing practice items for a test-prep publisher before I taught full time. That job is mostly designing wrong answers — the distractor for the student who forgets to distribute, the one for the student who solves for x when the question wants 2x. Once you know those are deliberate, the answer choices stop being noise and start being information.

How the course is organised

Not by mathematical topic. By question archetype, because that is the unit the test actually deals in. Each archetype gets the same treatment:

  1. The archetype in its plainest form, so you can see the skeleton

  2. The four or five disguises the test puts on it

  3. The distractors it ships with, and the specific mistake each one is fishing for

  4. A speed drill — twelve of them in a row, timed, until recognition is automatic

  5. Mixed practice, where it appears alongside seven other archetypes and you have to identify it cold

On calculators

The exam gives you a graphing calculator throughout, and using it on the wrong question is one of the most reliable ways to lose time. We identify the six question types where it genuinely wins, drill those, and leave it alone everywhere else.

Timing

Speed is not something you add at the end. It comes from recognition, so it is built into every unit from the first week rather than bolted on in a final module. By the halfway point every drill is timed.

  • Twenty archetype units, each with a timed drill set

  • Six full-length adaptive practice tests with section-level analytics

  • A distractor catalogue — every common wrong-answer design, with the mistake it targets

  • A personal error log that sorts your mistakes into concept, method, misread and speed

I went from 610 to 740 and about half of that was just not falling for the answer that looked right. Learning that the wrong answers are designed, and by whom, changed how I read the question.

Priya S., grade 11, New Jersey


Take an official practice test before you start, and bring the score with you. The first unit will point you at the right entry point instead of making you sit through material you already own.

In this course you will be able to

Recognise which of roughly twenty recurring question archetypes you are looking at within ten seconds
Choose between algebra, back-solving and plugging in numbers on the basis of which is fastest, not which is most familiar
Use the built-in graphing calculator deliberately, for the six question types where it genuinely saves time, and ignore it elsewhere
Finish each module with three to five minutes left for a targeted second pass
Identify a wrong answer choice as a designed trap rather than a coincidence
Convert a word problem into an equation without re-reading it twice
Diagnose your own practice test by splitting errors into concept, method, misread and speed

Prerequisite

Taking the SAT within the next twelve months
Algebra I complete; Algebra II helpful but not required — every topic beyond Algebra I is taught here from scratch
A recent official practice test score, so we can point you at the right starting unit
Three to four hours a week, including one timed section
Willingness to redo questions you got right but guessed at, which is where quiet points hide

Topics covered

How the adaptive module structure changes what an early mistake costs youLinear equations, and the four ways the test disguises oneSystems of equations, and choosing substitution or elimination by inspectionLinear inequalities and word problems that hide a direction reversalRatios, rates, proportions and unit conversion under time pressurePercentages, percent change and the compounding trapExponents, radicals and rational exponent conversionsQuadratics: factoring, completing the square, the discriminant and vertex formPolynomial behaviour, remainder theorem and reading a graph for rootsFunction notation, transformations and compositionExponential growth and decay, and telling it apart from linear at a glanceCircle equations, arc length and radiansRight triangle trigonometry and the special triangles worth memorisingStatistics: mean, median, standard deviation described qualitatively, and margin of errorReading data from tables, scatterplots and lines of best fitBack-solving, plugging in numbers, and knowing which one is faster for a given question
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Kestrel is an online school based in Denver, Colorado, teaching students across the United States and in more than thirty countries. We run small live sections and self-paced courses in AP and honors subjects, SAT and ACT preparation, college application writing, and academic English for international applicants. Live sections cap at sixteen students, every course is taught by a licensed teacher or a subject specialist rather than a rotating pool of tutors, and every recording, transcript and worked solution stays in your library for a full year. Sections run in three time zone bands, so a student in Seoul or Sao Paulo is never asked to sit a calculus class at three in the morning.

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