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SAT Geometry and Trigonometry: Where a Memorized Formula Sheet Pays Off

The smallest math domain, and the one where a formula sheet you've actually memorized pays off the most.

4 min read · longer if you open every "Learn more"Covers: area and volume, triangles and angles, right-triangle trig, circles

Geometry and Trigonometry pulls from a wide range of formulas, but the digital SAT actually gives you a reference sheet with most of them at the start of the Math section. The real skill here isn't memorization, it's recognizing which formula a question wants and setting up the picture correctly.

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Did you know

Geometry and Trigonometry makes up roughly 15% of the Math section, the smallest of the four domains, tied with Problem-Solving and Data Analysis. Because it's a smaller slice, a short, focused review of the core formulas goes a long way relative to the time it takes.

What's tested

Area, perimeter, and volume

Rectangles, triangles, circles, and 3D solids, sometimes with the formula given, sometimes not.

Learn more: using the reference sheet without wasting time
  • The digital SAT provides a reference sheet with common area and volume formulas at the start of the Math section, glance at it once before you start so you know what's already given to you, instead of rediscovering that mid-test.
  • For composite shapes (a rectangle with a semicircle cut out, for example), break it into simple shapes, calculate each area separately, and add or subtract. Don't look for one formula that does it all at once.
  • Watch your units on volume questions specifically, area is squared, volume is cubed, and a question that gives you mismatched units (feet and inches, for instance) is testing whether you convert before calculating.

Lines, angles, and triangles

Angle relationships from parallel lines, triangle angle sums, and similar triangles.

Learn more: the angle rules that unlock most of these questions
  • A triangle's interior angles always sum to 180°. This single fact solves more geometry questions than any other rule on the test.
  • When a line crosses two parallel lines, the angles it creates come in only two values, and they repeat in a predictable pattern, angles that look equal (or supplementary) generally are. Learn to spot this pattern by eye rather than re-deriving it each time.
  • Similar triangles have proportional sides, if you can identify two triangles are similar (matching angles), you can set up a ratio between corresponding sides instead of solving for anything from scratch.
  • Mark up the figure. Write every angle and length you calculate directly on the diagram as you go, most of these questions are solved by chaining several small deductions together, and it's easy to lose track without writing them down.

Right triangles and trigonometry

Pythagorean theorem, and basic sine, cosine, and tangent.

Learn more: SOH-CAH-TOA and the triangles worth memorizing
  • SOH-CAH-TOA: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent. Identify which angle you're working from before labeling sides, "opposite" and "adjacent" depend entirely on which angle is the reference.
  • Memorize the 3-4-5 and 5-12-13 right triangles. They show up constantly, and recognizing one instantly saves you from working through the Pythagorean theorem by hand.
  • Sine and cosine of complementary angles are related: sin(x) = cos(90° − x). A question that looks like it wants a complicated calculation sometimes just wants you to recognize this relationship.
  • The calculator's trig functions work in degree mode by default on most setups, if an answer looks wildly wrong, check whether the mode matches what the question is using.

Circles

Radius, arc length, sector area, and the equation of a circle.

Learn more: arcs, sectors, and the circle equation
  • Arc length and sector area are both just a fraction of the full circle, figure out what fraction of 360° the central angle represents, then apply that same fraction to the circumference or area.
  • The equation of a circle, (x − h)² + (y − k)² = r², has its center at (h, k) and radius r. If a question gives you the equation in expanded form, you may need to complete the square to get it back into this form before reading off the center and radius.
  • Watch for r² versus r in the equation, a common careless error is reading the number on the right side of the equation as the radius when it's actually the radius squared.
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Gotcha

Given a circle's equation x² + y² = 49 and asked for the radius, it's easy to answer 49 instead of 7, the equation gives you r², not r. Any time a geometry question hands you a squared quantity, pause and make sure you're answering with the right power before you lock in a choice.

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Quick tip

If a figure isn't drawn to scale (the question will say so), don't trust your eyes for a rough estimate, solve it with the actual numbers. But if it looks reasonably close to scale and isn't flagged otherwise, a quick visual sanity check on your answer catches a surprising number of errors.

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