Sat · Math: Geometry & Trigonometry
The Complete SAT Bible · Digital SATMath: Geometry & Trigonometry
SAT Math: Geometry & Trigonometry is the most figure-dependent part of the Digital SAT Math section: about 5 to 7 of the 40 scored Math questions (roughly 15% of the Math score) come from this domain, and half the work is translating a diagram into the right equation. It spans the reference sheet and what you must memorize, lines and angles and triangles, right-triangle trigonometry, circles, and area and volume. Each concept is taught from the ground up with labelled figures and fully worked examples.
The Digital SAT presents these questions in two formats: multiple choice (four answer choices, A to D) and student-produced response (you type the answer directly; fractions or decimals are accepted, with no percent sign, dollar sign or commas). The single highest-value idea here is the reference sheet: the on-screen formula sheet hands you 12 items, but knowing the dozen formulas it leaves out (trapezoid and parallelogram area, every surface-area formula, arc length and sector area, SOH-CAH-TOA, and the circle equation) is worth several points. Built to mirror the official College Board specification.
What SAT Math: Geometry & Trigonometry covers
The whole domain → one exam-ready map. Five teaching chapters, the reference sheet through area and volume, then a formula page and 31 worked practice questions. Each links to its free chapter guide.
How the Digital SAT Math section assesses this
Only what this guide can support from its question set is stated below. Confirm current section structure, timing and on-screen tools on the official College Board test specifications before you rely on them.
| Item | Weight / count | What it means |
|---|---|---|
| Share of scored Math questions | ~15% | Geometry and Trigonometry is about 5 to 7 of the 40 scored Math questions. The biggest single levers on the Math score are Algebra and Advanced Math; this domain is the figure-dependent remainder. |
| Skills in this domain | 4 skills | Lines, angles and triangles; right triangles and trigonometry; circles; and area and volume. |
| Multiple choice | 4 choices (A to D) | Each multiple-choice question gives four answer choices, A to D, with exactly one correct answer. |
| Student-produced response | Type the answer | You enter the answer directly. Fractions or decimals are accepted; no percent sign, dollar sign or commas. |
| On-screen reference sheet | 12 formulas | The same reference sheet is one click away the whole section. It provides 12 formulas and facts; the dozen it leaves out are yours to memorize, which is where this domain is won or lost. |
Find a circle's center and radius from its general-form equation
- Step 1Group the x terms and the y terms, and move the constant to the right: (x squared minus 6x) plus (y squared plus 4y) = 12.
- Step 2Complete the square in x. Half of negative 6 is negative 3, squared is 9, so add 9 to both sides. Complete the square in y. Half of 4 is 2, squared is 4, so add 4 to both sides: (x squared minus 6x plus 9) plus (y squared plus 4y plus 4) = 12 plus 9 plus 4.
- Step 3Write each group as a perfect square and add the right side: (x minus 3) squared plus (y plus 2) squared = 25. This is standard form (x minus h) squared plus (y minus k) squared = r squared.
- Step 4Read off the center and radius. The signs flip from the parentheses, so h = 3 and k = negative 2. The radius is the square root of 25, which is 5 (not 25).
Key terms
- Hypotenuse
- The side opposite the right angle in a right triangle, always the longest side.
- Pythagorean triple
- A set of whole numbers a, b, c with a squared plus b squared equals c squared (for example 3-4-5, 5-12-13); recognizing them saves computation.
- Special right triangle
- A 45-45-90 (s, s, s root 2) or 30-60-90 (x, x root 3, 2x) triangle with fixed side ratios. Both are on the reference sheet.
- SOH-CAH-TOA
- The trig ratios: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, tangent equals opposite over adjacent. NOT on the reference sheet.
- Cofunction identity
- sine of an angle equals cosine of its complement: sin of theta equals cos of (90 degrees minus theta). So if sin x equals cos y, then x plus y equals 90.
- Similar triangles (AA)
- Triangles with equal corresponding angles; their sides are in proportion and their areas in the ratio (side ratio) squared. AA gives similar, not congruent.
- Central angle
- An angle with its vertex at the circle's center; it equals the measure of the arc it cuts off.
- Inscribed angle
- An angle with its vertex on the circle; it is half the central angle that subtends the same arc. An angle inscribed in a semicircle is 90 degrees.
- Arc length
- Part of the circumference: (theta over 360) times 2 pi r for a central angle theta in degrees. NOT on the sheet.
- Sector
- A pie slice of a circle; its area is (theta over 360) times pi r squared. NOT on the sheet. An arc is a length; a sector is an area, so do not swap them.
- Surface area
- The total area of a solid's faces; NOT on the reference sheet. Build it from the faces or unfold the solid into a net.
- Scale factor k
- The ratio of corresponding lengths between similar figures; areas scale by k squared, volumes by k cubed.
SAT Math: Geometry & Trigonometry FAQ
How many geometry and trigonometry questions are on the Digital SAT?
About 5 to 7 of the 40 scored Math questions (roughly 15%) come from Geometry and Trigonometry: area and volume, lines and angles, right triangles and trigonometry, and circles. It is the most figure-dependent part of SAT Math, so half the work is translating a diagram into the right equation.
What geometry formulas are on the SAT reference sheet?
The on-screen reference sheet gives you circle area pi r squared and circumference 2 pi r, rectangle area lw, triangle area one-half b h, the Pythagorean theorem, the 30-60-90 (x, x root 3, 2x) and 45-45-90 (s, s, s root 2) special right triangles, the volumes of a box, cylinder, sphere, cone and pyramid, and the facts that a circle has 360 degrees (2 pi radians) and a triangle's angles sum to 180 degrees.
What geometry formulas do I have to memorize for the SAT?
The sheet does NOT give you: trapezoid area one-half (b1 plus b2) h, parallelogram area bh, any surface-area formula, the slope formula, the distance and midpoint formulas, arc-length and sector-area formulas, SOH-CAH-TOA, the circle equation (x minus h) squared plus (y minus k) squared equals r squared, and degree-to-radian conversion. Knowing what the sheet leaves out is worth several points.
What are the special right triangles on the SAT?
A 45-45-90 triangle has legs s, s and hypotenuse s root 2. A 30-60-90 triangle has a short side x opposite the 30-degree angle, a long side x root 3 opposite the 60-degree angle, and a hypotenuse 2x. Both are on the reference sheet, but you should know them cold to save time.
How do I find a circle's center and radius from its equation?
Put it in standard form (x minus h) squared plus (y minus k) squared equals r squared. The center is (h, k), and the signs flip from the parentheses, so (x plus 1) means h equals negative 1. The radius is r, the square root of the right-hand side, so a right side of 25 means radius 5, not 25. From general form, complete the square in x and in y first.
How does scaling affect area and volume on the SAT?
If every length is multiplied by k, areas multiply by k squared and volumes by k cubed. Doubling a radius (k equals 2) makes the area 4 times and the volume 8 times. The same power applies to unit conversion: 1 ft equals 12 in, so 1 square foot is 144 square inches and 1 cubic foot is 1728 cubic inches.
Related SAT sections
Geometry and Trigonometry is about 15% of the Math score. The two domains below are the biggest single levers, and the exam overview ties the whole Math and Reading-and-Writing sections together.
How to study for SAT Math: Geometry & Trigonometry
Geometry rewards two things: knowing the formula and reading the figure. Drill both. (1) Start with the reference sheet. The single highest-value page is the exact list of the 12 formulas you are given and the dozen you must memorize, because students freeze hunting for a formula that was never there. Learn what the sheet leaves out (trapezoid and parallelogram area, every surface-area formula, arc length and sector area, SOH-CAH-TOA, and the circle equation) cold. (2) Work it in three passes: learn the method from each labelled figure (cover the answer and set it up yourself first), drill the practice questions cold, then re-draw the special triangles and the circle setup from memory the week of the test. (3) Name the traps before they catch you: trusting a "not drawn to scale" picture instead of the numbers, confusing similar with congruent, using a slanted side instead of the perpendicular height, dropping the theta-over-360 fraction on an arc or sector, flipping the center signs in the circle equation, leaving the radius as r squared, dropping the one-third on a cone or pyramid, and scaling area by k instead of k squared (or volume by k instead of k cubed). (4) Master the term distinctions the test rewards: arc length (a length) versus sector area (an area), central versus inscribed angle, similar versus congruent, surface area versus volume, and radius versus diameter. (5) Practise both formats: multiple choice (four choices) and student-produced response (type the answer; fractions or decimals, no percent sign, dollar sign or commas). (6) Confirm the current section structure, timing and on-screen tools on the official College Board specifications, since this guide states only what its question set supports.
