Quizzes, exams, and flashcards about Geometry and Trigonometry: Geometry 1 — triangles, circles and the facts to memorise.
← SAT
Area and volume, lines and angles, triangles, right-triangle trigonometry and circles — ≈15% of the Math section, 5 to 7 questions.
This is the smallest Math domain and the one students most often over-prepare, because school geometry is a whole year and this is five to seven questions. If your Algebra or Advanced Math is shaky, those are worth five times as much between them. Come here when the big two are solid, or when a specific idea below is missing.
That said, these questions are unusually learnable: the content is a short list of facts, most of the hard ones are given to you on the reference sheet in the app, and the reasoning is rarely long.
The reference sheet does not have everything. It gives you areas, volumes and the special right triangles. It does not give you the angle-sum facts, similarity, the circle theorems, or the definitions of sine, cosine and tangent — so those are the ones to know cold.
sin θ = cos(90° − θ). A sine and a cosine of complementary angles are equal. This appears on the SAT far more often than its share of the syllabus suggests, usually as "if sin x° = 0.6, what is cos(90 − x)°" — which is a one-second question if you know it and a lost minute if you do not.
Radians exist on this test. π radians is 180°, and a question may give you an angle either way. Arc length is rθ with θ in radians, and sector area is ½r²θ.
The equation of a circle is (x − h)² + (y − k)² = r². Centre (h, k), radius r — and note the minus signs: a circle centred at (3, −2) appears as (x − 3)² + (y + 2)². Questions that hand you an expanded equation want you to complete the square.
Draw it, and label everything you know on the drawing — including the thing you are looking for. A surprising share of these questions become obvious once the diagram has numbers on it, and a surprising share of wrong answers come from holding the configuration in your head. If a figure is given, redraw it large enough to write on.
And check what is being asked: a question about a sector often wants the arc length while the choices also contain the sector area, and one about similar triangles often wants the side of the smaller one while the choices contain the larger.
