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🇺🇸 PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) · flashcards
PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Geometry and Trigonometry Flashcards
50 question-and-answer cards covering Math: Geometry and Trigonometry as it is examined in PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Math: Geometry and Trigonometry deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
If two figures are similar with a scale factor of k, how do their corresponding lengths compare?
Corresponding lengths are in the ratio k to 1 (each length is multiplied by k).
If two similar figures have a linear scale factor of k, what is the ratio of their areas?
k^2 (the area scale factor is the square of the linear scale factor).
If two similar solids have a linear scale factor of k, what is the ratio of their volumes?
k^3 (the volume scale factor is the cube of the linear scale factor).
What makes two triangles similar?
Their corresponding angles are congruent and their corresponding sides are proportional (e.g., by AA, SAS, or SSS similarity).
What is the formula for the circumference of a circle?
Circumference = 2 x pi x r (or pi x d, where d is the diameter).
What is the formula for the area of a circle?
Area = pi x r^2.
How is the diameter of a circle related to its radius?
The diameter equals twice the radius (d = 2r).
What is the formula for arc length given a central angle in degrees?
Arc length = (central angle / 360) x 2 x pi x r.
What is the formula for the area of a sector given a central angle in degrees?
Sector area = (central angle / 360) x pi x r^2.
How does the measure of an arc relate to its central angle?
The arc measure (in degrees) equals the measure of its central angle.
How many radians are in 360 degrees?
2 x pi radians.
What is the standard (center-radius) equation of a circle with center (h, k) and radius r?
(x - h)^2 + (y - k)^2 = r^2.
A circle has equation (x - 3)^2 + (y + 2)^2 = 25. What are its center and radius?
Center (3, -2) and radius 5.
What technique converts a general circle equation like x^2 + y^2 + Dx + Ey + F = 0 into standard form?
Completing the square on the x-terms and the y-terms.
In a right triangle, what is the sine of an angle (SOH)?
Sine = opposite leg / hypotenuse.
In a right triangle, what is the cosine of an angle (CAH)?
Cosine = adjacent leg / hypotenuse.
In a right triangle, what is the tangent of an angle (TOA)?
Tangent = opposite leg / adjacent leg.
To find an unknown angle when you know two sides of a right triangle, what do you use?
An inverse trig function (arcsin, arccos, or arctan) of the appropriate ratio.
In a 45-45-90 triangle, what is the ratio of the legs to the hypotenuse?
1 : 1 : sqrt(2) (each leg : leg : hypotenuse).
In a 30-60-90 triangle, what is the ratio of the sides opposite 30, 60, and 90 degrees?
1 : sqrt(3) : 2.
In a 30-60-90 triangle, the side opposite 30 degrees is the shortest. How long is the hypotenuse relative to it?
The hypotenuse is twice the length of the side opposite the 30-degree angle.
What is the relationship between the sine of an angle and the cosine of its complement?
sin(x) = cos(90 - x); the sine of an angle equals the cosine of its complement.
If sin(40 degrees) = 0.643, what is cos(50 degrees)?
0.643, because 40 and 50 degrees are complementary, so cos(50) = sin(40).
What value do tan(x) x tan(90 - x) equal for an acute angle x?
1, because tan(90 - x) = 1/tan(x) (cotangent), so the product is 1.
What this deck covers
The Math: Geometry and Trigonometry deck follows the PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Geometry and Trigonometry syllabus — 4 chapters and 13 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 12.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 54 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Math: Geometry and Trigonometry flashcards FAQ
How many Math: Geometry and Trigonometry flashcards are in this PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Math: Geometry and Trigonometry cards cover?
They follow the PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Geometry and Trigonometry syllabus — 4 chapters and 13 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.