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New York State Regents Examinations Geometry (Regents Examination) Flashcards
50 question-and-answer cards covering Geometry (Regents Examination) as it is examined in New York State Regents Examinations. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Geometry (Regents Examination) deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
Define sine, cosine, and tangent for an acute angle in a right triangle (SOH-CAH-TOA).
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
What is the relationship between the sine and cosine of complementary angles?
sin(theta) = cos(90 degrees - theta); the sine of an angle equals the cosine of its complement.
What is the measure of an inscribed angle compared to its intercepted arc?
An inscribed angle is half the measure of its intercepted arc.
What is the measure of a central angle compared to its intercepted arc?
A central angle has the same measure as its intercepted arc.
What is the relationship between a tangent line to a circle and the radius at the point of tangency?
The tangent line is perpendicular to the radius drawn to the point of tangency.
What is the formula for arc length given a central angle theta in degrees and radius r?
Arc length = (theta/360) x 2(pi)r.
What is the formula for the area of a sector with central angle theta in degrees and radius r?
Sector area = (theta/360) x (pi)r^2.
Define radian measure of a central angle in terms of arc length.
Radian measure = arc length divided by radius (theta = s/r); one full circle is 2(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.
How do you find the center and radius of a circle given in general form by completing the square?
Group x-terms and y-terms, complete the square for each by adding (half the coefficient)^2, and rewrite in the form (x-h)^2 + (y-k)^2 = r^2; then center is (h,k) and radius is sqrt of the right side.
What is the distance formula between points (x1, y1) and (x2, y2)?
d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
What is the midpoint formula for the segment joining (x1, y1) and (x2, y2)?
Midpoint = ((x1 + x2)/2, (y1 + y2)/2).
What is the section/partition formula for the point that divides a segment from (x1,y1) to (x2,y2) in the ratio m:n?
Point = (x1 + (m/(m+n))(x2 - x1), y1 + (m/(m+n))(y2 - y1)).
How do you prove a quadrilateral is a parallelogram using coordinates?
Show both pairs of opposite sides are parallel (equal slopes), or both pairs of opposite sides are congruent (equal lengths via distance formula), or the diagonals bisect each other (same midpoint).
What slope relationships indicate parallel and perpendicular lines?
Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (their product is -1).
Write the slope-intercept and point-slope forms of a line.
Slope-intercept: y = mx + b. Point-slope: y - y1 = m(x - x1).
How do you write the equation of a line perpendicular to a given line through a given point?
Take the negative reciprocal of the given line's slope, then substitute that slope and the given point into point-slope form.
What is the formula for the area of a triangle, and the area of a trapezoid?
Triangle: A = (1/2)bh. Trapezoid: A = (1/2)(b1 + b2)h.
What is the formula for the area and circumference of a circle?
Area = (pi)r^2; circumference = 2(pi)r.
What is the formula for the volume of a cylinder and of a cone?
Cylinder: V = (pi)r^2 h. Cone: V = (1/3)(pi)r^2 h.
What is the formula for the volume of a sphere and of a pyramid?
Sphere: V = (4/3)(pi)r^3. Pyramid: V = (1/3)(base area)(height).
What solid of revolution is generated by rotating a rectangle about one of its sides, and what about rotating a right triangle about a leg?
Rotating a rectangle about a side produces a cylinder; rotating a right triangle about a leg produces a cone.
What is the cross-section of a solid, and what cross-sections result from slicing a cylinder parallel vs. perpendicular to its base?
A cross-section is the 2D shape formed when a plane cuts a solid; a cylinder cut perpendicular to its base (parallel to the axis) gives a rectangle, and cut parallel to its base gives a circle.
What is population density and how is it modeled with geometry?
Density = quantity per unit area (or volume); e.g., population density = number of people divided by the area of the region they occupy.
What this deck covers
The Geometry (Regents Examination) deck follows the New York State Regents Examinations Geometry (Regents Examination) syllabus — 6 chapters and 18 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 8.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 85 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.
Geometry (Regents Examination) flashcards FAQ
How many Geometry (Regents Examination) flashcards are in this New York State Regents Examinations 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 New York State Regents Examinations 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 Geometry (Regents Examination) cards cover?
They follow the New York State Regents Examinations Geometry (Regents Examination) syllabus — 6 chapters and 18 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.