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CAT Quantitative Aptitude: Geometry And Mensuration Flashcards
50 question-and-answer cards covering Quantitative Aptitude: Geometry And Mensuration as it is examined in CAT. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Aptitude: Geometry And Mensuration deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the measure of an angle inscribed in a semicircle?
90 degrees (the angle in a semicircle is a right angle).
State the tangent-radius relationship and the equal-tangents property for a circle.
A tangent is perpendicular to the radius at the point of contact; two tangents drawn from an external point are equal in length.
Give the formulas for the length of an arc and the area of a sector with central angle theta (in degrees), radius r.
Arc length = (theta/360) x 2(pi)r; Sector area = (theta/360) x (pi)r squared.
State the power of a point / intersecting chords theorem.
For two chords intersecting inside a circle, the products of their segments are equal: PA x PB = PC x PD.
What is the distance formula between two points (x1, y1) and (x2, y2)?
Distance = sqrt((x2 - x1) squared + (y2 - y1) squared).
What is the midpoint formula for the segment joining (x1, y1) and (x2, y2)?
Midpoint = ((x1 + x2)/2, (y1 + y2)/2).
State the section formula for a point dividing the segment from (x1,y1) to (x2,y2) in ratio m:n internally.
((m x2 + n x1)/(m + n), (m y2 + n y1)/(m + n)).
What is the slope of the line joining (x1, y1) and (x2, y2), and the slope-intercept form of a line?
Slope m = (y2 - y1)/(x2 - x1); slope-intercept form: y = mx + c.
What is the condition for two lines to be parallel, and for them to be perpendicular, in terms of slopes?
Parallel: slopes equal (m1 = m2). Perpendicular: product of slopes = -1 (m1 x m2 = -1).
Give the formula for the distance from a point (x0, y0) to the line ax + by + c = 0.
Distance = |a x0 + b y0 + c| / sqrt(a squared + b squared).
What is the standard equation of a circle with center (h, k) and radius r?
(x - h) squared + (y - k) squared = r squared.
Name the four conic sections obtained by slicing a cone and their defining eccentricity values.
Circle (e = 0), ellipse (0 < e < 1), parabola (e = 1), hyperbola (e > 1).
Give the standard equation of an ellipse centered at the origin and of a parabola opening rightward.
Ellipse: x squared/a squared + y squared/b squared = 1. Parabola: y squared = 4ax.
Define a parabola in terms of focus and directrix.
A parabola is the locus of points equidistant from a fixed point (focus) and a fixed line (directrix).
What is a locus, and what locus is defined by points equidistant from a fixed point?
A locus is the set of all points satisfying a given condition; points equidistant from a fixed point form a circle.
Give the formula for the area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3).
Area = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|.
Give the total surface area and volume of a cube of side a, and a cuboid of dimensions l x b x h.
Cube: TSA = 6a squared, Volume = a cubed. Cuboid: TSA = 2(lb + bh + hl), Volume = lbh.
Give the curved surface area, total surface area, and volume of a cylinder (radius r, height h).
CSA = 2(pi)rh; TSA = 2(pi)r(r + h); Volume = (pi)r squared h.
Give the curved surface area, total surface area, and volume of a cone (radius r, height h, slant l).
CSA = (pi)rl; TSA = (pi)r(r + l); Volume = (1/3)(pi)r squared h, where l = sqrt(r squared + h squared).
Give the surface area and volume of a sphere of radius r, and the volume of a hemisphere.
Sphere: SA = 4(pi)r squared, Volume = (4/3)(pi)r cubed. Hemisphere volume = (2/3)(pi)r cubed.
Give the formulas for the volume and lateral surface area of a prism.
Volume = base area x height; Lateral surface area = perimeter of base x height.
Give the formulas for the volume and lateral surface area of a pyramid.
Volume = (1/3) x base area x height; Lateral surface area = (1/2) x base perimeter x slant height.
State the values of sin, cos, and tan for 0, 30, 45, 60, and 90 degrees.
sin: 0, 1/2, 1/sqrt2, sqrt3/2, 1. cos: 1, sqrt3/2, 1/sqrt2, 1/2, 0. tan: 0, 1/sqrt3, 1, sqrt3, undefined.
In heights and distances, if the angle of elevation to a tower top from distance d is theta, what is the tower's height? And state the three fundamental trig identities.
Height = d x tan(theta). Identities: sin squared + cos squared = 1; 1 + tan squared = sec squared; 1 + cot squared = cosec squared.
What this deck covers
This deck covers the Quantitative Aptitude: Geometry And Mensuration portion of the CAT syllabus in question-and-answer form. Browse the full CAT syllabus to see how it fits with the rest.
Answers are written to be recallable, not just readable — averaging about 81 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.
Quantitative Aptitude: Geometry And Mensuration flashcards FAQ
How many Quantitative Aptitude: Geometry And Mensuration flashcards are in this CAT 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 CAT 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 Quantitative Aptitude: Geometry And Mensuration cards cover?
They follow the Quantitative Aptitude: Geometry And Mensuration portion of the CAT syllabus, in question-and-answer form.
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.