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CAT (Common Admission Test) Quantitative Aptitude (QA) - Geometry and Modern Math Flashcards
50 question-and-answer cards covering Quantitative Aptitude (QA) - Geometry and Modern Math as it is examined in CAT (Common Admission Test). 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 (QA) - Geometry and Modern Math deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the curved surface area, total surface area, and volume of a cone (radius r, height h, slant l).
CSA = pi*r*l; TSA = pi*r(r+l); Volume = (1/3)*pi*r^2*h, where l = sqrt(r^2+h^2).
State the surface area and volume of a sphere of radius r, and of a hemisphere.
Sphere: SA = 4*pi*r^2, Volume = (4/3)*pi*r^3. Hemisphere: CSA = 2*pi*r^2, TSA = 3*pi*r^2, Volume = (2/3)*pi*r^3.
What is the diagonal (space diagonal) of a cuboid with dimensions l, b, h?
sqrt(l^2 + b^2 + h^2).
State the distance formula between points (x1,y1) and (x2,y2).
Distance = sqrt((x2-x1)^2 + (y2-y1)^2).
State the section formula (internal division) and the midpoint formula.
Point dividing (x1,y1)-(x2,y2) in ratio m:n internally = ((m*x2+n*x1)/(m+n), (m*y2+n*y1)/(m+n)). Midpoint = ((x1+x2)/2, (y1+y2)/2).
What is 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)|.
What is the slope of a line through (x1,y1) and (x2,y2), and the slope from equation ax+by+c=0?
Slope = (y2-y1)/(x2-x1). From ax+by+c=0, slope = -a/b.
What are the conditions for two lines to be parallel and perpendicular in terms of slopes?
Parallel: equal slopes (m1 = m2). Perpendicular: product of slopes = -1 (m1*m2 = -1).
State the slope-intercept and point-slope forms of a straight line.
Slope-intercept: y = mx + c. Point-slope: y - y1 = m(x - x1).
What is the perpendicular distance from point (x0,y0) to the line ax+by+c=0?
|a*x0 + b*y0 + c| / sqrt(a^2 + b^2).
State the standard equation of a circle with center (h,k) and radius r.
(x-h)^2 + (y-k)^2 = r^2. General form: x^2 + y^2 + 2gx + 2fy + c = 0 with center (-g,-f) and radius sqrt(g^2+f^2-c).
Give the values of sin, cos, and tan for 30, 45, and 60 degrees.
sin: 1/2, 1/sqrt(2), sqrt(3)/2. cos: sqrt(3)/2, 1/sqrt(2), 1/2. tan: 1/sqrt(3), 1, sqrt(3).
State the three Pythagorean trigonometric identities.
sin^2 x + cos^2 x = 1; 1 + tan^2 x = sec^2 x; 1 + cot^2 x = cosec^2 x.
State the sine and cosine addition formulas: sin(A+B) and cos(A+B).
sin(A+B) = sinA cosB + cosA sinB; cos(A+B) = cosA cosB - sinA sinB.
State the double-angle formulas for sin 2A, cos 2A, and tan 2A.
sin2A = 2 sinA cosA; cos2A = cos^2A - sin^2A = 2cos^2A - 1 = 1 - 2sin^2A; tan2A = 2tanA/(1 - tan^2A).
In a height-and-distance problem, what is the angle of elevation versus the angle of depression?
Angle of elevation is measured upward from the horizontal to an object above the observer; angle of depression is measured downward from the horizontal to an object below. They are equal (alternate angles) for the same line of sight.
How are height and horizontal distance related using the angle of elevation theta?
tan(theta) = height / horizontal distance, so height = distance x tan(theta).
State the Addition (Sum) Rule and the Multiplication (Product) Rule of counting.
Addition rule: if a task is done in m OR n mutually exclusive ways, total = m + n. Multiplication rule: if one task in m ways AND another independently in n ways, total = m x n.
State the formula for permutations of n distinct objects taken r at a time, nPr.
nPr = n! / (n-r)!. (Order matters.)
How many distinct arrangements of n objects where some are identical (p alike, q alike, etc.)?
n! / (p! q! ...). Number of circular permutations of n distinct objects = (n-1)!.
State the formula for combinations nCr and its key symmetry property.
nCr = n! / (r!(n-r)!). Symmetry: nCr = nC(n-r); also nCr + nC(r-1) = (n+1)Cr (Pascal's rule).
State the classical (theoretical) definition of probability of an event.
P(event) = (number of favorable outcomes) / (total number of equally likely outcomes), a value between 0 and 1.
State the addition rule of probability for two events and the rule for mutually exclusive events.
P(A or B) = P(A) + P(B) - P(A and B). If mutually exclusive, P(A and B) = 0, so P(A or B) = P(A) + P(B). Complement: P(not A) = 1 - P(A).
State the inclusion-exclusion principle for the union of two and three sets.
|A∪B| = |A| + |B| - |A∩B|. |A∪B∪C| = |A|+|B|+|C| - |A∩B| - |B∩C| - |A∩C| + |A∩B∩C|.
What this deck covers
The Quantitative Aptitude (QA) - Geometry and Modern Math deck follows the CAT (Common Admission Test) Quantitative Aptitude (QA) - Geometry and Modern Math syllabus — 6 chapters and 19 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 89 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 (QA) - Geometry and Modern Math flashcards FAQ
How many Quantitative Aptitude (QA) - Geometry and Modern Math flashcards are in this CAT (Common Admission 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 CAT (Common Admission 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 Quantitative Aptitude (QA) - Geometry and Modern Math cards cover?
They follow the CAT (Common Admission Test) Quantitative Aptitude (QA) - Geometry and Modern Math syllabus — 6 chapters and 19 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.