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XAT Quantitative Ability Flashcards
51 question-and-answer cards covering Quantitative Ability as it is examined in XAT. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Ability deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
For a continuous function on a closed interval, where do maxima/minima occur?
At critical points where f'(x) = 0 or f' is undefined, or at the endpoints of the interval. Compare values to find absolute max/min.
What does the second derivative test say about a critical point?
If f'(c)=0 and f''(c) > 0, c is a local minimum; if f''(c) < 0, c is a local maximum; if f''(c)=0 the test is inconclusive.
State the Remainder Theorem and Factor Theorem for polynomials.
Remainder Theorem: dividing P(x) by (x − a) leaves remainder P(a). Factor Theorem: (x − a) is a factor of P(x) iff P(a) = 0.
What is the sum of the interior and exterior angles of any triangle?
Interior angles sum to 180°. Each exterior angle equals the sum of the two remote interior angles; exterior angles sum to 360°.
State the Pythagorean theorem and the three common Pythagorean triples.
In a right triangle, hypotenuse² = sum of squares of the other two sides. Common triples: (3,4,5), (5,12,13), (8,15,17).
What are the conditions for two triangles to be similar, and what follows about their areas?
Similar by AA, SAS, or SSS proportionality. Corresponding sides are in equal ratio k; their areas are in ratio k².
State the formula for the area of a triangle given its three sides (Heron's formula).
Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter.
What is the angle subtended by a diameter, and the relation between central and inscribed angles?
Angle in a semicircle (subtended by diameter) is 90°. The central angle is twice the inscribed angle subtending the same arc.
State the sum of interior angles and each interior angle of a regular n-sided polygon.
Sum of interior angles = (n−2)×180°. Each interior angle of a regular polygon = (n−2)×180°/n.
What is the distance formula and the midpoint formula in coordinate geometry?
Distance = √[(x₂−x₁)² + (y₂−y₁)²]. Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).
What is the slope of a line through two points, and the condition for two lines to be perpendicular?
Slope m = (y₂−y₁)/(x₂−x₁). Two lines are perpendicular when m₁·m₂ = −1; parallel when m₁ = m₂.
State the section formula for a point dividing a segment in ratio m:n internally.
Point = ((m·x₂ + n·x₁)/(m+n), (m·y₂ + n·y₁)/(m+n)).
State the surface area and volume of a sphere of radius r.
Surface area = 4πr². Volume = (4/3)πr³.
State the curved surface area, total surface area and volume of a cylinder (radius r, height h).
CSA = 2πrh; TSA = 2πr(r+h); Volume = πr²h.
State the volume and total surface area of a cone (radius r, height h, slant l).
Volume = (1/3)πr²h; CSA = πrl; TSA = πr(r+l), where l = √(r²+h²).
What are the values of sin, cos and tan at 0°, 30°, 45°, 60°, 90°?
sin: 0, 1/2, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, 1/2, 0. tan: 0, 1/√3, 1, √3, undefined.
State the three fundamental Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
What is the difference between a permutation and a combination, with formulas?
Permutation (order matters): ⁿPᵣ = n!/(n−r)!. Combination (order doesn't matter): ⁿCᵣ = n!/[r!(n−r)!].
How many ways can n distinct objects be arranged in a circle?
(n−1)! arrangements for a circle; if clockwise and counterclockwise are considered identical (e.g. a necklace), it is (n−1)!/2.
State the basic probability formula and the probability of the complement.
P(event) = favorable outcomes / total outcomes. P(not A) = 1 − P(A). P ranges from 0 to 1.
State the addition rule for probability of A or B, and the rule for independent events A and B.
P(A∪B) = P(A) + P(B) − P(A∩B). For independent events, P(A∩B) = P(A)·P(B).
State the inclusion-exclusion formula for 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|.
How many subsets does a set with n elements have, and how many proper subsets?
Total subsets = 2ⁿ; proper subsets (excluding the set itself) = 2ⁿ − 1; non-empty proper subsets = 2ⁿ − 2.
State the Binomial Theorem and the general (r+1)th term of (a + b)ⁿ.
(a+b)ⁿ = Σ_{k=0}^{n} ⁿCₖ a^(n−k) b^k. General term: T_{r+1} = ⁿCᵣ a^(n−r) bʳ. Sum of all coefficients = 2ⁿ (set a=b=1).
What this deck covers
The Quantitative Ability deck follows the XAT Quantitative Ability syllabus — 4 chapters and 21 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 12.8 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 93 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 Ability flashcards FAQ
How many Quantitative Ability flashcards are in this XAT deck?
51 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these XAT flashcards free?
Yes. The preview here is free to read with no signup, and the full 51-card deck is free inside the Examius app.
What do the Quantitative Ability cards cover?
They follow the XAT Quantitative Ability syllabus — 4 chapters and 21 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.