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AILET Quantitative Techniques Flashcards
51 question-and-answer cards covering Quantitative Techniques as it is examined in AILET. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Techniques deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
Classify natural, whole, integer, rational, and irrational numbers briefly.
Natural: 1,2,3,...; Whole: 0,1,2,...; Integers: ...,-2,-1,0,1,2,...; Rational: expressible as p/q (q!=0); Irrational: non-terminating non-repeating decimals (e.g., sqrt2, pi).
State the divisibility rules for 3, 9, and 11.
Divisible by 3: digit sum divisible by 3. By 9: digit sum divisible by 9. By 11: difference between sums of alternate digits is 0 or divisible by 11.
What is the relationship between LCM and HCF of two numbers a and b?
LCM x HCF = a x b (product of the two numbers).
Define prime, composite, and co-prime numbers.
Prime: exactly two factors (1 and itself). Composite: more than two factors. Co-prime: two numbers whose HCF is 1 (no common factor besides 1).
State the algebraic identity for (a + b)^2, (a - b)^2, and (a + b)(a - b).
(a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2; (a+b)(a-b) = a^2 - b^2.
Write the quadratic formula for solving ax^2 + bx + c = 0.
x = [-b +/- sqrt(b^2 - 4ac)] / (2a), valid when a != 0.
What does the discriminant (b^2 - 4ac) tell you about the roots of a quadratic?
If > 0: two distinct real roots; if = 0: two equal real roots; if < 0: no real roots (complex roots).
For ax^2 + bx + c = 0, state the sum and product of the roots.
Sum of roots = -b/a; Product of roots = c/a.
State the identity for a^3 + b^3 and a^3 - b^3.
a^3 + b^3 = (a + b)(a^2 - ab + b^2); a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Define an arithmetic progression (AP) and give its nth term formula.
An AP has a constant common difference d between consecutive terms. nth term a_n = a + (n-1)d, where a is the first term.
Write the formula for the sum of the first n terms of an AP.
S_n = n/2 [2a + (n-1)d] = n/2 (first term + last term).
Define a geometric progression (GP) and give its nth term and sum formula.
A GP has a constant ratio r between terms. nth term = a r^(n-1); Sum of n terms = a(r^n - 1)/(r - 1) for r != 1.
What is the sum of the first n natural numbers, and the sum of their squares?
Sum = n(n+1)/2; Sum of squares = n(n+1)(2n+1)/6.
State the order of operations (BODMAS/PEMDAS) used to evaluate expressions.
Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).
Write the formulas for area and perimeter of a rectangle.
Area = length x breadth; Perimeter = 2(length + breadth).
Write the area and circumference formulas for a circle of radius r.
Area = pi r^2; Circumference = 2 pi r (= pi d, where d is diameter).
State the area of a triangle given base and height, and Heron's formula.
Area = 1/2 x base x height. Heron's: Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2.
Write the area and perimeter of a square, and the area of a parallelogram.
Square: Area = side^2, Perimeter = 4 x side. Parallelogram: Area = base x height.
What is the formula for the area of a trapezium?
Area = 1/2 x (sum of the two parallel sides) x (perpendicular distance between them).
Define probability of an event and give its range.
P(E) = (number of favourable outcomes) / (total number of equally likely outcomes). P(E) lies between 0 and 1 inclusive.
State the addition rule for probability and the rule for complementary events.
P(A or B) = P(A) + P(B) - P(A and B). Complement: P(not A) = 1 - P(A).
Define mean, median, and mode in statistics.
Mean: arithmetic average. Median: middle value when data is ordered (average of two middle values if even count). Mode: the most frequently occurring value.
State the angle sum property of a triangle and the exterior angle theorem.
Interior angles of a triangle sum to 180 degrees. An exterior angle equals the sum of the two opposite (remote) interior angles.
What are complementary, supplementary, and vertically opposite angles?
Complementary: two angles summing to 90 degrees. Supplementary: two angles summing to 180 degrees. Vertically opposite angles (formed by two intersecting lines) are equal.
What this deck covers
The Quantitative Techniques deck follows the AILET Quantitative Techniques 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 12.8 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 98 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 Techniques flashcards FAQ
How many Quantitative Techniques flashcards are in this AILET 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 AILET 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 Techniques cards cover?
They follow the AILET Quantitative Techniques 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.