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CAT Quantitative Aptitude: Algebra Flashcards
50 question-and-answer cards covering Quantitative Aptitude: Algebra 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: Algebra deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the AM-GM inequality for two positive numbers and its general form.
For positive numbers, AM ≥ GM. For n positive numbers: (a1+...+an)/n ≥ (a1·...·an)^(1/n), with equality when all numbers are equal.
State the AM ≥ GM ≥ HM relationship for positive reals.
Arithmetic Mean ≥ Geometric Mean ≥ Harmonic Mean, with equality only when all the numbers are equal. Also GM² = AM × HM for two numbers.
By AM-GM, what is the minimum value of x + 1/x for x > 0?
Minimum value is 2, attained at x = 1 (since x + 1/x ≥ 2√(x·1/x) = 2).
What is the maximum/minimum value of the quadratic f(x) = ax² + bx + c?
Vertex at x = -b/2a. If a > 0, minimum value = c - b²/4a (= (4ac-b²)/4a); if a < 0, that is the maximum value.
For two positive numbers with a fixed sum, when is their product maximum? For a fixed product, when is their sum minimum?
Fixed sum → product is maximum when the numbers are equal. Fixed product → sum is minimum when the numbers are equal.
What defines a function (mapping) from set A to set B?
A rule assigning to each element of domain A exactly one element of codomain B. No input maps to two outputs.
Define the domain, codomain, and range of a function.
Domain = set of all valid inputs. Codomain = set in which outputs lie. Range = set of actual output values (range ⊆ codomain).
Distinguish one-one (injective), onto (surjective), and bijective functions.
Injective: distinct inputs give distinct outputs. Surjective: range = codomain (every codomain element is hit). Bijective: both injective and surjective.
Define even and odd functions with examples.
Even: f(-x) = f(x), symmetric about y-axis (e.g., x², cos x). Odd: f(-x) = -f(x), symmetric about origin (e.g., x³, sin x).
How is the composite function (f ∘ g)(x) defined?
(f ∘ g)(x) = f(g(x)): apply g first, then f. Generally f ∘ g ≠ g ∘ f (composition is not commutative).
What is the necessary condition for a function to have an inverse, and how do the domain/range relate?
The function must be bijective (one-one and onto). The inverse f⁻¹ swaps domain and range: domain of f⁻¹ = range of f, and vice versa.
How do you find the inverse of a function f(x) algebraically?
Set y = f(x), solve for x in terms of y, then swap variables to write f⁻¹(x). Verify f(f⁻¹(x)) = x.
What is the relationship between the graphs of f(x) and f⁻¹(x)?
They are reflections of each other across the line y = x.
Describe the graph transformations of y = f(x) + k and y = f(x + k).
y = f(x) + k shifts the graph vertically: up if k > 0, down if k < 0. y = f(x + k) shifts horizontally: left if k > 0, right if k < 0.
Describe the transformations y = -f(x), y = f(-x), and y = a·f(x).
y = -f(x): reflection across x-axis. y = f(-x): reflection across y-axis. y = a·f(x): vertical stretch (|a|>1) or compression (|a|<1).
How do you graph y = |f(x)| from the graph of y = f(x)?
Keep the parts of f(x) above the x-axis unchanged and reflect the parts below the x-axis upward (above the x-axis).
Define the greatest integer (floor) function and the fractional part function.
Floor [x] = greatest integer ≤ x (e.g., [2.7]=2, [-1.3]=-2). Fractional part {x} = x - [x], always in [0,1).
What is the signum function sgn(x)?
sgn(x) = 1 if x > 0, 0 if x = 0, and -1 if x < 0. It returns the sign of x.
Convert log_a(N) = x into exponential form, and state the domain conditions.
a^x = N. Requires N > 0, base a > 0 and a ≠ 1.
State the product, quotient, and power laws of logarithms.
log(MN) = log M + log N; log(M/N) = log M - log N; log(M^p) = p·log M (same base).
State the change of base formula for logarithms.
log_a(N) = log_b(N) / log_b(a). Also log_a(b) = 1 / log_b(a).
For an arithmetic progression with first term a and common difference d, give the nth term and the sum of n terms.
nth term: a_n = a + (n-1)d. Sum: S_n = n/2 × [2a + (n-1)d] = n/2 × (first term + last term).
For a geometric progression with first term a and common ratio r, give the nth term, sum of n terms, and the infinite sum.
a_n = a·r^(n-1); S_n = a(r^n - 1)/(r - 1) for r ≠ 1; infinite sum = a/(1 - r) when |r| < 1.
Give the standard sums of the first n natural numbers, their squares, and their cubes.
Σn = n(n+1)/2; Σn² = n(n+1)(2n+1)/6; Σn³ = [n(n+1)/2]².
What this deck covers
This deck covers the Quantitative Aptitude: Algebra 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 103 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: Algebra flashcards FAQ
How many Quantitative Aptitude: Algebra 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: Algebra cards cover?
They follow the Quantitative Aptitude: Algebra 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.