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CAT (Common Admission Test) Quantitative Aptitude (QA) - Algebra Flashcards
50 question-and-answer cards covering Quantitative Aptitude (QA) - Algebra 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) - Algebra deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the condition for a function to have an inverse, and what is the relationship between a function and its inverse graphically?
A function has an inverse iff it is bijective (one-to-one and onto). The graph of f⁻¹ is the reflection of f's graph about the line y = x.
Describe the graph transformations for f(x)+c, f(x+c), and -f(x).
f(x)+c: shift up by c (down if c<0). f(x+c): shift left by c (right if c<0). -f(x): reflect across the x-axis.
Describe the transformations f(-x), a·f(x) (a>1), and f(ax) (a>1).
f(-x): reflect across y-axis. a·f(x): vertical stretch by factor a. f(ax): horizontal compression by factor a.
How do you find the vertex of a parabola y = ax² + bx + c, and is it a maximum or minimum?
Vertex at x = -b/(2a), giving y = c - b²/(4a). If a>0 it is a minimum; if a<0 it is a maximum.
For a quadratic ax²+bx+c, what is the maximum/minimum value of the expression?
The extreme value is (4ac - b²)/(4a) = -D/(4a), attained at x = -b/(2a). Minimum if a>0, maximum if a<0.
State the laws of indices: aᵐ·aⁿ, aᵐ/aⁿ, (aᵐ)ⁿ, a⁰, and a⁻ⁿ.
aᵐ·aⁿ = aᵐ⁺ⁿ; aᵐ/aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1 (a≠0); a⁻ⁿ = 1/aⁿ.
How do you express a fractional exponent a^(m/n) in surd (radical) form?
a^(m/n) = ⁿ√(aᵐ) = (ⁿ√a)ᵐ, the nth root of a raised to the m.
What is the conjugate used to rationalize a denominator like 1/(√a + √b)?
Multiply numerator and denominator by the conjugate (√a - √b): 1/(√a+√b) = (√a-√b)/(a-b).
State the four basic logarithm properties: product, quotient, power, and change of base.
log(mn)=log m+log n; log(m/n)=log m-log n; log(mⁿ)=n·log m; change of base: logₐb = (log_c b)/(log_c a).
Evaluate logₐ1, logₐa, and a^(logₐx).
logₐ1 = 0; logₐa = 1; a^(logₐx) = x (for x>0).
What is the relationship between logₐb and log_b a?
logₐb = 1/(log_b a). Their product equals 1: logₐb × log_b a = 1.
What are the domain restrictions for logₐx (the argument and the base)?
The argument x must be > 0; the base a must be > 0 and a ≠ 1.
How does the sign of logₐx behave when the base a > 1 versus 0 < a < 1?
For a>1: logₐx > 0 when x>1, < 0 when 0<x<1 (increasing function). For 0<a<1: signs reverse (decreasing function).
When solving a logarithmic inequality logₐx < logₐy, how does the base affect the direction?
If a > 1, the inequality preserves direction: x < y. If 0 < a < 1, it reverses: x > y. (Both x, y must be positive.)
What is an Arithmetic Progression (AP), and what is the formula for its nth term?
An AP has a constant common difference d between consecutive terms. nth term: aₙ = a + (n-1)d, where a is the first term.
State the two formulas for the sum of the first n terms of an AP.
Sₙ = n/2·[2a + (n-1)d] = n/2·(a + l), where l is the last term.
What is the arithmetic mean of two numbers a and b, and how do you insert n AMs between them?
AM = (a+b)/2. To insert n means, the common difference d = (b-a)/(n+1); the means are a+d, a+2d, ..., a+nd.
What is a Geometric Progression (GP), and what is its nth term?
A GP has a constant common ratio r between consecutive terms. nth term: aₙ = a·r^(n-1), where a is the first term.
State the sum of n terms of a GP (for r ≠ 1).
Sₙ = a(rⁿ - 1)/(r - 1), or equivalently a(1 - rⁿ)/(1 - r).
What is the sum of an infinite GP, and the condition for it to converge?
S∞ = a/(1 - r), valid only when |r| < 1. Otherwise the series diverges.
What is the geometric mean of two numbers a and b, and what is the GM of n positive numbers?
GM of a, b = √(ab). GM of n numbers = (product of all n numbers)^(1/n).
What is a Harmonic Progression (HP), and how is its nth term found?
A sequence is an HP if the reciprocals of its terms form an AP. The nth term = 1/(corresponding AP term) = 1/[a + (n-1)d].
Give the formulas for the sum 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 = (Σn)².
For three numbers in AP, GP, and HP respectively, how is the middle term expressed in terms of a and c?
AP: b = (a+c)/2 (arithmetic mean). GP: b = √(ac) (geometric mean). HP: b = 2ac/(a+c) (harmonic mean).
What this deck covers
The Quantitative Aptitude (QA) - Algebra deck follows the CAT (Common Admission Test) Quantitative Aptitude (QA) - Algebra syllabus — 5 chapters and 15 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 90 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) - Algebra flashcards FAQ
How many Quantitative Aptitude (QA) - Algebra 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) - Algebra cards cover?
They follow the CAT (Common Admission Test) Quantitative Aptitude (QA) - Algebra syllabus — 5 chapters and 15 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.