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HEC USAT Quantitative Reasoning Flashcards
50 question-and-answer cards covering Quantitative Reasoning as it is examined in HEC USAT. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Reasoning deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the identities for (a + b)³ and a³ + b³.
(a + b)³ = a³ + 3a²b + 3ab² + b³; a³ + b³ = (a + b)(a² − ab + b²).
State the identity for a³ − b³.
a³ − b³ = (a − b)(a² + ab + b²).
What is the expansion of (a + b + c)²?
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
State the product laws of exponents: a^m × a^n and (a^m)^n.
a^m × a^n = a^(m+n); (a^m)^n = a^(mn).
What are the rules for a^m ÷ a^n, a^0, and a^(−n)?
a^m ÷ a^n = a^(m−n); a^0 = 1 (a≠0); a^(−n) = 1/a^n.
How is a fractional exponent a^(m/n) expressed as a radical?
a^(m/n) = n-th root of a^m = (ⁿ√a)^m.
How do you rationalize a denominator of the form 1/(√a)?
Multiply numerator and denominator by √a: 1/√a = √a/a. For 1/(a+√b), multiply by the conjugate (a−√b).
Simplify √a × √b and √(a/b).
√a × √b = √(ab); √(a/b) = √a / √b (for a,b ≥ 0, b≠0).
What is a function, and what are its domain and range?
A function maps each input from the domain to exactly one output. Domain = set of allowed inputs; Range = set of actual outputs produced.
What is the vertical line test for a function?
A graph represents a function if and only if no vertical line intersects it at more than one point (each x-value has only one y-value).
Distinguish one-to-one (injective), onto (surjective), and bijective functions.
Injective: distinct inputs give distinct outputs. Surjective: every element of the codomain is an output. Bijective: both injective and surjective (a one-to-one correspondence).
What is the composition of functions (f ∘ g)(x)?
(f ∘ g)(x) = f(g(x)): apply g first, then apply f to the result.
What is the nth term formula of an arithmetic progression (AP)?
aₙ = a + (n − 1)d, where a is the first term and d is the common difference.
What is the sum of the first n terms of an arithmetic progression?
Sₙ = (n/2)[2a + (n − 1)d] = (n/2)(a + l), where l is the last term.
What is the nth term of a geometric progression (GP)?
aₙ = a·r^(n−1), where a is the first term and r is the common ratio.
What is the sum of n terms of a GP, and the sum to infinity?
Sₙ = a(rⁿ − 1)/(r − 1) for r≠1. Sum to infinity S∞ = a/(1 − r) when |r| < 1.
How do you find the arithmetic mean and geometric mean of two numbers a and b?
Arithmetic mean = (a + b)/2; Geometric mean = √(ab).
What is the general form and solution of a linear equation in one variable ax + b = 0?
It is degree-one in x. Solution: x = −b/a (a ≠ 0).
What does the slope-intercept form y = mx + c tell you about a line?
m is the slope (rate of change), and c is the y-intercept (where the line crosses the y-axis).
What is the slope of the line through points (x₁,y₁) and (x₂,y₂)?
Slope m = (y₂ − y₁)/(x₂ − x₁).
State the standard form and the quadratic formula for ax² + bx + c = 0.
Standard form: ax² + bx + c = 0 (a≠0). Quadratic formula: x = [−b ± √(b² − 4ac)] / (2a).
What does the discriminant b² − 4ac reveal about the roots of a quadratic?
If > 0: two distinct real roots; if = 0: one repeated real root; if < 0: no real roots (two complex roots).
For ax² + bx + c = 0, what are the sum and product of the roots?
Sum of roots = −b/a; Product of roots = c/a.
What are the methods to solve a pair of simultaneous linear equations, and what does the solution represent?
Substitution, elimination, and graphical methods (also matrix/Cramer's rule). The solution is the point of intersection of the two lines; parallel lines mean no solution, identical lines mean infinitely many.
What this deck covers
The Quantitative Reasoning deck follows the HEC USAT Quantitative Reasoning syllabus — 6 chapters and 24 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 79 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 Reasoning flashcards FAQ
How many Quantitative Reasoning flashcards are in this HEC USAT 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 HEC USAT 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 Reasoning cards cover?
They follow the HEC USAT Quantitative Reasoning syllabus — 6 chapters and 24 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.