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HEC USAT Mathematics Flashcards
50 question-and-answer cards covering Mathematics 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 Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the double-angle formulas for sin 2θ and cos 2θ.
sin 2θ = 2 sinθ cosθ; cos 2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ.
What is the formula for tan(A + B)?
tan(A + B) = (tanA + tanB) / (1 − tanA tanB).
State the Law of Sines for a triangle with sides a, b, c opposite angles A, B, C.
a/sinA = b/sinB = c/sinC = 2R, where R is the circumradius.
State the Law of Cosines for side a of a triangle.
a² = b² + c² − 2bc cosA (and cyclic versions for b² and c²).
Give two formulas for the area of a triangle used in solution of triangles.
Area = (1/2) ab sinC (two sides and included angle); or Heron's formula √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2.
In solving triangles, which case can produce two possible triangles (the ambiguous case)?
The SSA case (two sides and a non-included angle) when using the Law of Sines.
What is the domain and range of y = sin⁻¹ x (arcsin)?
Domain: −1 ≤ x ≤ 1; Range: −π/2 ≤ y ≤ π/2.
What is the domain and range of y = cos⁻¹ x (arccos)?
Domain: −1 ≤ x ≤ 1; Range: 0 ≤ y ≤ π.
What is the domain and range of y = tan⁻¹ x (arctan)?
Domain: all real numbers; Range: −π/2 < y < π/2.
What is the derivative of sin⁻¹ x and of tan⁻¹ x?
d/dx (sin⁻¹ x) = 1/√(1 − x²); d/dx (tan⁻¹ x) = 1/(1 + x²).
Define an injective (one-to-one), surjective (onto), and bijective function.
Injective: distinct inputs give distinct outputs. Surjective: every element of the codomain is an image. Bijective: both injective and surjective.
What is the difference between an even function and an odd function?
Even: f(−x) = f(x), symmetric about the y-axis. Odd: f(−x) = −f(x), symmetric about the origin.
What condition must a function satisfy to have an inverse, and how are their graphs related?
It must be one-to-one (bijective on its range). The graph of f⁻¹ is the reflection of f across the line y = x.
How do you find the domain of a function?
Find all real x for which the function is defined: exclude values making a denominator zero, a square-root argument negative, or a logarithm argument ≤ 0.
What is the range of f(x) = x² and of f(x) = √x (principal root)?
For x²: range is [0, ∞). For √x: domain [0, ∞) and range [0, ∞).
How does y = f(x) + k and y = f(x − h) transform the graph of f?
f(x) + k shifts the graph up by k (down if k < 0); f(x − h) shifts it right by h (left if h < 0).
How do y = −f(x) and y = f(−x) transform a graph?
−f(x) reflects the graph in the x-axis; f(−x) reflects it in the y-axis.
How does y = a·f(x) (a > 1) versus y = f(bx) (b > 1) transform a graph?
a·f(x) stretches vertically by factor a; f(bx) compresses horizontally by factor 1/b.
State the formal definition of a function being continuous at x = a.
f is continuous at a if: f(a) is defined, lim(x→a) f(x) exists, and lim(x→a) f(x) = f(a).
What is the standard limit lim(x→0) sin x / x?
It equals 1 (with x in radians).
State the limit definition (first principle) of the derivative f'(x).
f'(x) = lim(h→0) [f(x + h) − f(x)] / h.
State the power rule, product rule, and quotient rule for differentiation.
Power: d/dx xⁿ = n xⁿ⁻¹. Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v − uv')/v².
State the chain rule for differentiating a composite function y = f(g(x)).
dy/dx = f'(g(x)) · g'(x), i.e. dy/dx = (dy/du)(du/dx).
State the derivatives of sin x, cos x, e^x, and ln x.
d/dx sin x = cos x; d/dx cos x = −sin x; d/dx e^x = e^x; d/dx ln x = 1/x.
What this deck covers
The Mathematics deck follows the HEC USAT Mathematics syllabus — 6 chapters and 19 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 75 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.
Mathematics flashcards FAQ
How many Mathematics 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 Mathematics cards cover?
They follow the HEC USAT Mathematics syllabus — 6 chapters and 19 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.