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🇵🇰 COMSATS Admission Test · flashcards
COMSATS Admission Test Mathematics Flashcards
51 question-and-answer cards covering Mathematics as it is examined in COMSATS 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 Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the chain rule for differentiation.
d/dx f(g(x)) = f'(g(x)) * g'(x). Differentiate the outer function, keep the inner, then multiply by the derivative of the inner.
What are the derivatives of sin x and cos x?
d/dx sin x = cos x; d/dx cos x = -sin x.
What are the derivatives of e^x and ln x?
d/dx e^x = e^x; d/dx ln x = 1/x (for x>0).
What is the derivative of tan x?
d/dx tan x = sec^2 x.
What does the first derivative tell you about increasing/decreasing behavior?
Where f'(x) > 0 the function is increasing; where f'(x) < 0 it is decreasing. f'(x)=0 indicates a critical point.
State the First Derivative Test for local extrema.
At a critical point, if f' changes from + to -, it is a local maximum; if f' changes from - to +, it is a local minimum; if no sign change, it is neither.
What does the second derivative tell you about concavity and inflection points?
f''(x) > 0 means concave up; f''(x) < 0 means concave down. An inflection point is where concavity changes (f''=0 and sign changes).
State the Second Derivative Test for a critical point where f'(c)=0.
If f''(c) > 0, f has a local minimum at c; if f''(c) < 0, a local maximum; if f''(c)=0, the test is inconclusive.
What is the geometric meaning of the derivative at a point?
f'(a) is the slope of the tangent line to the curve y=f(x) at the point (a, f(a)); it also gives the instantaneous rate of change.
What is an indefinite integral and why is +C included?
The indefinite integral of f(x) is the family of all antiderivatives F(x)+C, where F'(x)=f(x). +C accounts for the fact that constants vanish under differentiation.
State the power rule for indefinite integration.
Integral of x^n dx = x^{n+1}/(n+1) + C, for n != -1.
What is the integral of 1/x dx?
Integral of 1/x dx = ln|x| + C (this covers the n=-1 case excluded by the power rule).
What are the integrals of sin x and cos x?
Integral of sin x dx = -cos x + C; Integral of cos x dx = sin x + C.
State the integration-by-parts formula.
Integral of u dv = u v - Integral of v du.
State the Fundamental Theorem of Calculus (evaluation part).
If F is an antiderivative of f on [a,b], then the integral from a to b of f(x) dx = F(b) - F(a).
What property results from swapping the limits of a definite integral?
Integral from a to b of f dx = - Integral from b to a of f dx. Swapping the limits negates the value.
How do you change the limits when using substitution in a definite integral?
Replace the x-limits with the corresponding u-values from u=g(x), so no need to convert back to x. Evaluate the new integrand between the new limits.
How do you compute the area under a curve y=f(x) above the x-axis from a to b?
Area = Integral from a to b of f(x) dx, provided f(x) >= 0 on [a,b].
How do you find the area between two curves f(x) and g(x) on [a,b]?
Area = Integral from a to b of [f(x) - g(x)] dx, where f is the upper curve and g is the lower curve over the interval.
State the Pythagorean trigonometric identities.
sin^2(x) + cos^2(x) = 1; 1 + tan^2(x) = sec^2(x); 1 + cot^2(x) = csc^2(x).
State the sine and cosine sum identities.
sin(A+B) = sin A cos B + cos A sin B; cos(A+B) = cos A cos B - sin A sin B.
State the double-angle identities for sine and cosine.
sin(2x) = 2 sin x cos x; cos(2x) = cos^2 x - sin^2 x = 2cos^2 x - 1 = 1 - 2sin^2 x.
State the period, amplitude, and range of y = a sin(bx).
Amplitude = |a|; period = 2π/|b|; range = [-|a|, |a|]. The graph oscillates b times faster than sin x.
State the Law of Sines and the Law of Cosines for solving triangles.
Law of Sines: a/sin A = b/sin B = c/sin C. Law of Cosines: c^2 = a^2 + b^2 - 2ab cos C (used for SAS or SSS cases).
What this deck covers
The Mathematics deck follows the COMSATS Admission Test Mathematics syllabus — 9 chapters and 27 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 5.7 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 94 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 COMSATS Admission Test 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 COMSATS Admission Test 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 Mathematics cards cover?
They follow the COMSATS Admission Test Mathematics syllabus — 9 chapters and 27 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.