Examius
🇮🇳 AP EAMCET / TS EAMCET · flashcards
AP EAMCET / TS EAMCET Mathematics - Calculus, Geometry and Probability Flashcards
55 question-and-answer cards covering Mathematics - Calculus, Geometry and Probability as it is examined in AP EAMCET / TS EAMCET. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics - Calculus, Geometry and Probability deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
State the first principle (definition) of the derivative of f(x).
f'(x) = lim(h->0) [f(x+h) - f(x)] / h
State the product rule and quotient rule for differentiation.
Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v - uv')/v^2.
State the chain rule for differentiating y = f(g(x)).
dy/dx = f'(g(x)) * g'(x), i.e., dy/dx = (dy/du)(du/dx).
Give the derivatives of sin x, cos x, tan x, and ln x.
d/dx(sin x) = cos x; d/dx(cos x) = -sin x; d/dx(tan x) = sec^2 x; d/dx(ln x) = 1/x.
How do you find the maxima and minima of a function using the second derivative test?
At a stationary point where f'(x) = 0: if f''(x) < 0 it is a local maximum, if f''(x) > 0 it is a local minimum, and if f''(x) = 0 the test is inconclusive.
What is the geometric meaning of the derivative f'(x) at a point?
It is the slope of the tangent to the curve y = f(x) at that point; the slope of the normal is -1/f'(x).
State Rolle's Theorem.
If f is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there exists c in (a, b) such that f'(c) = 0.
State the Lagrange Mean Value Theorem.
If f is continuous on [a, b] and differentiable on (a, b), then there exists c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a).
Give the integrals of x^n and 1/x.
Integral of x^n dx = x^(n+1)/(n+1) + C (n != -1); Integral of (1/x) dx = ln|x| + C.
State the formula for integration by parts.
Integral of u dv = u*v - Integral of v du. Choose u by ILATE order (Inverse, Log, Algebraic, Trig, Exponential).
Give the integrals of sin x, cos x, and sec^2 x.
Integral of sin x dx = -cos x + C; Integral of cos x dx = sin x + C; Integral of sec^2 x dx = tan x + C.
State the Fundamental Theorem of Calculus for definite integrals.
If F is an antiderivative of f, then the integral from a to b of f(x) dx = F(b) - F(a).
State the property: integral from a to b of f(x) dx equals what in terms of f(a+b-x)?
Integral from a to b of f(x) dx = Integral from a to b of f(a + b - x) dx.
When is the integral from -a to a of f(x) dx equal to 2 times integral from 0 to a, and when is it zero?
It equals 2 * integral from 0 to a of f(x) dx if f is even (f(-x) = f(x)), and equals 0 if f is odd (f(-x) = -f(x)).
Define the order and degree of a differential equation.
Order is the order of the highest derivative present; degree is the power of the highest-order derivative after the equation is made polynomial in derivatives (free of radicals/fractions).
How do you solve a first-order linear differential equation dy/dx + Py = Q?
Find integrating factor IF = e^(Integral P dx); the solution is y * IF = Integral (Q * IF) dx + C.
How is a variable-separable differential equation solved?
Rewrite as f(y) dy = g(x) dx, then integrate both sides: Integral f(y) dy = Integral g(x) dx + C.
Define mean deviation, variance, and standard deviation as measures of dispersion.
Mean deviation = mean of absolute deviations from a central value; Variance = mean of squared deviations from the mean; Standard deviation = sqrt(variance).
State the addition theorem of probability for two events A and B.
P(A union B) = P(A) + P(B) - P(A intersection B). For mutually exclusive events, P(A union B) = P(A) + P(B).
State the conditional probability formula and the multiplication theorem.
P(A|B) = P(A intersection B)/P(B). Multiplication: P(A intersection B) = P(A)*P(B|A) = P(B)*P(A|B). For independent events P(A intersection B) = P(A)P(B).
State Bayes' Theorem for events A_i with prior probabilities.
P(A_i|B) = [P(A_i)*P(B|A_i)] / sum over j of [P(A_j)*P(B|A_j)].
For a binomial distribution with parameters n and p, give P(X = r), the mean, and the variance.
P(X = r) = C(n, r) p^r q^(n-r) with q = 1 - p; mean = np; variance = npq.
For a Poisson distribution with parameter lambda, give P(X = r), the mean, and the variance.
P(X = r) = (e^(-lambda) * lambda^r)/r!; mean = lambda; variance = lambda.
What is the expected value (mean) and variance of a discrete random variable X?
Mean E(X) = sum of x_i * P(x_i); Variance Var(X) = E(X^2) - [E(X)]^2 = sum x_i^2 P(x_i) - (E(X))^2.
What this deck covers
The Mathematics - Calculus, Geometry and Probability deck follows the AP EAMCET / TS EAMCET Mathematics - Calculus, Geometry and Probability syllabus — 5 chapters and 17 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 11.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 101 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 - Calculus, Geometry and Probability flashcards FAQ
How many Mathematics - Calculus, Geometry and Probability flashcards are in this AP EAMCET / TS EAMCET deck?
55 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these AP EAMCET / TS EAMCET flashcards free?
Yes. The preview here is free to read with no signup, and the full 55-card deck is free inside the Examius app.
What do the Mathematics - Calculus, Geometry and Probability cards cover?
They follow the AP EAMCET / TS EAMCET Mathematics - Calculus, Geometry and Probability syllabus — 5 chapters and 17 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.