Examius
🇮🇳 ISC Class 12 · flashcards
ISC Class 12 Mathematics Flashcards
61 question-and-answer cards covering Mathematics as it is examined in ISC Class 12. 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.
How do you solve a variable-separable differential equation?
Write it as f(y) dy = g(x) dx, then integrate both sides separately to get the general solution.
What is the integrating factor and solution form of a linear ODE dy/dx + Py = Q?
Integrating factor IF = e^(integral of P dx). Solution: y times IF = integral of (Q times IF) dx + C.
Define a homogeneous differential equation and its standard substitution.
dy/dx = f(y/x) where f is a function of y/x. Substitute y = vx, so dy/dx = v + x(dv/dx), making it separable.
How is the dot (scalar) product of two vectors a and b defined, and what does it give?
a dot b = |a| |b| cos theta = a1b1 + a2b2 + a3b3; it is a scalar. a dot b = 0 means the vectors are perpendicular.
How is the cross (vector) product a x b defined and directed?
|a x b| = |a| |b| sin theta; it is a vector perpendicular to both a and b, with direction by the right-hand rule. Its magnitude equals the area of the parallelogram on a and b.
What is the formula for the projection of vector a on vector b?
Scalar projection = (a dot b) / |b|.
What is the scalar triple product [a b c] and its geometric meaning?
[a b c] = a dot (b x c); its absolute value is the volume of the parallelepiped. If it equals 0, the three vectors are coplanar.
Give the direction cosines relation for a line and the formula for distance between two points in 3D.
Direction cosines satisfy l squared + m squared + n squared = 1. Distance = square root of [(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2].
What is the equation of a plane in normal form and the shortest distance from a point to it?
Plane: ax + by + cz + d = 0. Distance from point (x1,y1,z1) = |ax1 + by1 + cz1 + d| / square root of (a^2 + b^2 + c^2).
In Linear Programming, define the objective function and constraints.
The objective function is the linear expression (e.g. Z = ax + by) to be maximized or minimized; constraints are the linear inequalities restricting the variables.
What is the feasible region and where do optimal solutions occur in an LPP?
The feasible region is the set of all points satisfying all constraints. The optimal value of the objective function occurs at a corner (vertex) point of the feasible region (Corner Point Theorem).
Name common types of Linear Programming problems.
Manufacturing (production) problems, diet problems, transportation problems, and allocation/optimal-mix problems.
State the formula for conditional probability P(A given B).
P(A | B) = P(A intersect B) / P(B), provided P(B) > 0.
What does it mean for events A and B to be independent, in terms of probability?
A and B are independent if P(A intersect B) = P(A) times P(B); equivalently P(A | B) = P(A).
State the Multiplication Theorem of Probability.
P(A intersect B) = P(A) times P(B | A) = P(B) times P(A | B).
State the Theorem of Total Probability.
If E1, E2, ..., En are mutually exclusive and exhaustive events, then P(A) = sum of P(Ei) times P(A | Ei).
State Bayes' Theorem.
P(Ei | A) = [P(Ei) times P(A | Ei)] / [sum over j of P(Ej) times P(A | Ej)].
What is the difference between prior and posterior probability in Bayes' Theorem?
Prior probability P(Ei) is known before the event A; posterior probability P(Ei | A) is the revised probability after observing A.
What is a probability distribution of a random variable, and what must the probabilities sum to?
It lists each value of the random variable X with its probability P(X). All probabilities are between 0 and 1 and their sum equals 1.
How is the mean (expectation) E(X) of a discrete random variable computed?
E(X) = sum of [x_i times P(x_i)] over all values.
How is the variance of a discrete random variable computed?
Var(X) = E(X squared) - [E(X)] squared = sum of [x_i squared times P(x_i)] minus the mean squared. Standard deviation is its square root.
State the conditions for a Bernoulli trials / binomial experiment.
Fixed number of trials n, each trial has two outcomes (success/failure), trials are independent, and the probability of success p is constant.
State the binomial distribution probability formula P(X = r).
P(X = r) = nCr times p^r times q^(n - r), where q = 1 - p and r = 0, 1, ..., n.
What are the mean and variance of a binomial distribution?
Mean = np; Variance = npq; Standard deviation = square root of npq. Note variance is always less than the mean since q < 1.
What this deck covers
The Mathematics deck follows the ISC Class 12 Mathematics syllabus — 6 chapters and 18 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.2 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 111 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 ISC Class 12 deck?
61 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these ISC Class 12 flashcards free?
Yes. The preview here is free to read with no signup, and the full 61-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the ISC Class 12 Mathematics syllabus — 6 chapters and 18 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.