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🇮🇳 CBSE Class 12 · flashcards
CBSE Class 12 Mathematics Flashcards
50 question-and-answer cards covering Mathematics as it is examined in CBSE 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 is the area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) found using a determinant?
Area = ½ |Δ| where Δ = the 3×3 determinant with rows (x1, y1, 1), (x2, y2, 1), (x3, y3, 1).
How does multiplying every element of one row (or column) of a determinant by k affect its value?
The value of the determinant is multiplied by k.
What is the value of a determinant if two rows (or columns) are identical?
The determinant equals 0.
What is the adjoint (adj A) of a square matrix A?
The transpose of the matrix of cofactors of A.
State the relation A(adj A) = (adj A)A.
A(adj A) = (adj A)A = |A| I, where I is the identity matrix of the same order.
What is the formula for the inverse of a non-singular matrix A?
A⁻¹ = (1/|A|) adj A, valid when |A| ≠ 0.
When is a square matrix A invertible (non-singular)?
A is invertible if and only if |A| ≠ 0.
For |A| of order n, what is |adj A| in terms of |A|?
|adj A| = |A|^(n−1).
In the matrix method, how is the system AX = B solved when A is invertible?
X = A⁻¹B, where A is the coefficient matrix, X the variable matrix, and B the constants matrix.
When does the system AX = B have a unique solution, and what is it called when |A| = 0?
If |A| ≠ 0, there is a unique solution X = A⁻¹B (consistent). If |A| = 0, the system may be inconsistent (no solution) or have infinitely many solutions.
State the condition for a function f to be continuous at x = c.
f is continuous at c if lim(x→c) f(x) = f(c); i.e., the left limit, right limit, and value at c are all equal and finite.
State the chain rule for differentiation.
If y = f(u) and u = g(x), then dy/dx = (dy/du)(du/dx).
What is the derivative of a function defined parametrically as x = f(t), y = g(t)?
dy/dx = (dy/dt)/(dx/dt), provided dx/dt ≠ 0.
State Rolle's Theorem.
If f is continuous on [a, b], differentiable on (a, b), and f(a) = f(b), then there exists c ∈ (a, b) with f'(c) = 0.
State the Mean Value Theorem (Lagrange).
If f is continuous on [a, b] and differentiable on (a, b), then there exists c ∈ (a, b) with f'(c) = [f(b) − f(a)]/(b − a).
What does the sign of f'(x) tell about a function on an interval?
f'(x) > 0 means f is increasing; f'(x) < 0 means f is decreasing on that interval.
State the second derivative test for local extrema at a critical point c (f'(c) = 0).
If f''(c) > 0, c is a point of local minimum; if f''(c) < 0, c is a local maximum; if f''(c) = 0, the test fails.
What is ∫ xⁿ dx for n ≠ −1?
∫ xⁿ dx = x^(n+1)/(n+1) + C.
What is the integration by parts formula?
∫ u v dx = u ∫v dx − ∫ [ (du/dx) ∫v dx ] dx (ILATE order to choose u).
State the Fundamental Theorem of Calculus (evaluation part).
If F is an antiderivative of f, then ∫ from a to b of f(x) dx = F(b) − F(a).
What is the property ∫ from a to b of f(x) dx in terms of ∫ from 0 to a of f(a−x)?
∫ from 0 to a of f(x) dx = ∫ from 0 to a of f(a − x) dx.
How is the area bounded by a curve y = f(x), the x-axis, and lines x = a, x = b found?
Area = ∫ from a to b of |f(x)| dx (take absolute value or split where the curve is below the axis).
What is the order and degree of a differential equation?
Order = order of the highest derivative present. Degree = power of the highest-order derivative, after the equation is made polynomial (free of radicals/fractions) in derivatives.
State the integrating factor (I.F.) method for a linear differential equation dy/dx + Py = Q.
I.F. = e^(∫P dx); solution: y·(I.F.) = ∫ Q·(I.F.) dx + C.
What this deck covers
The Mathematics deck follows the CBSE Class 12 Mathematics syllabus — 3 chapters and 13 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 16.7 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 77 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 CBSE Class 12 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 CBSE Class 12 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 CBSE Class 12 Mathematics syllabus — 3 chapters and 13 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.