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🇮🇳 ISC Class 11 · flashcards
ISC Class 11 Mathematics Flashcards
51 question-and-answer cards covering Mathematics as it is examined in ISC Class 11. 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.
What is the value of nCr + nC(r−1)?
(n+1)Cr (Pascal's rule).
State the Binomial Theorem for (a + b)^n where n is a positive integer.
(a+b)^n = Σ (k=0 to n) nCk · a^(n−k) · b^k.
What is the general (r+1)th term in the expansion of (a + b)^n?
T_(r+1) = nCr · a^(n−r) · b^r.
How many terms are there in the expansion of (a + b)^n?
n + 1 terms.
What is the nth term of an arithmetic progression (AP) with first term a and common difference d?
a_n = a + (n − 1)d.
What is the sum of the first n terms of an AP?
S_n = n/2 [2a + (n − 1)d] = n/2 (a + l), where l is the last term.
What is the nth term and sum to n terms of a geometric progression (GP) with first term a, ratio r?
a_n = a·r^(n−1); S_n = a(r^n − 1)/(r − 1) for r ≠ 1.
What is the sum to infinity of a GP with |r| < 1?
S_∞ = a / (1 − r).
State the relationship between the arithmetic mean (AM) and geometric mean (GM) of two positive numbers.
AM ≥ GM, with equality only when the numbers are equal.
What is the slope of a line passing through points (x₁, y₁) and (x₂, y₂)?
m = (y₂ − y₁) / (x₂ − x₁).
State the slope-intercept and point-slope forms of a straight line.
Slope-intercept: y = mx + c. Point-slope: y − y₁ = m(x − x₁).
What are the conditions for two lines (slopes m₁, m₂) to be parallel or perpendicular?
Parallel: m₁ = m₂. Perpendicular: m₁ · m₂ = −1.
What is the formula for the distance of a point (x₁, y₁) from the line Ax + By + C = 0?
d = |Ax₁ + By₁ + C| / √(A² + B²).
State the standard equation of a circle with centre (h, k) and radius r.
(x − h)² + (y − k)² = r².
What is the standard equation of a parabola opening rightward, and its focus?
y² = 4ax; focus at (a, 0), directrix x = −a.
State the standard equation of an ellipse and define eccentricity for it.
x²/a² + y²/b² = 1 (a > b); eccentricity e = √(1 − b²/a²), with 0 < e < 1.
State the standard equation of a hyperbola and the range of its eccentricity.
x²/a² − y²/b² = 1; eccentricity e = √(1 + b²/a²), with e > 1.
What is the distance formula between two points in three-dimensional space?
d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²].
What is the section formula for a point dividing the segment joining (x₁,y₁,z₁) and (x₂,y₂,z₂) in ratio m:n internally?
((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n), (mz₂+nz₁)/(m+n)).
State two standard limits used in calculus involving sin and polynomials.
lim(x→0) sin x / x = 1; and lim(x→a) (x^n − a^n)/(x − a) = n·a^(n−1).
What is the derivative definition (first principles) of f(x)?
f'(x) = lim(h→0) [f(x+h) − f(x)] / h.
State the power rule and product rule of differentiation.
Power rule: d/dx(x^n) = n·x^(n−1). Product rule: (uv)' = u'v + uv'.
State the formula for variance of n observations using mean x̄.
σ² = (1/n) Σ(xᵢ − x̄)²; standard deviation σ = √variance.
For mutually exclusive events A and B, what is P(A ∪ B)? And for any two events?
Mutually exclusive: P(A∪B) = P(A) + P(B). General: P(A∪B) = P(A) + P(B) − P(A∩B).
What this deck covers
The Mathematics deck follows the ISC Class 11 Mathematics syllabus — 5 chapters and 15 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 45 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 11 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 ISC Class 11 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 ISC Class 11 Mathematics syllabus — 5 chapters and 15 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.