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BITSAT Mathematics Flashcards
52 question-and-answer cards covering Mathematics as it is examined in BITSAT. 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 are the principal value ranges of sin^(-1)x, cos^(-1)x, and tan^(-1)x?
sin^(-1)x ∈ [-π/2, π/2]; cos^(-1)x ∈ [0, π]; tan^(-1)x ∈ (-π/2, π/2).
State the identity relating sin^(-1)x and cos^(-1)x, and tan^(-1)x and cot^(-1)x.
sin^(-1)x + cos^(-1)x = π/2; tan^(-1)x + cot^(-1)x = π/2 (for x in valid domains).
State the Law of Sines and the Law of Cosines for a triangle.
Law of Sines: a/sin A = b/sin B = c/sin C = 2R. Law of Cosines: c^2 = a^2 + b^2 - 2ab cos C.
Give two formulas for the area of a triangle in terms of its sides/angles.
Area = (1/2)ab sin C; and Heron's formula: Area = sqrt[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2.
What is the slope-intercept form and the point-slope form of a straight line?
Slope-intercept: y = mx + c; point-slope: y - y_1 = m(x - x_1).
What are the conditions for two lines to be parallel and perpendicular in terms of slopes?
Parallel: m_1 = m_2; perpendicular: m_1·m_2 = -1.
What is the perpendicular distance from point (x_1, y_1) to the line ax + by + c = 0?
d = |a·x_1 + b·y_1 + c| / sqrt(a^2 + b^2).
State the standard equation of a circle with centre (h, k) and radius r, and the general form.
Standard: (x-h)^2 + (y-k)^2 = r^2. General: x^2 + y^2 + 2gx + 2fy + c = 0, with centre (-g, -f) and radius sqrt(g^2 + f^2 - c).
Compare the eccentricities of the conic sections (circle, parabola, ellipse, hyperbola).
Circle: e = 0; Parabola: e = 1; Ellipse: 0 < e < 1; Hyperbola: e > 1.
For the parabola y^2 = 4ax, give the vertex, focus, directrix, and length of latus rectum.
Vertex (0,0); focus (a,0); directrix x = -a; length of latus rectum = 4a.
For the ellipse x^2/a^2 + y^2/b^2 = 1 (a > b), give the eccentricity and foci.
e = sqrt(1 - b^2/a^2); foci at (±ae, 0). Sum of focal distances = 2a.
What is the distance formula and the section formula in three-dimensional geometry?
Distance = sqrt[(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2]. Internal division in ratio m:n: ((mx2+nx1)/(m+n), (my2+ny1)/(m+n), (mz2+nz1)/(m+n)).
What are direction cosines, and what relation do they satisfy?
Direction cosines (l, m, n) are the cosines of the angles a line makes with the x, y, z axes, satisfying l^2 + m^2 + n^2 = 1.
Define the limit condition for continuity of a function f at x = a.
f is continuous at a if lim(x→a) f(x) exists, f(a) is defined, and lim(x→a) f(x) = f(a).
State the two standard trigonometric limits as x → 0.
lim(x→0) (sin x)/x = 1; lim(x→0) (1 - cos x)/x^2 = 1/2.
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 a composite function y = f(g(x)).
dy/dx = f'(g(x))·g'(x), i.e., dy/dx = (dy/du)·(du/dx).
How do you use the first and second derivatives to find and classify a local extremum?
At a critical point f'(x) = 0: if f''(x) > 0 it's a local minimum; if f''(x) < 0 it's a local maximum; if f''(x) = 0 the test is inconclusive.
State the formula for integration by parts.
∫ u dv = uv - ∫ v du. (Choose u by ILATE order: Inverse, Log, Algebraic, Trig, Exponential.)
State the Fundamental Theorem of Calculus for definite integrals.
If F is an antiderivative of f, then ∫_a^b f(x) dx = F(b) - F(a).
How do you solve a first-order linear differential equation dy/dx + Py = Q?
Use integrating factor IF = e^(∫P dx); solution: y·(IF) = ∫ Q·(IF) dx + C.
Give the formulas for the dot product and cross product of two vectors in terms of the angle θ.
a·b = |a||b| cos θ (scalar); |a×b| = |a||b| sin θ, with a×b perpendicular to both (vector).
State Bayes' theorem and the formula for conditional probability.
Conditional: P(A|B) = P(A∩B)/P(B). Bayes: P(A|B) = P(B|A)·P(A) / P(B).
State the binomial probability distribution: probability of r successes in n trials.
P(X = r) = nCr · p^r · q^(n-r), where q = 1 - p; mean = np, variance = npq.
What this deck covers
The Mathematics deck follows the BITSAT Mathematics syllabus — 12 chapters and 45 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 4.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 82 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 BITSAT deck?
52 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these BITSAT flashcards free?
Yes. The preview here is free to read with no signup, and the full 52-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the BITSAT Mathematics syllabus — 12 chapters and 45 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.