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KCET Mathematics Flashcards
67 question-and-answer cards covering Mathematics as it is examined in KCET. 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.
State the product rule and quotient rule for differentiation.
Product: (uv)' = u'v + uv'. Quotient: (u/v)' = (u'v − uv')/v².
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).
What is the first derivative test for determining local maxima and minima?
At a critical point where f'(x) = 0: if f' changes from + to −, it is a local maximum; if from − to +, a local minimum; if no sign change, neither.
State the second derivative test for local extrema.
At a critical point c where f'(c) = 0: if f''(c) < 0, local maximum; if f''(c) > 0, local minimum; if f''(c) = 0, the test is inconclusive.
State the integrals of 1/x, e^x, and sec²x.
∫(1/x)dx = ln|x| + C; ∫e^x dx = e^x + C; ∫sec²x dx = tan x + C.
State the power rule for integration of x^n.
∫x^n dx = x^(n+1)/(n+1) + C, for n ≠ −1.
State the integration by parts formula.
∫u dv = uv − ∫v du.
State the Fundamental Theorem of Calculus (evaluation part).
If F is an antiderivative of f on [a, b], then ∫(a to b) f(x) dx = F(b) − F(a).
What is the order and degree of a differential equation?
Order = highest derivative present. Degree = power of the highest-order derivative, after the equation is made polynomial (free of radicals/fractions) in derivatives.
How do you solve a linear first-order differential equation dy/dx + Py = Q?
Find the integrating factor IF = e^(∫P dx). Then solution: y·(IF) = ∫Q·(IF) dx + C.
How do you solve a variable-separable differential equation?
Write it as f(y)dy = g(x)dx, then integrate both sides: ∫f(y)dy = ∫g(x)dx + C.
Define the dot (scalar) product of two vectors and state its formula.
a·b = |a||b|cos θ = a₁b₁ + a₂b₂ + a₃b₃, where θ is the angle between them. The result is a scalar.
Define the cross (vector) product of two vectors and its magnitude.
a × b is a vector perpendicular to both a and b, with magnitude |a||b|sin θ. It equals the determinant with rows i,j,k; a₁,a₂,a₃; b₁,b₂,b₃.
State the conditional probability formula P(A|B).
P(A|B) = P(A ∩ B)/P(B), provided P(B) ≠ 0.
State Bayes' theorem for two events.
P(A|B) = [P(B|A)·P(A)] / P(B), where P(B) = P(B|A)P(A) + P(B|A')P(A').
State the multiplication theorem of probability for independent events A and B.
If A and B are independent, P(A ∩ B) = P(A)·P(B).
State the formulas for mean and variance of a binomial distribution B(n, p).
Mean = np; Variance = npq, where q = 1 − p.
State the formula for the variance of a set of n observations using the mean.
Variance σ² = (1/n)Σ(xᵢ − x̄)², where x̄ is the mean. Standard deviation σ = √(variance).
What is the relationship between mean, median, and mode in a moderately skewed distribution?
Empirical relation: Mode = 3·Median − 2·Mean.
State the condition for two matrices to be multipliable and the order of the product.
Matrix A (m×n) can multiply B (p×q) only if n = p; the product AB has order m×q.
What is the formula for the inverse of a square matrix A in terms of its adjoint and determinant?
A⁻¹ = (1/|A|)·adj(A), provided |A| ≠ 0 (A is non-singular).
State the property of determinants when two rows (or columns) are interchanged.
Interchanging two rows or two columns changes the sign of the determinant.
Define a symmetric and a skew-symmetric matrix.
Symmetric: A' = A (aᵢⱼ = aⱼᵢ). Skew-symmetric: A' = −A (aᵢⱼ = −aⱼᵢ, with all diagonal elements zero).
State Cramer's rule conditions for a system of linear equations using determinants.
For a system AX = B, if |A| = D ≠ 0, a unique solution exists: x = D₁/D, y = D₂/D, etc. If D = 0, the system has no unique solution (inconsistent or infinitely many).
What this deck covers
The Mathematics deck follows the KCET Mathematics syllabus — 5 chapters and 22 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 13.4 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 83 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 KCET deck?
67 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these KCET flashcards free?
Yes. The preview here is free to read with no signup, and the full 67-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the KCET Mathematics syllabus — 5 chapters and 22 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.