Karnataka II PUC Basic Mathematics (KSEAB) study guide
Karnataka II PUC Basic Mathematics (KSEAB) · Work through your exam, one topic at a time.
Basic Mathematics is the second-year subject in the Karnataka Pre-University Course for students who need working quantitative skills rather than the full optional Mathematics syllabus. It is examined by the Karnataka School Examination and Assessment Board (KSEAB), and the score contributes to the II PUC marks statement used for university admission, pre-degree eligibility and commerce- or management-oriented degree programmes. The Karnataka II PUC Basic Mathematics (KSEAB) study guide has 11 sections and about 3,397 words.
01Sets, Relations and Functions
This domain tests set language and counting formulae, the classification of relations, and whether a mapping is a function and, if so, one-one or onto. Roster form lists elements; set-builder states a property.
344 words, about 2 min02Matrices and Determinants
Questions here test matrix algebra, the meaning of a determinant, inverse of a square matrix, and solving a small linear system by matrix or Cramer's rule. Equality requires the same order and equal corresponding entries.
317 words, about 2 min03Permutations, Combinations and Binomial Theorem
The exam checks counting with arrangement and selection formulae and the general term of a binomial expansion, especially finding a specified coefficient. nPr = n!/(n−r)!, nCr = n!/(r!(n−r)!), with nCr = nC(n−r) and nCr + nC(r−1) = (n+1)Cr.
268 words, about 1 min04Sequences and Series
This domain tests the nth term and sums of arithmetic and geometric progressions, means, and the standard sigma formulae. With first term a and common difference d: tₙ = a + (n−1)d, Sₙ = (n/2)[2a + (n−1)d] = (n/2)(a + l).
288 words, about 1 min05Straight Lines
The exam tests slope, the several forms of a line's equation, angle and perpendicularity conditions, and perpendicular distance from a point to a line. m = (y₂−y₁)/(x₂−x₁).
308 words, about 2 min06Circles and Conic Sections
Questions cover the equation of a circle (centre, radius, tangency) and the standard forms of parabola, ellipse and hyperbola with their foci, directrices and eccentricities. General form x² + y² + 2gx + 2fy + c = 0 has centre (−g, −f) and radius √(g² + f² − c), real only when g² + f² − c 0.
284 words, about 1 min07Limits, Continuity and Differentiation
This domain tests evaluation of limits, the continuity test at a point, and differentiation by the standard rules including chain, product, quotient and implicit forms. Standard results: lim(x→0) sin x / x = 1, lim(x→0) (aˣ − 1)/x = log a, lim(x→0) (1+x)^(1/x) = e, lim(x→0) (1−cos x)/x² = 1/2.
298 words, about 1 min08Applications of Derivatives and Integration
The exam links derivatives to tangents, rates and optimisation, then tests standard integrals, substitution, integration by parts and area under a curve. Tangent slope at (x₁,y₁) is dy/dx there; normal slope is −1/(dy/dx).
344 words, about 2 min09Statistics and Probability
The statistics part tests central tendency and dispersion of grouped data; the probability part tests classical probability, the addition rule, and independence. Mean by step deviation: x̄ = a + h(Σfᵢuᵢ/Σfᵢ), where uᵢ = (xᵢ − a)/h.
283 words, about 1 min10Linear Programming
Linear programming questions ask you to formulate an objective and constraints from a word problem, then solve graphically in two variables using the corner point theorem. Name the decision variables x and y and their units.
325 words, about 2 min11Financial and Business Mathematics
This domain tests simple and compound interest, annuities, and bill discounting - areas where a single formula slip loses the whole mark. Simple interest SI = PRT/100.
338 words, about 2 min