CHSE Odisha Elective Mathematics study guide
CHSE Odisha Elective Mathematics · Work through your exam, one topic at a time.
CHSE Odisha Elective Mathematics is the Class XII mathematics paper taken under the Council of Higher Secondary Education, Odisha, by +2 students who offer Mathematics as an elective - most often science-stream candidates, plus commerce students heading for quantitative degrees. It is a board-assessed school-leaving subject: the mark on this paper, rather than a separate entrance test, is what appears on the CHSE certificate and what colleges and universities in Odisha read when screening applicants for engineering, statistics, economics and B.Sc. The CHSE Odisha Elective Mathematics study guide has 13 sections and about 3,042 words.
01Relations and Functions
Relations and Functions is the language of mapping between sets. The exam tests Cartesian products, types of relations, domain and range, injective, surjective and bijective functions, composition and inverse functions.
244 words, about 1 min02Inverse Trigonometric Functions
Inverse Trigonometric Functions reverses sine, cosine and tangent only after restricting domains so that each inverse is a function. The exam tests principal values, domains and ranges, identities and simple equations.
242 words, about 1 min03Matrices and Determinants
Matrices and Determinants tests algebra of matrices, transpose and special matrices, evaluation and properties of determinants, adjoint and inverse, and solution of linear systems. Matrix addition requires the same order; multiplication AB requires columns of A equal rows of B, and AB is usually not BA.
246 words, about 1 min04Complex Numbers and Quadratic Equations
Complex Numbers and Quadratic Equations covers i^2=-1, modulus, argument, conjugate, polar form, roots of quadratics and the relation between roots and coefficients. For z=a+bi, modulus z =sqrt(a^2+b^2) and conjugate is a-bi.
227 words, about 1 min05Permutations and Combinations
Permutations and Combinations tests counting arrangements and selections, restrictions, circular permutations and combinations with conditions. If order matters, count permutations: nPr=n!/(n-r)!.
229 words, about 1 min06Binomial Theorem and Sequences & Series
Binomial Theorem and Sequences & Series tests expansion of (a+b)^n, general and middle terms, and arithmetic and geometric progressions with sums and means. (a+b)^n=sum from r=0 to n of nCr a^(n-r)b^r.
208 words, about 1 min07Limits, Continuity and Differentiability
Limits, Continuity and Differentiability tests evaluation of limits, one-sided behaviour, continuity at a point and derivative rules. A limit exists only when left-hand and right-hand limits agree.
234 words, about 1 min08Applications of Derivatives
Applications of Derivatives tests tangents and normals, increasing and decreasing intervals, maxima and minima, and simple optimisation. Slope of tangent at x=a is f'(a); normal slope is -1/f'(a) when f'(a)≠0.
233 words, about 1 min09Integrals and Applications of Integrals
Integrals and Applications of Integrals tests indefinite and definite integration, standard forms, substitution, integration by parts, partial fractions and area under curves. Indefinite integrals require +C; definite integrals are numbers and use limits.
244 words, about 1 min10Differential Equations
Differential Equations tests order and degree, formation of equations, variable separable equations, homogeneous equations and linear first-order equations. Order is the highest derivative; degree is the power of the highest derivative after the equation is polynomial in derivatives.
220 words, about 1 min11Vector Algebra and Three-Dimensional Geometry
Vector Algebra and Three-Dimensional Geometry tests vector addition, dot and cross products, direction cosines, lines and planes, angles and distances. Dot product a·b= a b cos θ is a scalar; cross product a×b is a vector perpendicular to both, with a×b = a b sin θ.
234 words, about 1 min12Linear Programming
Linear Programming tests formulation of an objective and constraints, graphical solution of two-variable problems, feasible regions and the corner point theorem. Write the objective as maximise or minimise Z=ax+by, with constraints as linear inequalities and non-negativity restrictions.
254 words, about 1 min13Probability and Statistics
Probability and Statistics tests classical and conditional probability, independent events, Bayes theorem, random variables, binomial distribution, and measures of central tendency and dispersion. P(A B)=P(A∩B)/P(B), with P(B) 0.
227 words, about 1 min