PSEB Class 12 Maths study guide
PSEB Class 12 Maths · Work through your exam, one topic at a time.
PSEB Class 12 Mathematics (Senior Secondary) is the Punjab School Education Board examination taken by senior secondary students in affiliated schools. It is a written paper, and the syllabus spans relations and functions, inverse trigonometric functions, matrices and determinants, continuity and differentiability, applications of derivatives, integrals, applications of integrals, differential equations, vector algebra, three-dimensional geometry, linear programming and probability. The PSEB Class 12 Maths study guide has 10 sections and about 2,839 words.
01Relations, Functions and Inverse Trigonometric Functions
This domain tests whether you can classify relations, decide one-one and onto behaviour, compose and invert functions, and evaluate inverse trigonometric expressions using principal branches. A relation R on A is reflexive, symmetric and transitive; an equivalence relation splits A into disjoint classes.
275 words, about 1 min02Matrices and Determinants
The exam checks matrix algebra, symmetry, invertibility through the adjoint, determinant properties and solving linear systems with inverse matrices or Cramer's rule. Matrices add only with the same order; AB requires columns of A = rows of B, and generally AB ≠ BA.
322 words, about 2 min03Continuity and Differentiability
This domain tests left and right continuity, differentiability at a point, derivatives of composite, implicit, inverse-trigonometric and exponential functions, and the mean value theorems. f is continuous at a if lim(x→a) f(x) = f(a); for piecewise functions check LHL = RHL = value.
268 words, about 1 min04Applications of Derivatives
The exam tests rates of change, equations of tangents and normals, intervals of increase and decrease, and local or absolute maxima and minima, including simple word problems. Rate of change: if y = f(x), then dy/dt = f′(x)·dx/dt; relate the given rates carefully.
320 words, about 2 min05Integrals
The exam tests indefinite and definite integration using standard forms, substitution, integration by parts, partial fractions and properties of definite integrals. Standard forms: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1; ∫(1/x) dx = ln x + C; ∫eˣ dx = eˣ + C.
315 words, about 2 min06Applications of Integrals
The exam tests the area under a curve, the area between two curves, and standard areas such as those of circles, ellipses and parabolas using definite integrals. Area under y = f(x) from x = a to x = b is ∫ₐᵇ f(x) dx.
282 words, about 1 min07Differential Equations
The exam tests order and degree, formation of differential equations, general and particular solutions, and solving variable-separable, homogeneous and first-order linear equations. Order is the highest derivative present; degree is the power of the highest derivative when the equation is polynomial in derivatives.
269 words, about 1 min08Vector Algebra and Three-Dimensional Geometry
The exam tests vector addition, dot and cross products, projections, direction cosines and ratios, equations of lines and planes, angles and shortest distances. a·b = a b cosθ and a×b = a b sinθ n̂.
281 words, about 1 min09Linear Programming
The exam tests formulation of linear programming problems, graphical solution of two-variable problems, identification of the feasible region, and the corner point method for optimising an objective function. Identify decision variables, the objective function Z = ax + by, and all constraints as linear inequalities, including non-negativity x ≥ 0, y ≥ 0.
278 words, about 1 min10Probability
The exam tests conditional probability, independence, the multiplication theorem, total probability and Bayes' theorem, plus random variables and the binomial distribution. Conditional probability: P(A B) = P(A∩B)/P(B), provided P(B) 0.
229 words, about 1 min