UPMSP Intermediate Mathematics study guide
UPMSP Intermediate Mathematics · Work through your exam, one topic at a time.
The UPMSP Intermediate Mathematics examination is the Class 12 mathematics paper set by the Uttar Pradesh Madhyamik Shiksha Parishad (UP Board) for students completing the intermediate stage of schooling in Uttar Pradesh. It is a school-leaving and board certification examination: results feed into higher education admission in the state and are commonly required for undergraduate programmes in science, engineering-entrance preparation, commerce and education. The UPMSP Intermediate Mathematics study guide has 12 sections and about 2,777 words.
01Relations and Functions
UPMSP Intermediate Mathematics tests whether you can move between a relation, its graph, and a function rule, and whether you can justify inverse and composition claims. A relation from A to B is any subset of A×B; a function is a relation in which every input in the domain has exactly one output.
237 words, about 1 min02Inverse Trigonometric Functions
This domain checks principal values, identities, and the ability to undo a trigonometric function only inside its chosen branch. UPMSP questions often combine a value with a domain restriction or ask for a simplified expression.
209 words, about 1 min03Matrices and Determinants
UPMSP tests conformability, matrix algebra, determinant properties, and solving small linear systems. A matrix of order m×n has m rows and n columns; addition requires the same order, while AB requires columns of A to equal rows of B.
236 words, about 1 min04Continuity and Differentiability
This domain asks whether a function has no break at a point and whether its graph has a defined tangent there. At x=c, continuity requires lim {x→c} f(x)=f(c); both one-sided limits must exist, agree, and equal the function value.
249 words, about 1 min05Application of Derivatives
UPMSP uses derivatives to describe change: rates, tangents, monotonicity, and extrema. For a differentiable function, f′(x) 0 on an interval means increasing, f′(x)<0 means decreasing, and f′(x)=0 at stationary points; endpoints of a closed interval must also be checked.
247 words, about 1 min06Integrals and Application of Integrals
This domain tests antiderivatives, definite integrals, and area. An indefinite integral represents a family of antiderivatives, so a constant C is required.
238 words, about 1 min07Differential Equations
UPMSP checks whether you can classify an equation and choose a solution method. The order is the highest derivative present; the degree is the power of the highest derivative after the equation is made polynomial in derivatives.
222 words, about 1 min08Vector Algebra and Three-Dimensional Geometry
This domain tests vectors in component form, products, and spatial lines and planes. A vector has magnitude and direction; its position vector from the origin is written with i, j, k components.
224 words, about 1 min09Linear Programming
UPMSP tests formulation and graphical solution of two-variable linear programming problems. An LPP has an objective function to maximize or minimize, linear constraints, and usually non-negativity restrictions x≥0, y≥0.
256 words, about 1 min10Probability
This domain covers conditional probability, independence, total probability, Bayes’ theorem, and random variables. For events A and B with P(B) 0, P(A B)=P(A∩B)/P(B).
199 words, under 1 min11Coordinate Geometry (Straight Lines and Conic Sections)
UPMSP tests equations, slopes, distances, and standard conic forms. A straight line can be written as y=mx+c, ax+by+c=0, or through a point with a given slope.
224 words, about 1 min12Algebra and Elementary Calculus Foundations
This domain supplies the algebraic and limiting skills used across the paper: quadratic equations, progressions, binomial expansions, and basic limits and derivatives. A quadratic ax^2+bx+c=0 has discriminant D=b^2−4ac; D 0 gives two distinct real roots, D=0 equal real roots, and D<0 no real roots.
236 words, about 1 min