UP Board syllabus for maths class 12 is designed by officials of Uttar Pradesh Board of high school and intermediate Education. This syllabus makes students aware of the syllabus being asked in the UP class 12 Board exams. It will also help students prepare for the competitive national engineering entrance exams like JEE and UP state entrance exams for engineering.
In this article, the detailed syllabus of UP Board Math class 12 will be discussed, which will help students for preparation of UP class 12 board exam, JEE, and UP state entrance exam for engineering. This detailed syllabus will help students make an efficient study schedule and understand marking patterns and types of questions being asked in exams.
Students must have basic knowledge of integration and differentiation calculus, matrices, probability, geometry, and trigonometry, etc., to understand the syllabus for UP Board class 12. This class 12 syllabus of Math of UP board consists of theory only. There is no practical.
The UP board syllabus for class 12 was reduced to 30% for the academic year 2020-21 because of the Covid-19 pandemic, which is the same for the academic year 2021-22. The UP Board Math for class 12 is divided into six units. Weightage for every unit is different. The evaluation is done based on a written exam only; the exam paper carries 100 marks.
Theory syllabus of Class XII UP Board Mathematics
| Unit number and name | Topics | Weightage (Marks) |
| 1. Relationship and function | 1) Relations and Functions – Types of relations: Reflexive, symmetric, transitive, and equivalence relations. One to one and onto functions. 2) Inverse Trigonometric Functions – Definition, range, domain, principal value branches. | 10 |
| 2. Algebra | 1) Matrices –Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non- commutativity of multiplication of matrices and existence of non-zero matrices, the concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse. 2) Determinants – Determinant of a square matrix, properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. | 13 |
| 3. Calculus | 1 Continuity and Differentiability – Continuity and differentiability, a derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second-order derivatives. 2 Applications of Derivatives-Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima, and minima. 3 Integrals -Integration as the inverse process of differentiation. Integration of a variety of functions by substitution, partial fractions, and by parts. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals. 4 Applications of the Integrals –Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only), Area between any of the two above said curves. 5 Differential Equations –Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equations whose general solution is given. Solution of differential equations by separating variables, solutions of homogeneous differential equations of the first order and first degree. Solutions of linear differential equation | 44 |
| 4. Vectors and three-dimensional geometry | 1 Vector- Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties, and application of scalar (dot) product of vectors, vector (cross) product of vectors. 2 Three-dimensional Geometry –Direction cosines and direction ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. Distance of a point from a plane. | 17 |
| 5. Linear programming | Linear Programming- Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints). | 06 |
| 6. Probability | Probability – Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem. Random Variable and its probability distribution. | 10 |
| Total | 10 |
Summary of UP Board Class 12 Maths Theory syllabus
All six units are essential for board exams and competitive exams. The weightage of Unit 3 “calculus” is the highest, and it carries 44 marks. This unit has five chapters, and all are important for both UP board exams and engineering entrance exam because it deals with integrals and differentiation calculus and their applications. The second most essential unit is unit 4, “vectors and three-dimensional geometry,” which carries 17 marks. This unit describes the vectors, scalars, their addition, multiplication, and Cartesian equation. Algebra is the third most crucial unit with 13 marks weightage. Students will learn various types of matrices and determinants. Unit 1 “relation and function” and unit 6 “probability” carries ten marks weightage each. These two units are relatively more straightforward because students already studied functions and probability in previous classes. The fifth unit of “linear programming” carries only 6 marks.
Class 12 UP Board Mathematics FAQs
Q. 1 Is the unit-wise weightage of marks the same in the question paper as given in the syllabus?
Ans: Yes, the unit-wise weightage of marks will be the same in the question paper also. For example, questions carrying 10 marks will be asked from unit 6 because its weightage in the syllabus is 10 marks.
Q. 2 Is the weightage of marks the same as this syllabus in engineering entrance exams like JEE?
Ans: No, in JEE, the marks weightage will be slightly different, but still, the crucial units like calculus, vectors and three-dimensional geometry, algebra, and probability are important. These units demand more practice and focus if a student is preparing for JEE and other engineering entrance exams.
Q. 3 What is the use of UP board class 12 Maths syllabus?
Ans: Class 12 is a significant turning point for students in deciding career and opting for professions courses, like engineering and core science courses. Core science and engineering streams require a strong knowledge of calculus, algebra, probability, functions, etc. So, to score high in UP board class 12 maths and engineering entrance exams, students need to have thorough knowledge about the subject.
Q. 4 Is there any reduction or addition in the UP class 12 maths syllabus for the year 2021-22?
Ans: The syllabus was reduced to 30% for the year 2020-21 because of the Covid-19 pandemic, and the same syllabus is being repeated for the year 2021-22. There is no addition or reduction for the year 2021-22 from the previous year.
Q. 5 Is the syllabus of UP board 12 maths very difficult?
Ans: No, the syllabus is not so difficult if a student is sincere and focused. Apart from this, practice is vital. As we know, “practice makes a man perfect.”