The Uttar Pradesh State Entrance Exam (UPSEE) will be conducted on April 21, 2019 (Sunday) by Dr. A.P.J. Abdul Kalam Technical University (AKTU). A total of 150 multiple choice questions (50 each from Physics, Chemistry and Mathematics) will be asked in UPSEE 2019. Each question will carry 4 marks. There will be no negative marking in UPSEE 2019. Mathematics is one the most scoring subjects as students need not to remember so much theory like in Chemistry. Students can easily score full marks if they know how to apply any formula to solve any question. Here, we are providing you the complete syllabus of Mathematics for UPSEE/UPTU 2019. You will have to do a lot of practice to master this subject and score good marks in UPSEE 2019.

**1. Algebra: **

Sets relations & functions, De-Morgan's Law, Mapping Inverse relations, Equivalence relations, Peano's axioms, Definition of rational and integers through equivalence relation, Indices and surds, Solutions of simultaneous and quadratic equations, A.P., G.P. and H.P., Special sums i.e. ∑n^{2} and ∑n^{3} (n∑N), Partial fraction, Binomial theorem for any index, exponential series, Logarithm and Logarithmic (series. Determinants and their use in solving simultaneous linear equations, Matrices, Algebra of matrices, Inverse of a matrix, Use of matrix for solving equations.

**2. Probability: **

Definition, Dependent and independent events, Numerical problem on addition and multiplication, theorem of probability

**3. Trigonometry: **

Identities, Trigonometric equations, properties of triangles, solution of triangles, heights and distances, Inverse function, Complex numbers and their properties, Cube roots of unity,De-Moivre's theorem.

**4. Co-ordinate Geometry: **

Pair of straight lines, Circles, General equation of second degree, parabola, ellipse and hyperbola, tracing of conics

**5. Calculus:**

Limits & continuity of functions, Differentiation of function of function, tangents & normal, Simple examples of Maxima & Minima, Indeterminate forms, Integration of function by parts, by substitution and by partial fraction, definite integral, application to volumes and surfaces of frustums of sphere, cone and cylinder. Differential equations of first order and of first degree

**6. Vectors: **

Algebra of vectors, scalar and vector products of two and three vectors and their applications

**7. Dynamics: **

Velocity, composition of velocity, relative velocity, acceleration, composition of accelerations, Motion under gravity, Projectiles, Laws of motion, Principles of conservation of momentumand energy, direct impact of smooth bodies.

**8. Statics: **

Composition of coplanar, concurrent and parallel forces moments and couples resultant of set of coplanar forces and condition of equilibrium, determination of centroid in simple cases, Problems involving friction.