There are three sections in UPSEE/UPTU Examination i.e., Physics, Chemistry and Mathematics. Each section has 50 questions of 4 marks each. The UPSEE Examination is easier than JEE Main and JEE Advanced. If we are going to appear for any Entrance examination, the most important thing is to get to know about the syllabus first. Here, we are going to provide you the complete syllabus of Mathematics for UPSEE/UPTU Examination 2018. Mathematics is one of the easiest and scoring subjects for UPSEE/UPTU Examination if you prepare well. You will have to do a lot of practice to master this subject and score good marks in UPSEE/UPTU Examination 2018. This will give you the detailed information about all the topics of Mathematics like Algebra, Probability, Trigonometry, Co-ordinate Geometry, Complex Numbers, Calculus, Vectors, Statics and so on.

**UPSEE 2017-2018: Syllabus-Chemistry**

**About the exam: **

**Uttar Pradesh State Entrance Examination (UPSEE)** is a state level engineering entrance examination for degree level engineering institutions and other professional colleges. It is regulated by Dr. A.P.J. Abdul Kalam Technical University (AKTU) formerly known as Uttar Pradesh Technical University (UPTU).

**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. Un2 and Un3 (nUN), 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.

**UPSEE 2017-2018: Syllabus-Physics**

**Important Questions and Preparation Tips – Relations and Functions**

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