UP Board reduced syllabus for Class 10 Maths (English Syllabus) is provided here. This syllabus will be applicable for the upcoming UP Board Class 10 Maths Exam 2021. Go through the full syllabus carefully to avoid reading any irrelevant topics that are not going to be tested in the board exam.

**Check below the UP Board Class 10 Maths Syllabus 2020-2021:**

As the regular teaching – learning in schools, during the session 2020-21, has widely been affected due to the Covid – 19 pandemic, the subject experts committee, after due consideration, has recommended to reduce the syllabus by 30% in the following manner:

**Almost 30% reduced syllabus:- **

**UNIT II: ALGEBRA**

**1. Polynomials**

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.

**4. Arithmetic Progressions**

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of an A.P. and their application in solving daily life problems.

**UNIT IV: GEOMETRY**

**2. Circles**

Tangent to a circle at, point of contact.

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

**UNIT V: TRIGONOMETRY**

**2. Trigonometric Identities**

Proof and applications of the identity sin^{2}A + cos^{2}A = 1. Only simple identities to be given.

**UNIT VII: STATISTICS AND PROBABILITY**

**2. Probability:** Classical definition of probability. Simple problems on finding the probability of an event.

**Class: 10**

**Subject: Mathematics**

**Only Paper**

Approximately 70% Syllabus:

**UNIT I: NUMBER SYSTEMS (05 Marks)**

**1. Real Numbers**

Periods Euclid’s division lemma, Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples. Proofs of irrationality of √2, √3, √5, decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

**UNIT II: ALGEBRA (18 Marks)**

**2. Pair of Linear Equations in Two Variables**

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Solution of a pair of linear equations in two variables Unit Name of Unit Marks I Number System 05 II Algebra 18 III Co-ordinate Geometry 05 IV Geometry 12 V Trigonometry 10 VI Mensuration 10 VII Statistics and Probability 10 Total 70 Project Work 30 (Written 70marks + project work 30marks) 100 3 algebraically - by substitution, by elimination and by cross multiplication method. Simple problems on equations reducible to linear equations.

**3. Quadratic Equations**

Standard form of a quadratic equation ax^{2} + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, by completing the square and by using quadratic formula. Relationship between discriminant and nature of roots. Situation problems based on quadratic equations related to day to day activities to be incorporated.

**UNIT III: COORDINATE GEOMETRY (05 Marks)**

**1. Lines (In two-dimensions)**

**Review:** Concepts of coordinate geometry, graphs of linear equations, Distance formula, Section formula (internal division), Area of a triangle.

**UNIT IV: GEOMETRY (12 Marks)**

**1. Triangles**

Definitions, examples, counter examples of similar triangles.

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.

5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.

6. (Motivate) If a perpendicular is drawn from the vertex of the right angle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.

7. (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

8. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

9. (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right angle.

**3. Constructions**

1. Division of a line segment in a given ratio (internally).

2. Tangents to a circle from a point outside it.

3. Construction of a triangle similar to a given triangle.

**UNIT V: TRIGONOMETRY (10 Marks )**

**1. Introduction to Trigonometry**

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0^{o} and 90^{o} . Values of the trigonometric ratios of (30^{o} , 45^{o }, 60^{o} ,0^{o} and 90^{o} ). Relationships between the ratios.

**2. Trigonometric Identities**

Trigonometric ratios of complementary angles.

**3. Heights and Distances: Angle of elevation, Angle of Depression**

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30^{o}, 45^{o}, 60^{o}.

**UNIT VI: MENSURATION (10 Marks)**

**1. Areas Related to Circles**

Periods Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 1200 only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.

**2. Surface Areas and Volumes**

1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Frustum of a cone.

2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken).

**UNIT VII: STATISTICS AND PROBABILITY (10 Marks)**

**1. Statistics**

Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.

**PROJECT WORK (30 Marks)**

**a- Internal Assessment (15 Marks) **

(Questions should also be asked from the book “Bharat ka Paramparagat Ganit Gyan” – Class 10th )

**b- Project Work (15 Marks) **

Note: Student should prepare any two projects from the following (serial no- 1 to 11), teachers can also give other projects related to the subject from their level and one project from point 12 should be compulsorily prepared by the students.

1- Verification of Pythagoras Theorem by constructing triangles and the squares on a cardboard or chart paper.

2- Use of statistics in demography.

3- To study the role of the different geometrical shapes in architecture and construction.

4- Knowledge of sign of trigonometrical ratio through charts / expressing through diagram in the corresponding ratio of triangles the trigonometric ratio of angles, complementary angles etc.

5- Any one of North Medival Mathematician’s (Ramanujan, Narayan Pandit etc.) life and their contributions in Mathematics.

6- Make 2 different cylinders by taking two papers of 24 × 42 cm size and turning them by its length and width direction and calculate whose curved surface and volume will be greater or maximum.

7- To study of different direct and indirect taxes imposed by the Government.

8- Functional analysis of the statement that “Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle”.

9- Making of Sextent (for measuring distance) and its use.

10- Utility of Mathematical Principles in Drawing.

11- Give the detail of different steps for granting the loan from Bank to buy a car or house.

12- Any one project from the following three parts of the recommended book

“Bharat ka Paramparagat Ganit Gyan” – Class 10th.

Part a. Bright tradition of Mathematics in India.

Part b. Traditional methods of calculation.

Part c. Renowned Mathematicians of India.

**Given below is the link to download the complete syllabus of UP Board Class 10 Maths:**