# UP Board Class 10 Mathematics 2022-23 Reduced Syllabus

Mathematical skills are demanded in almost all careers nowadays. It is very important to study mathematics as it enhances logical and analytical abilities of the students.It opens the door for the students to various domains and as it is a practical subject its applications are extensively applied in real life applications as well.

UP Board Class 10 syllabus is a detailed set of content that covers all the topics taught in previous classes in a deeper way, which also makes it more extensive and tougher to cover for some students. The first step for any student to prepare for UP Board exams is to have a clear understanding of the syllabus.

In this page, we have provided direct and free access to the Reduced Class 10 Maths Paper Syllabus PDF for the 2022-23 session.

Reduced Syllabus for 2022-23 Academic Session

In the table given below, we have also provided the Reduced Syllabus for the 2022-23 session.

UP Board Class 9 Maths Blueprint 2022-23
Units Unit Name Marks
I Number Systems 05
II Algebra 18
III Coordinate Geometry 05
IV Geometry 12
V Trigonometry 10
VI Mensuration 10
VII Probability 10
TOTAL 100

### Mathematics Chapters

#### ‍UNIT I: NUMBER SYSTEM

1. Real Numbers

• Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √2, √3, √5

#### UNIT II: ALGEBRA

<red> 2. Polynomials <red>

• <red> Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials. <red>

3. Pair of Linear Equations in Two Variables

• Periods Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.
• Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.

• Periods Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formulas.
• Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day to day activities to be incorporated.

5. Arithmetic Progression

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

#### UNIT III: COORDINATE GEOMETRY

6. Coordinate Geometry

• Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

#### UNIT IV: GEOMETRY

7. Triangles

• Definitions, examples, counter examples of similar triangles.
• 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.
• If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
• If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
• If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
• 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.

<red> 8. Circles <red>

• <red> Tangent to a circle at, point of contact <red>
• <red> The tangent at any point of a circle is perpendicular to the radius through the point of contact. <red>
• <red> The lengths of tangents drawn from an external point to a circle are equal. <red>

#### UNIT V: TRIGONOMETRY

9. 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 0o and 90o. Values of the trigonometric ratios of 300 , 450 and 600. Relationships between the ratios.

<red> 10. Trigonometric Identities <red>

• <red> Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given. <red>

11. 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°, 45°, and 60°.

#### UNIT VI: Mensuration

12. Areas Related to Circles

• Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating the area or segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only.

13. Surface Areas and Volumes

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

#### UNIT VII: STATISTICS AND PROBABILITY

14. Statistics

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

<red> 15. Probability <red>

• <red> Classical definition of probability. Simple problems on finding the probability of an event. <red>