 # CBSE Class 10 Syllabus Science(Theory + Practical)

The Central Board of Secondary Education (CBSE) is one of the most prestigious and preferred educational boards in India. It aims to provide a holistic and healthy education to all its learners so that students can get adequate space to develop mentally and physically. CBSE is known for its comprehensive syllabus and well structured exam pattern which helps students to get a detailed idea about the entire curriculum. There are around 20,102 schools under the board which follows the NCERT curriculum.

The CBSE class 10 board exam is undoubtedly the first important exam in an individual’s life because this phase of life shapes the future of the students for their next successive years. The CBSE class 10 board exam is the first nationalised external exam that the students undertake and hence gives a nightmare to many students appearing for the exam.

The subjects are designed very strategically and helps the students to get influenced by the lessons and knowledge imparted to them. The subjects, especially science and maths require the students to get completely immersed in them and enjoy learning along with gathering knowledge.

COURSE STRUCTURE

CLASS –X (2021-22)

FIRST TERM

Time: 90 Minutes

 NO. UNIT NAME MARKS I NUMBER SYSTEMS 6 II ALGEBRA 10 III COORDINATE GEOMETRY 6 IV GEOMETRY 6 V TRIGONOMETRY 5 VI MENSURATION 4 VII STATISTICS & PROBABILITY 3 Total 40 INTERNAL ASSESSMENT 10 TOTAL 50
 INTERNAL ASSESSMENT MARKS TOTAL MARKS Periodic Tests 3 10 marks for the term Multiple Assessments 2 Portfolio 2 Student Enrichment Activities-practical work 3

UNIT-NUMBER SYSTEMS

1. REALNUMBER

Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples. Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

UNIT-ALGEBRA

1. POLYNOMIALS

Zeroes of a polynomial. Relationship between zeroes and coefficients of quadratic polynomials only.

1. PAIR OF LINEAR EQUATIONS IN TWOVARIABLES

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 and by elimination. Simple situational problems. Simple problems on equations reducible to linear equations.

UNIT-COORDINATE GEOMETRY

1. COORDINATEGEOMETRY

LINES (In two-dimensions)

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

UNIT-GEOMETRY

1. TRIANGLES

Definitions, examples, counter examples of similar triangles.

(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.

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

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

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

(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.

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

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

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

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

UNIT- TRIGONOMETRY

1. INTRODUCTION TOTRIGONOMETRY

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). Values of the trigonometric ratios of $30^{\circ}, 45^{\circ}$ and $60^{\circ} .$ Relationships between the ratios.

TRIGONOMETRIC IDENTITIES

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

UNIT-MENSURATION

1. AREAS RELATED TOCIRCLES

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 $60^{\circ}$ and $90^{\circ}$ only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)

UNIT- STATISTICS & PROBABILITY

1. PROBABILITY

Classical definition of probability. Simple problems on finding the probability of an event.

SECOND TERM

 NO. UNIT NAME MARKS I ALGEBRA(Cont.) 10 II GEOMETRY(Cont.) 9 III TRIGONOMETRY(Cont.) 7 IV MENSURATION(Cont.) 6 V STATISTICS & PROBABILITY(Cont.) 8 Total 40 INTERNAL ASSESSMENT 10 TOTAL 50

UNIT-ALGEBRA

Standard form of a quadratic equation $a x^{2}+b x+c=0,(a \neq 0)$. Solutions of

formula. Relationship between discriminant and nature of roots. Situational

problems based on quadratic equations related to day-to-day activities (problems on equations reducible to quadratic equations are excluded)

1.  ARITHMETICPROGRESSIONS

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. (Applications based on sum to n terms of an A.P. are excluded)

UNIT- GEOMETRY

1. CIRCLES

Tangent to a circle at, point of contact

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

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

1. CONSTRUCTIONS

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

Tangents to a circle from a point outside it.

UNIT-TRIGONOMETRY

1. SOME APPLICATIONS OFTRIGONOMETRY

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 $30^{\circ}, 45^{\circ}, 60^{\circ}$.

UNIT-MENSURATION

1. SURFACE AREAS ANDVOLUMES

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

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-STATISTICS & PROBABILITY

1. STATISTICS

Mean, median and mode of grouped data (bimodal situation to be avoided). Mean by Direct Method and Assumed Mean Method only

 INTERNAL ASSESSMENT MARKS TOTAL MARKS Periodic Tests 3 10 marks for the term MultipleAssessments 2 Portfolio 2 Student Enrichment Activities-practicalwork 3

PRESCRIBED BOOKS

Mathematics – Textbook for class IX – NCERT Publication

Mathematics – Textbook for class X – NCERT Publication

Guidelines for Mathematics Laboratory in Schools, class IX – CBSE Publication

Guidelines for Mathematics Laboratory in Schools, class X – CBSE Publication

Laboratory Manual – Mathematics, secondary stage – NCERT Publication

Mathematics exemplar problems for class IX, NCERT publication.

Mathematics exemplar problems for class X, NCERT publication.

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