 # Class 10 Maths Term 1 Syllabus

## CBSE Class 10 Maths Syllabus

As per the CCE guidelines, the syllabus for class 9 and class 10 maths has been divided term wise. In each term, there will be formative assessments each carrying 10% of weightage and summative assessments each carrying 30% weightage. The Class 10 Maths Term 1 syllabus is listed below.

## Unit – 1: Number Systems

• ### Real Numbers

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

## Unit – 2: Algebra

• ### 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.
• ### Pair of Linear Equations In Two Variables

• Pair of linear equations in two variables and their graphical solution
• Geometric representation of different possibilities of solutions/inconsistency.
• Algebraic conditions for number of solutions
• Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method.
• Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.

## Unit – 3: Geometry

• ### 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 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.
• (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on 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.
• (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 triangle.

## Unit – 4: Trigonometry

• ### Introduction to Trigonometry

• Trigonometric ratios of an acute angle of a right-angled triangle.
• Proof of their existence (well defined)
• Forest and wild life, coal and petroleum conservation
• Motivate the ratios, whichever are defined at 0° and 90°
• Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°.
• Relationships between the ratios.
• ### Trigonometric Identities

• Proof and applications of the identity sin2A + cos2A = 1 (Only simple identities to be given).
• Trigonometric ratios of complementary angles

## Unit – 5: Statistics and Probability

• ### Statistics

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

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