Table of Contents

# CBSE Class 10th Maths Syllabus, Topic wise

**Marks 90:**

**UNIT I: NUMBER SYSTEMS:**

**1. 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 the irrationality of Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

Also Read – Trigonometry Formula PDF Download (All List)

**UNIT II: ALGEBRA:**

**1. Polynomials-**

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

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

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.

Algebraic conditions for a number of solutions. A solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method. Simple situational problems. 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 the quadratic formula. A relationship between discriminant and nature of roots.

Situational problems based on quadratic equations related to day to day activities to be incorporated.

**4. Arithmetic Progressions-**

A motivation for studying Arithmetic Progression Derivation of the n^{th} term and sum of the first n terms of an A.P. and their application in solving daily life problems.

**UNIT III: COORDINATE GEOMETRY:**

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

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

Also Read – Top 10 Tips to make Mathematics Easy

**UNIT IV: GEOMETRY:**

**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 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.

**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.

**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.

**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.

Also Read – CBSE Class 9th Maths Syllabus, Topic wise

**UNIT V: TRIGONOMETRY:**

**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 (with proofs) of the trigonometric ratios of 30^{o}, 45^{o} and 60^{o}. Relationships between the ratios.

**2. Trigonometric Identities-**

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

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

Simple problems with 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}.

Also Read – Trigonometry formulas for class 11th PDF

**UNIT VI: MENSURATION:**

**1. Areas Related to Circles-**

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 the area of a segment of a circle, problems should be restricted to a central angle of 60°, 90° and 120° 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 a combination of not more than two different solids be taken).

Also Read – List of Trigonometry formulas for class 10th PDF

**UNIT VII: STATISTICS AND PROBABILITY:**

**1. Statistics-**

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

**2. Probability-**

A classical definition of probability. Simple problems on single events (not using set notation).