Class 10 CBSE Maths Syllabus

Unit 1: Number Systems

1. Real Number (15 Periods) – After examining past work and after illuminating and inspiring through examples, Euclid’s division lemma, the Fundamental Theorem of Arithmetic, Proofs of the irrationality of the representation of rational numbers in decimal form in terms of terminating or non-terminating repeating decimals.

Unit 2: Algebra

1. Polynomials (7 Periods) – Definition of a polynomial in one variable, with examples and counterexamples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials.  Zeros and quadratic polynomial coefficients are related. Statement and straightforward issues with the polynomials with real coefficients division procedure.
2. Pair of Linear Equations In Two Variables (15 Periods) – A pair of two-variable linear equations with a graphic representation of their consistency/inconsistency. Algebraic requirements for the number of solutions. Two linear equations in two variables are solved algebraically using the cross multiplication, substitution and elimination methods. Situational issues that are easy. Simple equations issues that can be reduced to linear equations.
3. Quadratic Equations (15 Periods) – Quadratic equation in standard form: ax2 + bx + c = 0, (a ≠ 0). Quadratic equations can be solved by factoring and using the quadratic formula, but only for real roots. Relationship between the root’s nature and the discriminant. Situational quadratic equation-based issues pertaining to daily activities should be included.
4. Arithmetic Progressions (8 Periods) – Driving force behind studying arithmetic progression Application of the nth term and the sum of the first n terms of A.P. in solving problems of daily life.

Unit 3: Coordinate Geometry

1. Lines (In Two-Dimensions) (14 Periods) – Coordinate geometry ideas and graphs of linear equations. Distance formula. The formula in Section (internal division). Dimensions of a triangle.

Unit 4: Geometry

1. Triangles (15 Periods) – Definitions, illustrations, and contrast illustrations of related triangles.

• The other two sides of a triangle are divided in the same ratio if a line drawn parallel to one side of a triangle intersects the other two sides in clearly defined points.
• A line is parallel to the third side of a triangle of it divides the first two sides of the triangle in the same ratio.
• If two triangles’ corresponding angles and sides are equal and proportional to one another, the triangles are similar.
• If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
• Two triangles are similar if their angles are equal to each other and the sides that include these angles are proportional.
• The triangles on either side of a perpendicular drawn from the right angle vertex of a right triangle to its hypotenuse are similar to the triangle as a whole and to one another.
• The ratio of the squares of the corresponding sides of two similar triangles is equal to the ratio of the areas of the triangles.
• The square on the hypotenuse of a right triangle equals the sum of the squares on the other two sides.
• The angle opposite the first side of a triangle is a right angle if the square on one side equals the sum of the squares on the other two sides.

2. Circles (8 Periods) – At the point of contact, tangent to a circle.

• The radius through the point of contact is perpendicular to the tangent at any point on a circle.
• Tangents drawn from an outside point to a circle have equal lengths.
• The Theorem of the Alternate Segments: If a chord is drawn through the intersection of a circle and a tangent, the angles the chord makes with the tangent are equal to the angles the chord subtends in the alternate segments.

3. Constructions (8 Periods) -:

• Splitting a line segment into a specified ratio (internally).
• Directional tangents from a point outside a circle.
• Building a triangle that is similar to a given triangle.

Unit 5: Trigonometry

1. Introduction To Trigonometry (10 Periods) – The acute angle trigonometric ratios of a right angled triangle. The ratios that are defined at 0o and 90o should be motivated as evidence of their existence (clearly defined). Values for the 300, 450 and 600 trigonometric ratios. Ratios and their relationships.
2. Trigonometric Identities (15 Periods) – Applications of the identity sin2A + cos2A = 1 and evidenced for it. To be given are only simple identities. Complementary angle trigonometric ratios.
3. Heights and Distances: Angle of Elevation, Angle of Depression (8 Periods) – Simple height and distance calculations. There shouldn’t be more than two right triangles in a problem. Only 30°, 45° and 60° should be used as elevation/depression angles.

Unit 6: Mensuration

1. Areas Related To Circles (12 Periods) – Motivate the circle’s area, as well as the areas of its sectors and segments. 
2. Surface Areas And Volumes (12 Periods):

• Combinations of the surfaces and volumes of cubes, cuboids, spheres, hemispheres and right circular cylinder/cones. A cone’s frustum.
• Converting one type of metallic solid into another problem, as well as other mixed problems. 

Unit 7: Statistics and Probability

1. Statistics (18 Periods) – Data grouping average, median and mode (bimodal situation to be avoided). Graph of cumulative frequency.
2. Probability (10 Periods) – Probability as it is typically understood. Simple issues with calculating an event’s probability.