CBSE Class 10 Mathematics

The Students may be provided with opportunities individually/in groups and encouraged to –

1. Extend the methods of finding LCM and HCF of large numbers learnt earlier to general form.
2. discuss different aspects of polynomials, such as - their degree, type (linear, quadratic, cubic), zeroes etc., relationship between their visual representation and their zeroes.
3. Play a game which may involve a series of acts of factorising a polynomial and using one of its factors to form a new one.  For example, one group factorising says, (x³ – 2x² – x – 2) and using one of its factor x-1 to construct another polynomial which is further factorised by another group to continue the process.
4. Discuss different aspects of linear equations by engaging students in the activities of the following nature:
   1. One group may ask another to form linear equation in two variables with coefficients from a particular number of systems i.e. natural numbers/ numbers that are not integers etc.
   2. Graphically representing a linear equation in 1D or 2 D and try to explain the difference in their nature.
   3. Encouraging students to observe identities & equations and segregate them.
5. Use graphical ways to visualise different aspects of linear equations such as visualising linear equations in two variables or to find their NCERT Solution for Class 10 Mathematics.
6. Observe and analyse patterns in their daily life situations to check if they form an Arithmetic Progression and, if so, find rule for getting their nth term and sum of n terms. The situations could be - our savings/ pocket money, games such as playing cards and snakes & ladders, etc.
7. Analyse and compare different geometrical shapes, charts, models made using paper folding and tell about their similarity and congruence.
8. Discuss in groups different situations such as constructing maps etc. In which the concepts of trigonometry are used.
9. Work in projects related to heights and distances, that may include situations in which methods have to be devised for measuring the angle of inclination of the top of a building and their own distance from the building.
10. Device ways to find values of different trigonometric ratios for a given value of a trigonometric ratio.
11. Observe shapes in the surroundings that are a combination of shapes studied so far such as cone, cylinder, cube, cuboid, sphere, hemisphere etc. They may work in groups and may provide formulas for different aspects of these combined shapes.
12. To determine areas of various materials, objects, designs around them. For e.g. design on a handkerchief, design of tiles on the floor, geometry box etc by doing Worksheets and referring to NCERT Books for Class 10
13. Discuss and analyse situations related to surface areas and volumes of different objects such as, (a) given two boxes of a certain shape with different dimensions, if one box is to be changed exactly like another box , which attribute will change, surface area or volume? (b) By what percent will each of the dimensions of one box have to be changed to make it exactly of the same size as the other box?
14. Discuss and analyse the chance of happening of different events through simple activities like tossing a coin, throwing two dice simultaneously, picking up a card from a deck of 52 playing cards etc.
15. Generalise the formulas of mean, median and mode read in the earlier classes by providing situations for these central tendencies Sample papers for Class 10 Mathematics
16. To draw tangents to a circle from a point which lies outside and a point which lies inside the circle. They may be motivated to evolve different ways to verify the properties of such tangents.

Unit I: NUMBER SYSTEMS (06 Marks)

• 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.

Note for Students: This unit focuses on the fundamental properties of real numbers and algebraic proofs for irrationality.

Unit II: ALGEBRA (20 Marks)

• POLYNOMIALS: Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.
• 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 number of solutions.
• Solution of a pair of linear equations in two variables algebraically - by substitution, by elimination. Simple situational problems.
• QUADRATIC EQUATIONS: 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 formula.
• Relationship between discriminant and nature of roots.
• Situational problems based on quadratic equations related to day-to-day activities to be incorporated.
• ARITHMETIC PROGRESSIONS: Motivation for studying Arithmetic Progression.
• Derivation of the nth term and sum of the first n terms of AP and their application in solving daily life problems.

Note for Students: This major unit covers the core algebraic structures including equations, polynomials, and sequences used in problem-solving.

Unit III: COORDINATE GEOMETRY (06 Marks)

• Coordinate Geometry: Review: Concepts of coordinate geometry.
• Distance formula. Section formula (internal division).

Note for Students: Students will learn to establish relationships between geometrical shapes and coordinates using standard mathematical formulae.

Unit IV: GEOMETRY (15 Marks)

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

Note for Students: This unit involves rigorous proofs and theorems related to the properties of similar triangles and circular tangents.

Unit V: TRIGONOMETRY (12 Marks)

• INTRODUCTION TO TRIGONOMETRY: Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined).
• Values of the trigonometric ratios of 30°, 45° and 60°. Motivate the ratios whichever are defined at 0° and 90°.
• Relationships between the ratios.
• TRIGONOMETRIC IDENTITIES: Proof and applications of the identity sin²A + cos²A = 1. Only simple identities to be given.
• 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°.

Note for Students: You will explore the relationship between angles and sides of triangles and apply them to solve real-world distance problems.

Unit VI: MENSURATION (10 Marks)

• 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 area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only).
• 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.

Note for Students: This unit focuses on calculating the physical measurements of 2D circular parts and 3D combined solid objects.

Unit VII: STATISTICS AND PROBABILITY (11 Marks)

• STATISTICS: Mean, median and mode of grouped data (bimodal situation to be avoided).
• PROBABILITY: Classical definition of probability.
• Simple problems on finding the probability of an event.

Note for Students: This unit covers data interpretation through central tendencies and the mathematical calculation of the likelihood of events.