Mathematics deals with numbers and its operations. It finds its applications in our daily lives. It contains hidden concepts which helps us in cracking problems and arriving at solutions. It is accurate and precise enough a subject. Involves calculations, measurements, computations at a larger scale. This information helps in inferring human behavior and also the behavior of naturally occurring phenomena, space exploration etc, mathematics is everywhere.
Syllabus for mathematics is a very helpful tool for students to crack board examinations efficiently. It conveys expectations in the most systematic and organized manner to be comprehensible enough for students.
Find below the detailed description of syllabus for class 10 by the HPBOSE :
Unit I : Number Systems
1. Real Numbers (15 Periods)
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 , decimal expansions of rational numbers in terms of terminating / non-terminating recurring decimals.
Unit II: Algebra
1. Polynomials (6 Periods)
Zeros of a polynomial. Relationship between zeros and coefficients of a polynomial with particular reference to quadratic polynomials. Statement and simple problems on division algorithm for polynomials with real coefficients.
2. Pair of Linear Equations in Two Variables. (15 Periods)
Pair of linear equations in two variables. Geometric representation of different possibilities of solutions inconsistency.
Algebraic conditions for number of solutions. Solution of pair of linear equations in two variables algebraically by substitution, by elimination and by cross multiplication. Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.
3. Quadratic Equations
Standard form of a quadratic equation ax2 + bx + c = 0, (a ¹ 0). Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e by using the quadratic formula. Relationship between discriminant and nature of roots.
Problems related to day to day activities to be incorporated.
4. Arithmetic Progression 8 Periods (8 Periods)
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.
Unit III : Trigonometry
1. Trigonometric Ratios (15 Periods)
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° & 90°. Values (with proof) of the trigonometric ratios of 30°, 45° & 60°. Relationships between the ratios.
2. Trigonometric Identities (16 Periods)
Proof and applications of the identity sin2 A + cos2 A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.
3. Heights and Distances (8 Periods)
Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, 60°.
Unit-IV : Coordinate Geometry
1. Lines (In two-dimensions) (15 Periods)
Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.
Unit-V : Geometry
1. Triangles (15 Periods)
Definitions, examples, counter examples of similar triangles
1. (Prove) if a line drawn parallel to one side of a triangle to intersect to 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 angles 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 on 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 the sum of the squares on the other two sides, the angles opposite to the first side is a right triangle.
2. Circles (8 Periods)
Tangents to a circle motivated by chords drawn from points coming closer and closer and closer to the point.
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 (8 Periods)
1. Division of a line segment in a given ratio (internally)
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.
1. Areas of Plane Figures (12 Periods)
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°, 90° & 120° only. Plane figures involving triangles, simple quadrilaterals and circle should be taken).
2. Surface Areas And Volumes (12 Periods)
Unit VII : Statistics And Probability
1. Statistics (15 Periods)
Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph.
Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation.