 # Class 10 SEBA Mathematics Syllabus

Syllabus outlines a structure for a chapter. It sets the tune and clearly states its expectations from students. Mathematics syllabus gives an insight to students about various topics and its subtopics with time frame for each subject. It serves as an important tool to crack examinations successfully.

Mathematics syllabus of Class 10 SEBA Board covers topics such as Number System, Algebra, Trigonometry, etc., which gives the students a basic understanding of the concepts that they need to study in their higher classes. Going through the Class 10 Maths syllabus is necessary because the final board question paper will be framed as per the syllabus.

Find below the detailed syllabus for Mathematics for SEBA Class 10:

 Subject Syllabus Mathematics Unit I: Number Systems Real Numbers (Periods 15) 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 II: Algebra 1. Polynomials (Periods 6) 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 (Periods 15) 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 (Periods 15) Standard form of a quadratic equation, (a ≠ 0). Solution of 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 Progressions (AP) (Periods 8) Motivation for studying A.P. Derivation of standard results of finding the nth terms and sum of first n terms. Unit III : Trigonometry 1. Introduction to Trigonometry (Periods 18) 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 and 90. Values (with proof) of the trigonometric ratios of 30, 45 and 60. Relationship between the ratios. Trigonometric Identities : Proof and applications of the identity . Only simple identities to be given. Trigonometric ratios of complementary angles. 2. Heights and Distances (Periods 8) 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 and 60 Unit IV : Coordinate Geometry Lines (In two-dimensions) (Periods 15) 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 (Periods 15) Definitions, examples, counterexamples 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 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 angle opposite to the first side is a right triangle. 2. Circle (Periods 8) Tangents to a circle motivated by chords drawn from points coming 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 (Periods 8) 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 Unit VI: Mensuration 1. Areas Related to Circles (Periods 12) 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 60,90and 120 only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.) 2. Surface Areas and Volumes (Periods12) 1. Problems on finding 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 combination of not more than two different solids be taken.) Unit – VII : Statistics and Probability 1. Statistics (Periods 15) Mean, median and mode of grouped data (bimodal situation to be avoided). Cumulative frequency graph. 2. Probability (Periods 10) Classical definition of probability. Connection with probability as given in Class IX. Simple problems on single events, not using set notation. Appendix 1. Proof in Mathematics Further discussion on the concept of ‘statement’. ‘Proof’ and ‘argument’. Further illustrations of deductive proof with complete arguments using simple results from arithmetic, algebra and geometry. Simple theorems of the “Given….. and assuming….. prove……”. Training of using only the given facts (irrespective of their truths) to arrive at the required conclusion. Explanation of ‘converse’, ‘negation’, constructing converses and negations of given result/statements. 2. Mathematical Modelling Reinforcing the concept of mathematical modelling, using simple examples of models where some constraints are ignored. Estimating probability of occurrence of certain events and estimating averages may be considered. Modelling fair instalments payments, using only simple interest and future value (use of AP).

### Class 10 Mathematics Chapterwise Marking Scheme

 Sl No Chapters Marks Half Yearly Final 1 Number system 8 5 2 Polynomials 7 4 3 Pair of Linear Equations in two variables 12 8 4 Quadratic Equations 12 6 5 Arithmetic Progression 6 Triangles 14 6 7 Co-ordinate Geometry 14 8 8 Introduction to Trigonometry 13 8 9 Some applications of Trigonometry 10 8 10 Circles 6 11 Constructions 4 12 Areas related to Circles 6 13 Surface Area and Volumes 6 14 Statistics 6 15 Probability 3 Theory Total 90 90 Internal Assessment 10 10 Grand Total 100 100

Students can go through the Class 10 SEBA Board Maths chapterwise marking scheme, which will help them while preparing for their board exams. By going through it they will get an idea on which unit to concentrate more.

### List of Practicals in Mathematics prescribed for Class 10

1. Solve a pair of linear equation by graphical method and to verify the result by any other algebraic method. (Chapter-3)
2. To find the zeros of a quadratic polynomial graphically and verification of the result by any other algebraic method (Chapter-2)
3. Verification of the formula for:- (Chapter-5)
1. 1. Sum of first n terms of an AP
2. 2. Sum of first n natural numbers
3. 3. Sum of first n odd natural numbers
4. 4. Sum of first n even natural numbers
1. Verification of Basic Proportionality Theorem. (Chapter-6)
1. Verification of converse of Basic Proportionality theorem. (Chapter-6)
1. To verify that the ratio of the area of to two similar triangles is equal to the ratio of the squares of their correspoding sides. (Chapter-6)
1. Verification of Phythagoras Theorem.
1. Verification of the formula of area of triangle (in coordinate geometry) with the help of the formula of plane geometry. (Chapter-7)
1. Applying Trigonometry to find the height or distance of an object (e.g. height of a door, height of goal post breadth of a path, distance of a wall from a post etc.) (Chapter-9)
1. Construction of a tangent to a circle at any point on it, when the centre of the circle is given (Chapter-10)
1. To verify that the length of the tangent drawn from an external point to a circle are equal. (Chapter-10)
1. To obtain the formula for the area of a circle with radius r. (Chapter-12)
1. To construct a right circular cylinder with given height and circumference. (Chapter-13)
1. To construct a right circular cone with given height and circumference of the circular base. For the cone so formed, to determine its radius and height. (Chapter- 13)
1. To construct a quadrilateral with given measure and then to construct a similar quadrilateral.
1. To find mean, median and mode from a primary data collected by the students in a specific subject
1. To Find the median from a given distribution using graph mentioned below and to verify the result. (Chapter-14)

(i) Using less than type ogive.

(ii) Using more than type ogive.

(iii) Using both less than and more than type ogive.

1. Probability : (Chapter-15)

(a) To find the probability of getting head or tail from the experiment of tossing a coin 100 times.

(b) To obtain the probabiltiy of an event associated with throwing a pair of dice.

1. Displacement and rotation of triangle. (Chapter-7)

To verify that under any displacement and rotation of a triangle –

(a) Distance between the verities remain unchanged.

(b) Area of the triangle remains unaltered.

1. Project :

1) (a) Write a note on Euclid’s Division Lemma

(b) Wrte a note on Pythagoras Theorem

2) Write short life history of 3/4 great Mathematicians

N.B. : Students should do at least 15 practicals and at least one project work.

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