- Pair of Liner 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.
- Quadratic Equations (Periods 15)
Standard form of a quadratic equation ax2 + bx + c = 0, (a ¹ 0). Solution of quadratic equations (only real roots) by factorization and by completing the square, i.e. by using a quadratic formula. Relationship between discriminant and nature of roots. Problems related to day-to-day activities to be incorporated.
- 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
- 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 00 and 900. Values (with proof) of the trigonometric ratios of 30o, 45o and 60o. Relationship between the ratios.
Trigonometric Identities: Proof and applications of the identity sin2 A + cos2 A=1, sec2 A - tan2 A=1, cosec2 A - cot2A = 1. Only simple identities to be given. Trigonometric ratios of complementary angles.
- Heights and Distances (Not from the examination point of view) (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 300, 450, 600.
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
- Triangles (Periods 15)
Definitions, examples, and counter examples of similar triangles.
i) (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.
ii) (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
iii) (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
iv) (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and two triangles are similar.
v) (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.
vi) (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.
vii) (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
viii) (Prove) In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
ix) (Prove) In a triangle, if the square of one side is equal to sum of the squares of the other two sides, the angle opposite to the first side is a right triangle.
2. Circle (Periods - 8)
Tangent to a circle at any point on it is motivated by chords drawn from points coming closer and closer to the point.
i) (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
ii) (Prove) The lengths of tangents drawn from an external point to a circle are equal.
Constructions (Periods - 8)
i) Division of a line segment in a given ratio (internally).
ii) Tangent to a circle from a point outside it.
iii) Construction of a triangle similar to a given triangle.
Unit : VI. Mensuration :
- 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 60o , 90o , and 120o only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)
- Surface Areas and Volumes (Periods 12)
i) 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.
ii) Problems involving converting one type of metalic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken.)
Unit : VII. Statistics and Probability
- Statistics (Periods 15)
Mean, median and mode of grouped data (bimodal situation to be avoided).
Cumulative frequency graph.
- Probability (Periods 10)
Classical definition of probability. Connection with probability as given in Class IX.
Simple problems on single events, not using set notation.
List of Practicals in Mathematics Prescribed for SEBA Class 10
- Solve a pair of linear equation by graphical method and to verify the result by any other algebraic method. (Chapter-3)
- To find the zeros of a quadratic polynomial graphically and verification of the result by any other algebraic method (Chapter-2)
- Verification of the formula for :- (chapter-5)
i Sum of first n terms of an AP
ii Sum of first n natural numbers
iii Sum of first n odd natural numbers
iv Sum of first n even natural numbers
4. Verification of Basic Proportionality Theorem. (Chapter-6)
5. Verification of converse of Basic Proportionality theorem. chapter-6)
6. 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)
7. Verification of Phythagoras Theorem.
8. Verification of the formula of area of triangle (in co ordinate geometry) with the help of the formula of plane geometry. (Chapter-7)
9. Construction of a tangent to a circle at any point on it, when the centre of the circle is given (Chapter-10)
10. To verify that the length of the tangents the drawn from an external point to a circle are equal. (Chapter-10)
11. To obtain the formula for the area of a circle with radius r. (Chapter -12)
12. To construct a right circular cylinder with given height and circumference. (Chapter-13)
13. 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)
14. To construct a quadrilateral with given measure and then to construct a similar quadrilateral.
15. To find mean, median and mode from a primary data collected by the students in a specific subject.
16. 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.
- 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 probability of an event associated with throwing a pair of dice.
- 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.
- Project :
1) (a) Write a note on Euclid’s Division Lemma
(b) Write 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.
SEBA Assam Board Class 10 Revised Syllabus 2023-24
The topics mentioned in the table below under the omitted column are no longer part of Assam Board SEBA Class 10 HSLC syllabus 2023-24. Thus, students are advised not to cover these topics for their upcoming HSLC exam 2024.
| Chapter No. | Chapter Name | Units Required | Units Omitted | Marks |
| Half Yearly | HSLC Exam |
| | Revision Chapter | Part I & II | Part III | 10 | 6 |
| 1 | Real Number | Whole Chapter | Nil | 10 | 5 |
| 2 | Polynomials | Whole Chapter | Nil | 12 | 8 |
| 3 | Pair of Linear Equations in two variables | Whole Chapter | Nil | 12 | 7 |
| 4 | Quadratic Equations | Whole Chapter | Nil | 12 | 6 |
| 5 | Arithmetic Progressions | Whole Chapter | Nil | - | 6 |
| 6 | Triangles | Upto Unit 6.4 (i.e. up to exercise 6.3) | Unit 6.5 onwards | 12 | 6 |
| 7 | Coordinate Geometry | Whole Chapter | Nil | 10 | 7 |
| 8 | Introduction to Trigonometry | Whole Chapter | Nil | 12 | 7 |
| 9 | * | * | * | - | * |
| 10 | Circles | Whole Chapter | Nil | - | 6 |
| 11 | Constructions | Upto unit 11.2 (i.e. Upto Exercise 11.1) | Unit 11.3 – 4 onwards | - | 4 |
| 12 | Areas Related to Circles | Upto unit 12.3 (i.e. Upto Excercise 12.2) | Unit 12.4 onwards | - | 6 |
| 13 | Surface Area and Volume | Upto unit 13.3 (i.e. upto exercise 13.2) | Unit 13.4 onwards | - | 6 |
| 14 | Statistics | Upto unit 14.4 (i.e., exercise 14.3) | Unit 14.5 onwards | - | 5 |
| 15 | Probability | Whole Chapter | Nil | - | 5 |
*Chapter 9 is totally excluded from the syllabus.
