Assam Board Class 9 Advanced Mathematics (E) Syllabus 2024-25: Download Syllabus PDF For Free

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Unit-I. System of Numeration:

History of Numeration and numerals, Different systems of Numerals: Roman and Indo-Arabian. Different Scales of Numeration with bases 2,8, 10 and 16. Change of base. Arithmetic of Binary numbers. 

Unit-II. Basic Set Theory:

 (A) Fundamentals of Statement Algebra

(B) Operations of Sets, Algebra of Sets, Proofs of Laws of Algebra of Sets. 

Unit-III. Logarithm and properties

Unit-IV. Special product and Factorization of : 

(i) a3+b3+c3 +3 (b+c) (c+a) (a+b) 

(ii) x3+ (a+b+c) x2+ (ab+bc+ab)x + abc 

(iii) (a+b+c) (bc+ca+ab) - abc 

(iv) a3+b3+c3 - 3abc 

(v) a2 (b+c)+b2(c+a)+c2(a+b)+2abc 

(vi) bc(b+c)+ca(c+a)+ab (a+b)+2abc 

(vii) a(b2+c2) + b(c2+a2) + c(a2+b2)+2abc 

(viii) a2(b+c) + b2(c+a) + c2(a+b)+3abc 

(ix) bc(b+c) +ca (c+a) +ab(a+b)+3abc 

(x) a(b2+c2) + b(c2+a2) +c (a2+b2)+3abc

 (xi) a2(b-c) + b2(c-a) + c2(a-b) 

(xii) bc (b-c) + ca(c-a) + ab(a-b)

(xiii) a3 (b-c) + b3 (c-a) + c3 (a-b) 

(xiv) a3(b2-c2) + b3 (c2-a2) + c3 (a2-b2)

Unit-V: Concept of inequalities, Trichotomy property (Order relation in R) Elementary properties of inequalities, Simple applications) Inequations and solutions of inequations in two variables, Graphs of inequations (simple cases). 

Unit-VI: Sequence and series:

(A) Idea of a sequence of numbers - 

(B) Arithmetic Progression (AP)- 

AP as a special kind of a sequence, General term of an AP, to find an AP having given any two terms of it. If each term of an AP is increased or decreased or multiplied or divided by the same number then the resulting sequence is also an AP, Arithmetic mean (A.M.), insertion of any number of AM between two given positive numbers, Arithmetic series and its sum to n terms and related problems.

 (C) Geometric Progression (GP)- GP as a special kind of sequence and its general terms; to find a GP having given any two terms of it. If each term of GP is multiplied or divided by the same number the resulting sequence is also a GP. Geometric mean (G.M), insert any number of GM between any two given positive numbers. To prove the relation AM>GM in case of any positive real numbers. Geometric series and its sum to n terms and related problems. 

(D) Sum of the three series

1. i) 1 +2+3+ ...................................... + n
2. ii) 12+22+32+ .................................... + n2 

iii) 13+23+33+ ................................... + n3

Unit-VII: Plane Geometry 

Proofs of the following theorems and exercises on the theorems. 

1. The Perpendicular bisectors of the sides of a triangle are concurrent. 
2. The internal bisectors of the angles of a triangle are concurrent 
3. The perpendiculars drawn from the vertices of a triangle to the opposite sides are concurrent. 4. The medians of a triangle are concurrent. 

Unit-VIII: Some special Geometrical Constructions:

(1) Construction of a triangle given its two sides and a median corresponding to these sides. 

(2) (i) Construct a triangle with given Perimeter and the two suitable base angles. 

(ii) Construct a triangle with given (unequal) medians. 

(iii) Draw a square equal in area to a given rectangle.

 (iv) Draw a rectangle having given one side and a diagonal. 

(v) Draw a regular polygon in a given circle. 

3) Construction of figures (Triangles, quadrilaterals) similar to the given figure as per the given scale factor. 

4) Construction of circumcircle and incircle.