WB MADHYAMIK CLASS-IX MATHEMATICS SYLLABUS
Mathematics
Class IX
Syllabus
1. Real Numbers :
(i) Concept of natural numbers, whole numbers, Integers, Rational Numbers, Algebric numbers.
(ii) Conversion of rational numbers to decimal number
(iii) Representing real numbers on the number line.
(iv) Addition, Subtraction, Multiplication, Division of real numbers.
(v) Concept of the axioms on real numbers and solution of simple practical problems using that axioms.
2. Laws of Indices
(i) Concept of base, index, root, power.
(ii) Concept of index as integers, fractions.
(iii) Fundamental laws of indeces and their applications.
(iv) Equation and Identity on indices
3. (i) Concept of right angular cartesion plane and co-ordinates.
(ii) Concept of co-ordinates of point and represent it on cartesion plane.
(iii) Concept of linear equations with one variable and two variables and the drawing of their graphs.
(iv) Solution of linear simultaneous equations by graph. Concept of one solution, many solutions and no solution.
4. Co-ordinate geometry (Distance formula)
(i) Concept of the formula of distance between two points on a cartesion plane and its application.
5. Linear simultaneous equations (with two variables)
(i) Solution of liner simultaneous equations (Elimination, Comparison, Substitutions and cross-multiplication method.
(ii) Solution of practical problems of linear simultaneous equation.
6. Properties of parallelogram
(i) Concept of quadrilaternal, trapezium, parallelogram, rectangle, square and rhombus.
(ii) Opposite sides and opposite angles of a parallelogram are equal and each diagonal divides it into two congruent
triangles.—proof
(iii) The diagonals of a parallelogram bisect each other. —proof
(iv) If the opposite sides of a quadrieateral are equal then the quadrilateral is a parallelogram—proof.
(v) If the opposite angles of quadrilateral are equal then the quadrilateral is a parallelogram—proof.
(vi) If a pair of opposite sides of a quadrilateral are equal and parallel then the quadrilateral is a parallelogram—
proof.
(vii) If the diagrals of a quadrilateral bisect each other then the quadrilateral is a parallelogram—proof
(viii) Applications of the above statements.
7. Polynomials:
(i) Concept of polynomials of one or more than one variables
(ii) Concept of addition, subtraction, multiplication and division of polynomials
(iii) Concept of functions from polynomial
(iv) Concept of zero of polyamials
(v) Remainder theorem
(vi) Factor theorem
(vii) Concept of zero polynomial
(viii) Application of each of the above concepts
8. Factorisation : a2 – b2, a3 + b3, a3 – b3, a3+b3+c3–3abc, vanishing method
9. Theorems on transvarsal and mid-point :
(i) The line-segment joining the mid-points of any two sides of a triangle is paralled to and half of the third side–
proof.
(ii) The straight line drawn through the mid-point of a side of a triangle paralleled to second side bisects the third side
and the intercept thus obtained from the paralleled straight line by two sides of the triangle is half of the second
side—proof.
(iii) If the lengths of the intercepts made by three or more parallel straight lines on a transversal are equal, then the
lengths of the intercepts made by them on any other transversal will also be equal—No proof is required, only
verification
(iv) Application of the above statements
10. Profit & Loss : Concept and application of Cost-price, selling-price, Profit, Loss, Marked price, percentage of profit
and loss on selling-price, Discount, Equivalent discount etc.
11. Statistics :
(i) Concept of tabulation of data.
(ii) Concept of formation of frequency distribution table.
(iii) Concept of cumulative frequency.
(iv) Construction of Histogram.
(v) Construction of frequency Polygon.
12. Theorems involving area
Concept of the Axiom :Area of a rectangle = length × breath
(i) “Parallelograms on the same base and between the same parallel are equal in area”—proof
(ii) Parallelograms on the equal bases and between the same parallels are equal in area. [Corollary]
(iii) Area of a parallelogram = Base of the parallelogram × Height [Corollary]
(iv) If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is half
that of the parallelogram. — Proof
(v) Area of a triangle = ½ × Base × Height [Corollary]
(vi) Triangles on the same base and between the same parallels are equal in area — Proof.
(vii) Triangles on equal bases and between the same parallels are equal in area. [Corollary]
13. Construction : Construction of a parallelogram whose measurement of one angle is given and equal in
area to a triangle and its application.
14. Construction : Construction of a triangle equal in area to a quadrilateral and its application.
15. Determination of the perimeter and area of a triangle and quadrilateral :
(i) Determination of the perimeter and area of a triangle. Concept of Heron’s formula.
Application in practical problems.
(ii) Determination of the perimeter and area of Rectangle, Square, Parallelogram, Rhombus,
Trapezium and application in practical problems.
16. Circumference of Circle : Ditermination of the circumference of circle. Concept of and solution of practical problems
using the formula of circumference of circle.
17. Concurrent : Theorems on Concurrence.
(i) The perpendicular bisectors of the sides of a triangle are concurrent. — Proof. concept of Circum centre, Circum
radius, Circum circle.
(ii) The perpendiculars on the sides of a triangle from its opposite vertices are concurrent – Proof.
(iii) The internal bisectors of the angles of a triangle are concurrent. — Proof. Concept of in-centre, in-radius and incircle.
(iv) The medians of a triangle are concurrent. Proof. Concept of centroid and centroid divides each memedian in the
ratio 2 : 1.
(v) Applications of the above Statements.
18. Area of circular region : Concept of the formula of the area of a circular region, concept of the formula of the area of
Sector of a Circle and Solution of practical problems.
19. Co-ordinate Geometry : Concept of the determination of formula of coordinates of a point when a Straight line Segment
is divided internally or externally in a given ratio.
20. Co-ordinate Geometry :
(i) Area of triangular region formed by three points.
(ii) Area of quadrilateral shaped region formed by four point.
(iii) Condition of collinearity of three points.
(iv) Determination of the centroid of a triangle.
21. Logarithm :
(i) Necessity
(ii) Definition
(iii) Concept of Common Logarithm and Natural Logarithm.
(iv) Properties of Logarithm
(v) Application of Common Logarithm
Addenda : (Not for Evaluation)
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