Class IX Maths Formulas  Basics  Assignments  SP
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NCERT
Mathematics Book[9] with solutions 

NCERT Book 
NCERT Sol. 
NCERT Book 
NCERT Sol. 


CHAPTER WISE EXPLANATION 
Syllabus: REAL NUMBERS (18) Periods 1. Review of representation of natural numbers, integers,
and rational numbers on the number line. Rational numbers as recurring/
terminating decimals. Operations on real numbers. 2. Examples of nonrecurring/nonterminating decimals. Existence
of nonrational numbers (irrational numbers) such as , and their representation
on the number line. Explaining that every real number is represented by a
unique point on the number line and conversely, viz. every point on the number
line represents a unique real number. 3. Definition of nth root of a real number. 4. Rationalization (with precise meaning) of real numbers of the type , and (and their combinations) where x and y are natural number and a and b are integers. 5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.) Basics & FormulasAssignment Solved Explanation of the questions Multiple Choice Questions Ch1 Class IX Lesson Plan Mathematics 
Syllabus: Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax^{2} + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification
of identities:
Algebraic Identities Assignment Multiple Choice Questions Ch2 Class IX Lesson Plan Mathematics 
Syllabus: The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations. Basics & FormulasAssignment Lesson Plan Mathematics 
Syllabus: Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c = 0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Multiple Choice Questions Ch4 Class IX 
Syllabus: History  Geometry in India and Euclid's geometry. Euclid's method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom) 1. Given two distinct points, there exists one and only one line through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common. Lesson Plan Mathematics 
Syllabus: 1. (Motivate) If a ray stands on a line, then the sum of the
two adjacent angles so formed is 180^{O} and the converse. 2. (Prove) If two lines intersect, vertically opposite
angles are equal.
3. (Motivate) Lines which are parallel to a given line are
parallel. Lesson Plan Mathematics 
1. (Motivate) Two triangles are congruent if any two sides
and the included angle of one triangle is equal to any two sides and the
included angle of the other triangle (SAS Congruence). 2. (Prove) Two triangles are congruent if any two angles and
the included side of one triangle is equal to any two angles and the included
side of the other triangle (ASA Congruence). 3. (Motivate) Two triangles are congruent if the three sides
of one triangle are equal to three sides of the other triangle (SSS
Congruence). 4. (Motivate) Two right triangles are congruent if the
hypotenuse and a side of one triangle are equal (respectively) to the
hypotenuse and a side of the other triangle. (RHS Congruence) 5. (Prove) The angles opposite to equal sides of a triangle
are equal.
6. (Motivate) The sides opposite to equal angles of a triangle are equal. Congruence of TrianglesProperties of Triangle Lesson Plan Mathematics 
Syllabus: 1. (Prove) The diagonal divides a parallelogram into two
congruent triangles. 2. (Motivate) In a parallelogram opposite sides are equal,
and conversely. 3. (Motivate) In a parallelogram opposite angles are equal,
and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair
of its opposite sides is parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each
other and conversely.
6. (Motivate) In a triangle, the line segment joining the
mid points of any two sides is parallel to the third side and in half of it and
(motivate) its converse. Theorems on chapter 8 Lesson Plan Mathematics 
Deleted for the session 202223 Planning 
1.(Prove) Equal chords of a circle subtend equal angles at
the center and (motivate) its converse. 2.(Motivate) The perpendicular from the center of a circle to
a chord bisects the chord and conversely, the line drawn through the center of
a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) Equal chords of a circle (or of congruent
circles) are equidistant from the center (or their respective centers) and
conversely. 4.(Prove) The angle subtended by an arc at the center is
double the angle subtended by it at any point on the remaining part of the
circle. 5.(Motivate) Angles in the same segment of a circle are
equal. 6.(Motivate) If a line segment joining two points subtends
equal angle at two other points lying on the same side of the line containing
the segment, the four points lie on a circle.
7.(Motivate) The sum of either of the pair of the opposite
angles of a cyclic quadrilateral is 180° and its converse. Planning 

CHAPTER 12 Heron's Formula (Area of Triangles)Syllabus: Area of a triangle using Heron's formula (without proof)Planning 
Syllabus: Surface areas and volumes of spheres (including hemispheres) and right circular cones. Basics & FormulasPlanning 
Basics & FormulasPlanning 
CHAPTER 15: Probability (Tossing of Coins & Dice)Deleted for session 202223 Basics & FormulasAssignments 
Maths STUDY – MATERIAL (For 9th Standard) Exemplar SolutionClick Here 
Question Bank (Maths): Click Here 

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