### Dictionary Rank of a Word | Permutations & Combinations

PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

### Class IX Maths Formulas | Basics | Assignments | SP

CBSE Class IX Maths Syllabus and Sample Papers
Study Material for Class VIII (8th)
CBSE syllabus, sample papers, unit tests and solutions of sample papers, CBSE syllabus for class IX and VIII for all subjects, chapter-wise basic concepts of mathematics for class IX, chapter-wise planning in mathematics for class IX, Study material for class VIII.

 NCERT Mathematics Book with solutions NCERT Book NCERT Sol. NCERT Book NCERT Sol.

# CHAPTER WISE EXPLANATION

## CHAPTER 1:  Number System (Algebra)

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 non-recurring/non-terminating decimals. Existence of non-rational 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 & Formulas

Assignment

Solved Explanation of the questions

Multiple Choice Questions Ch-1 Class IX

Lesson Plan Mathematics

## CHAPTER 2:  Polynomials

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 ax2 + 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: and their use in factorization of polynomials.

Basics & Formulas

Algebraic Identities

Assignment

Multiple Choice Questions Ch-2 Class IX

Lesson Plan Mathematics

## CHAPTER 3:  Coordinate Geometry

Syllabus: The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

Basics & Formulas

Assignment

Lesson Plan Mathematics

## CHAPTER 4: Linear Equations in two variables

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 Ch-4 Class IX

Lesson Plan Mathematics

## CHAPTER 5: Euclid's Geometry

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

## CHAPTER 6: Lines and angles (Geometry)

Syllabus:  1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O 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.

Basics & Formulas

Lesson Plan Mathematics

## CHAPTER 7: Triangles (Geometry)

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 Triangles

Properties of Triangle

Lesson Plan Mathematics

## CHAPTER 8: Quadrilaterals (Geometry)

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.

Basics & Formulas

Theorems on chapter 8

Lesson Plan Mathematics

## CHAPTER 9: Area Related to Quadrilaterals

Deleted for the session 2022-23

Basics & Formulas

Planning

## CHAPTER 10: Circles (Geometry)

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.

Basics & Formulas

Planning

## CHAPTER 12 Heron's Formula (Area of Triangles)

Syllabus: Area of a triangle using Heron's formula (without proof)
Planning

## CHAPTER 13:  Surface area and Volumes (Solid Geometry)

Syllabus: Surface areas and volumes of spheres (including hemispheres) and right circular cones.

Basics & Formulas

Planning

## CHAPTER 14:  Statistics (Mean, Mode, Median)

Basics & Formulas
Planning

## CHAPTER 15: Probability (Tossing of Coins & Dice)

Deleted for session 2022-23

Basics & Formulas

Assignments

Maths STUDY – MATERIAL (For 9th Standard)

Exemplar Solution

 STUDY MATERIAL FOR CLASS VIII (8TH)DAV BOARD (All Subjects) Social Science Previous Question Papers and other study material Science Previous Question Papers and other study material Mathematics Previous Question Papers and other study material English Previous Question Papers Bank Hindi Previous Question Papers Bank

DAV Sample Paper For Class VIII
 DAV – SP-1 –Maths - 2020-21 Sol-1- (Maths) DAV – SP-2 –Maths - 2020-21 Sol-2- (Maths)

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