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Class IX - Maths

COURSE STRUCTURE CLASS IXFirst Term

Marks : 90

Units Marks

I Number Systems 17

II Algebra 25

III Geometry 37

IV Coordinate Geometry

V Mensuration 11

Total (Theory) 90

UNIT I : Number Systems

1. Real Numbers (18 Periods)

1. Review of representation of natural numbers, integers, rational numbers on thenumber line. Representation of terminating / non-terminating recurring decimalson the numbers line through successive magnification. Rational numbers asrecurring / terminating decimals.

2. Examples of non-recurring / non-terminating decimals. Existence of non-rationalnumbers (irrational numbers) such as 2, 3 and their representation on thenumber line. Explaining that every real number is represented by a unique pointon the number line and conversely, viz. every point on the number line representsa unique real number.

3. Existence of x for a given positive real number x and its representation on thenumber line with geometric proof.

4. Definition of nth root of a real number.

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Class IX - Maths

5. Recall of laws of exponents with integral powers. Rational exponents with positivereal bases (to be done by particular cases, allowing learner to arrive at the generallaws.)

6. Rationalization (with precise meaning) of real number of the type

1and

a b x

1x y (and their combinations) where x and y are natural number and a and

b are integers.

Unit II : Algebra

1. Polynomials

Definition of a polynomial in one variable, with example and counter examples.Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degreeof a polynomial. Constant, linear, quadratic and cubic polynomial. Monomials,binomials, trinomials. Factors & Multiples. Zeros of a polynomials. Motivate andState and Remainder Theorem with examples. Statement and proof of the FactorTheorem. 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 : (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz, (x ± y)3 = x3 ± y3 ± 3xy (x ± y), x3 ± y3 = (x ± y) (x2 xy+ y2), x3 + y3 + z3 – 3xyz = (x + y + z), (x2 + y2 + z2 – xy – yz – zx) and their use in factorizationof polynomials.

Unit III : Geometry

1. Introduction of Euclid's Geometry

History : Geometry in India and Euclid's geometry. Euclid's method of formalizingobserved phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms / postulates and theorems. The five postulates of Euclid.Equivalent versions of the fifth postulate. Showing the relationship between axiomand theorem, for example :

(Axiom) 1. Given two distinct points, there exists one and only one line throughthem.

(Theorem) 2. (Prove) Two distinct lines cannot have more than one point incommon.

2. Lines and Angles (13 Periods)

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles soformed is 180° and the converse.

2. (Prove) If two lines intersect, vertically opposite angles are equal.

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Class IX - Maths

3. (Motivate) Results on corresponding angles, alternate angles, interior angles whena transversal intersects two parallel lines.

4. (Motivate) Lines which are parallel to a given lines a parallel.

5. (Prove) The sum of the angles of a triangle is 180°.

6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equalto the sum of the two interior opposite angles.

3. Triangles (20 Periods)

1. (Motivate) Two triangles are congruent if any two sides and the included anglesof one triangle is equal to any two sides and the included angles of the othertriangle (SAS Congruence).

2. (Prove) Two triangles are congruent if any two angles and the included side ofthe one triangle is equal to any two angles and the included side of the othertriangle (ASA Congruence).

3. (Motivate) Two trignales are congruent if the three sides of one triangle are equalto three sides of the other triangle (SSS Congruence).

4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of onetriangle 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.

7. (Motivate) Triangle inequalities and relation between 'angle and facing side'inequalities in triangles.

Unit IV : Coordinate Geometry

Coordinate Geometry (6 Periods)

The Cartesian plane, coordinates of a point, names and terms associated withthe coordinate plane, notions, plotting points in the plane.

Unit V : Mensuration

1. Areas (4 Periods)

Area of a triangle using Heron's formula (without proof) and its application infinding the area of a quadrilateral.

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Class IX - Maths

Mathematics (Code No. 041) Time : 3 Hours Marks : 90S.No. Typology of Questions Very Short Short Long Total %

Short Answer Answer Answer Marks WeightageAnswer I II (LA)(VSA) (SA) (SA) (4 Marks)

(1 Mark) (2 Marks) (3 Marks)

1. Remembering (Knowledge Based 1 2 2 3 23 26%Simple recall questions, to knowspecific facts, terms, concepts,principles, or theories; identify,define, or recite, information)

2. Understanding (Comprehension 2 1 1 4 23 26%-to be familiar with meaning and tounderstand conceptually, interpret,compare, contrast, explain,paraphrase, or interpret information)

3. Application (Use abstract infor-mation in concrete situation, to apply 1 2 3 2 22 24%knowledge to new situations; Usegiven content to interpret a situationprovide an example, or solve a problem)

4. Higher Order Thinking Skills – 1 4 – 14 16%(Analysis & Synthesis - Classifycompare, contrast, or differentiatebetween pieces of information;Organize and/or integrate variety ofsoursces)

5. Creating : Eveluation and Multi- – – – 2* 8 8%Disciplinary- (Generating new ideas ,product of ways of viewing thingsAppraise, jduge and/or justify the valuesor worth of a decision or outcome, orto predict outcomes based on values).

Total 4 ×1 = 4 6×2=11 10x3 = 30 11x4 = 44 90 100%Note : The question paper will included a section on Open Text based assessment (questions of 10 marks). The

case studies will be supplied to students in advance. These case studies of designed to test the analyticaland higher order thinking skills of students.*One of the LA (4 Marks) will be to assess the values inherent in the text.

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Class IX - Maths

N

W

Z I

(a)pq p q q

0.

(b)2 0.45

(c)

o o0.1234 0.12 3 4 0.1234234.....

(a)pq p q

q 0.

(b)

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Class IX - Maths

r s

r+s, r-s, r.s, rs

1 ,a b

– ,a ba b

a

b

a > 0 m n

1. am. an = am + n 2. am an = am – n

3. (am)n = amn 4. am. bm =(ab)m

5. a0 = 1 6. –mm1a

a

a b

1. a . b ab 2. aa bb

3. a b a b a b 4. 2

a b a 2 ab b

5. 2a b a b a – b

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Class IX - Maths

( ... -3, -2, -1, 0, 1, 2, 3 ... )

(0)(1, 2 ,3 ...)

1 5 7, ,2 3 5

(0, 2, 4, 6, 8 ....) (1, 3, 5, 7, 9...)

(2) (4, 6, 8. 10 ...)

(3, 5, 7 ....) (9, 15 ...)(1)

1 5 7, ,2 3 5

( ... -3, -2, -1,)

2, 3, 5,

( 0, 1, 2, 3 ... )

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Class IX - Maths

(N)

(W)

(Z I)

(Q)

q = 2 x 5m n

2 0.45

2 1.414...

10 3.33... 3.33

pq

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Class IX - Maths

1. pq p q q

0

2. 17 3 2, , ,8 15 7

503

3.29

37

4. 23 24

5. 23 24

6. 2 5

7.

8.57

9.

10. (256)0.16 × (256)0.09

11. 2016 2017

12. 75

13. 5

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Class IX - Maths

14. 3 + 2.6

15.23

32

16. :

5 380 48 45 27

17. [13 + 23 + 33 + 82] –5/2

18. x x1/2 = (36)0.5

19. x (3)x = 37

20. 5x x 52 2 32. x

21. x y y z z xa .a . a .

22. 2 25 512 . 5 .

23.

(i)13550

(ii)411

(iii)87

(iv)368

(v)559

(vi)2 3

35 3

2 5 27

(vii)

51 .60

24.

(i) 0.1666.... (ii) 0.250 ....... (iii) 1.01001000100001....

(iv) 0.27696 (v) 2.142857142857.... (vi) 0.3

(vii) 0.2359872785.... (viii) 0.48484884848.... (ix) 2.502500250002....

(x) 4.123456789

25.

(i) 27 (ii) 36 (iii) 5 125 (iv) 2 3

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Class IX - Maths

(v) 7 7343

(vi) 2 21 (vii) 5 2 3 25 92

(viii) 227

(ix) (x) 3 27

26. pq p q q 0.

(i) 0.0875 (ii) 2.123456789 (iii) 0.181818....

(iv) 0.437 (v) 3.651 (vi)o o

0. 428571

27. :

(i) : 125 2 27 5 5 3

(ii) : 7 11 5 11 13

(iii) : 2 2 5 2

(iv) : 3 5 3

(v) : 7 5 14 125

(vi) : 2 216 3 27 3

28. :

(i) 2 2 3 3 2 2 3 3 (ii) 2

2 8 3 2

(iii) 2

7 6 (iv) 6 2 2 3

29. :

(i)38 37 36

39 38 372 2 22 2 2

(ii)

211 6264

30. a

6 3 2 a 3.3 2 2 3

31. :

13 41 3 1 35 8 27

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Class IX - Maths

32. :

3 2 3 5

5 4 4 325 24316 8

33. 52x – 1 – (25)x – 1 = 2500, x

34. 0.6 0.7 0.47 pq p q q 0.

35.

13 5 7

36. a b

7 3 5 7 3 5 a b 52 5 2 5

37. x 3 2 2 ,

1x 2x

38. xyz = 1,

1 11 1 11 x y 1 y z 1 z x

39. x

(i) 2x 3 2x 325 5 (ii)

x 12x 14 16 384

40. :

a2a 16

a a 164 24 2

.

41. :

b a c a a b c b a c b c1 1 1

1 x x 1 x x 1 x x

42. : a b b c c aa b c

b c ax x xx x x

43. :

1 1 1 1 1 53 8 8 7 7 6 6 5 5 2

44.

7 6 7 6a and b ,7 6 7 6

a2 + b2 + ab

45. :

2 6 6 2 8 32 3 6 3 6 2

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Class IX - Maths

46. x 9 4 5,

(i) 1xx

(ii) 1xx

(iii) 22

1xx

(iv) 22

1xx

(v) 33

1xx

(vi) 33

1xx

(vii) 1xx

(viii) 1xx

(ix) 44

1xx

(x) 66

1xx

(xi) 14xx

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Class IX - Maths

1.0 1 2 3 4, , , ,1 1 1 1 1

2. 17 3 2 502.125, 0.2, 0.285714, 16.68 15 7 3

3.15 16 17 18, , ,63 63 63 63

4. 23 4.795, 24 4.898

5. 4.8010010001 ......., 4.8020020002 ......,

6. 2.1, 2.010010001 ......,

8. 6

10. 4

11. 2016.1010010001 ..... ; 2016.2020020002 ......;

15. 0.909009000 ......; 1.10100100010000 ......

16. 1

17. 51

10 18. 36 19. 14 20. 1x4

21. 1 22. (60)2/5

23. (i) (ii)

(iii)

CBSE Support Material For Class 9Mathematics (Hindi)

Publisher : Faculty Notes Author : Panel Of Experts

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