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Curriculum & Syllabus for Classes IX & X

ADDITIONAL SUBJECT

4. HIGHER MATHEMATICS

FOR CLASS - IX

1. Name of the text books :

Higher Mathematics Book- I
Published by the Board of Secondary Education, Manipur

II .Course Contents for Class IX

  1. Algebra or irrational numbers :

    Rationalisation of irrational denominators; Comparison of mixed surds ;square roots of mixed surds, equations involving surds.

  2. Sequences : Definition, and example :

    A. P.; G.P.; and H.P.
    A.P. nth term, A.M., sum of n terms Σx, Σxn,Σx n+1
    G.P. nth term, G.M., sum to n terms ; sum to infinity.
    H.P. nth term,H.M., relation of A.M., G.M. and H.M. of two positive numbers.

  3. Compound interest ; Bank and other accounts ; Present value, Instalments under simple and compound interest, Equated payment, Depreciation, Hire Purchase, Saving and Current Accounts ; Recurring Deposit, Term (fixed) Deposit.

  4. Mensuration :

    1. Area of triangle in terms of sides (Hero’s formula - proof); Area of triangle in terms of two sides and included angle; Area of circle (without proof), sector, segment.

    2. Surface area and volume of cube and cuboid.

  1. Natural numbers, whole numbers, integers, Divisibility (in Z or W). Prime and composite numbers, H.C.F. and L.C.M. of two numbers and their relation; Division algorithm.

  2. Trigonometrical Identities.

  3. Vector, Scalar, Addition of Vectors, properties, multiplication of a vector by a scalar.

  4. Velocity, Acceleration, Rectilinear motion, Resolution and composition of velocities. Newton's laws of motion.

  5. Permutations and combinations defined. Fundamental Principle, Factorial notation. permutations of things all Different; permutation in which things may be repeated ; permutation of things when they are not all different.

    Combinations of things all different. Complimentary combinations;nCr nC r-1 = n+1 C r
    Cr Restricted Combinations.

  6. Mathematical Logic; Logic statement (or sentence); Logical connective, simple and compound statements, Meet, Joint, Negation, implication, double implication, Truth values and truth tables.

DESIGN OF QUESTION PAPER FOR H.S.L.C. EXAMINATION.

Subject : Higher Mathematics ; Class : IX ; Time : 3 hours ; Marks =100

I. Weightage to Objectives:

Objectives K  U A S  Total
Percentage of marks 30  45  20 5  100
Marks 35  45 20  5 100

2. Weightage to Forms of Questions:

Forms of Questions E  SAI  SA2 VSA O Total
Number of Questions 9 9 6 7 4 35
Marks Allotted 50 27 12 7 4 100
Estimated Time (in mins.) 95 45 20 1 2 8 180

3. Weightage of Content:

SI. No. Chapters / Units Marks
1.  Algebra of irrational number 6
2.  Sequences 10
3.  Compound Interest 10
4. Mensuration 12
5.  Numbers 10
6. Trigonometrical Identities 6
7.  Vector 8
8.  Velocity, Acceleration etc. 12
9.  Permutation & Combination 12
10. Mathematical Logic 14
  Total: 100

4. Scheme of Section : No section

5. Scheme of option : Internal option may be given in (E) type questions provided they test the same objective.

6. Difficulty Level :  Difficult  : 15%
  Average  : 70%
  Easy  : 15%

Abbreviations: K (Knowledge), C (Comprehension), Ex (Expression), E (Essay Type), SA (Short Answer Type), VSA (Very Short Answer Type), O (Objective Type).

4. HIGHER MATHEMATICS

CLASS - X

I. Name of the text books :

Higher Mathematics Book- 11
Published by the Board of Secondary Education, Manipur

II. Course Content :

  1. Arithmetical Problems on clock, discount, stocks and shares.

  2. Factorisation (harder type) ; Identities (Conditional and unconditional)

  3. Simultaneous Linear Equations in two and three variables, two simultaneous. Equations - one linear and other quadratic equations.

  4. Quadratic equations and expressions.

  5. Trigonometric ratios of allied (associated) angles.

  6. . Mathematical Induction:
    Binomial Theorem (Positive integral index).

  7. Mensuration:
    Surface area and volume of spheres, prisms, pyramids and right circular cones.

  8. Linear Programming:
    Mathematical formulation graphical solution.

  9. Probability:
    Terms associated with probability. Mathematical (classical) definition of. probability. Theorems on sum and products of probabilities.

DESIGN OF QUESTION PAPER FOR H.S.L.C. EXAMINATION

Subject : Higher Mathematics ; Class : X ; Time : 3 hours ; Marks = 1 00

1. Weightage to Objectives :

Objectives  K U A S  Total
Percentage of marks 30 45  20 5 100
Marks 30 45 20  5  100

2. Weightage to Forms of Questions .

Forms of Questions E SAI SA2 VSA  0 Total
Number of Questions 9 9 6 7 4 35
Marks Allotted 50 27 12 7 4 100
Estimated Time (in mins.) 95 45 20 12 8 180

3. Weightage of Content :

SI. No. Chapters / Units Marks
1.  Problems on Clock, Discount, Stock & Shares 12
2. Factorisation, Identities 12
3. Equations, Linear, Quadratic Exponential 12
4. Quadratic Equations & Expression 12
5. Ratio of Allied Angels 8
6. Induction, Binomial Theorem 10
7.  Mensuration 10
8. Linear Programming 12
9.  Probability 12
  Total: 100

4. Scheme of Section : No Section

5. Scheme of option : Internal option may be given in (E) type questions provided they test the same objective.

6. Difficulty Level :  Difficult  : 15%
  Average  :  70%
  Easy : 15%

Abbreviations: K (Knowledge), C (Comprehension), Ex (Expression), E (Essay Type), SA (Short Answer Type), VSA (Very Short Answer Type), O (Objective Type).