BOARD OF SECONDARY EDUCATION, MANIPUR

Mathematics Book. 1
Published by the Board of Secondary Education, Manipur

11. Course Content:

Irrational number; Decimal representation of irrational number; Surds ; Type of surds; Comparison of surds; Rationalisation of surds; Real numbers; Field properties of real numbers; order properties of real numbers; Inequalities; Real numbers are dense; Absolute value of real numbers; Fundamental properties; Archemedian property.

2. SETS

Sets; Methods for describing a set; Null set; Singleton set etc. Subset; Equality of sets; Proper and improper subsets; Power sets; Equivalent sets; Universal set; Venn diagrams; Basic operation on sets; Union; Venn diagram of union; Union is associative; Union is commutative; Union of finite number of sets; Intersection; Intersection is associative; Intersection is commutative; Disjoint sets; Intersection of finite number of sets; difference ; Complement ; De-Morgan's law; basic facts about Complementation ; Distributive laws; Cardinal numbers; Theorem.

3. POLYNOMIALS

Degree of a polynomial; Special names of Polynomials; Factors of a Polynomial; Factors of ax² + bx + c; H.C F. and L.C.M. of polynomials; H.C.F.of monomials; H.C.F. of polynomials by factorisation; L.C.M. of monomials; L.C.M. of polynomials which can be factorised.

4. RATIONAL EXPRESSION

Rational expressions; Rational expressions in lowest term; Addition of rational expressions; Subtraction of Rational algebraic expressions; Multiplication of rational algebraic expressions; Division of rational algebraic expressions; Properties of rational algebraic expressions.

5. RATIO AND PROPORTION

Extremes and means; Continued proportion; Rules of proportion.

6. EQUATION

Linear Equation in one variable; Application of Linear Equations; Linear Equation in two variable; Algebraic Method; Graphs of Linear Equation in one and two variables.

7. LOGARITHMS

[ 65 Periods for Chapter 2 To 7 ]

Laws of Logarithms; Approximation; Significant figures. The Common Logarithm; Determination of Mantissa; Logarithms Applications; Depreciation of values.

8. TRIGONOMIETRY

 [ 15 Periods ]

Angles; Positive and Negative Angles; Different measures of an Angle; Sexa desimal System (Scale of Sixty),; Contesimal System (Scale of Hundred); Relation between two systems; number  (pi); Circular System; Relation among the three system; Relation between the Arc, Angle and radius ; Trigonometric ratio; Some useful identities. Trigonometric ratios of some standard angles. Trigonometric ratios of 30^o; Trigonometric ratio of 45^o; Concept of Infinity (α).

9. LINES AND ANGLES

Axioms; some definitions; Angle; Adjacent angle; A Linear pair of Angles; Vertically opposite Angles made by a Transversal with two lines; Triangle and Angles; Exterior Angles of a Triangle.

10. CONGUENCE OF TRIANGLES

Theorems on Congruence

11. PARALLELOGRAMS

Terms related to a quadrilateral. Parallelograms and their types; Properties of a Parallelogram; Sufficient conditions for a quadrilateral to be Parallelogram; Rectangle; Rhombus and Square.

12. INEQUALITIES OF A TRIANGLE

Theorems of inequality sides and angles of a Triangle.

13. LOCI

Discussion; Intersection of Loci.

14. AREAS

Polygon Regions; Fundamental Axioms; Area of a Parallelogram; Base and Altitude of a Parallelogram; Base and Altitude of
Triangle.

15. GEOMTRICAL CONSTRUCTION

 [65 PERIODS FOR CHAPTERS 9 TO 15]

Problems of Geometrical Construction; Simple Constructions; Construction of Triangle; Construction of Quadrilaterals; Construction of Regular Polygons; Construction of Equivalent Areas.

16. STATISTICS

 [10 PERIODS ]

Frequency Polygon; Cumulative Frequency Curve or the O give.

17. COMPUTING

 [15 PERIODS ]

System of Numeration; Decimal system (System with base ten); Other Systems; Binary system; Arithmetic Operations in Binary System; Introduction to Computers; Mathematics and Computers; Working of Computers; Computer Programming Language; Application of Binary system in Computers; Algorithm; Mathematics; Algorithms and Computers; Flowcharts.

MATHEMATICS

CLASS – X

        I.    Name of the text book:

                     Mathematics Book – II

                    Published by the Board of Secondary Education, Manipur

         II.  Course Contents

           1.      RELATION & FUNCTIONS

                         Ordered pairs; Cartesian product of two sets; Graph of A x B when A and B are subsets of R; Relations; Domain and Range of a relation; Relation in a set; Types of relation in a set; Functions or mappings; Functional Notations; Domain and Range of a Function; Diagrammatic Representation of Mappings; Types of Mappings; Graph of a Real Function; Representation of Mappings.

            2.            LINEAR EQUATIONS IN TWO UNKNOWNS

Solutions of Linear Equations in two unknowns by graphical method;

Inequations and their graphs; Application of Linear Equations in two unknowns in Problems.

             3.            REMAINDER THEOREM

Remainder Theorem; Factor Theorem; Cyclic Factors; To factorise; a²(b+c) + b²(c+a) + c²(a+b) + 3abc; To factorise: a³+b³+c³-3abc; To factorise: (a+b+c)²-a²-b²c²; To factorise: a²(b-c)+b²(c-a)+c²(a-b); To factorise: a3(b2-c2) + b3(c2-a2) + b3(c2-a2) + c3(a2-b2); To factorise; 2b2c2 + 2c2a2 + 2a2b2-a4-b4-c4; H.C.F. and L.C.M. of two polynomials by Division Method; L.C.M. of three or more polynomials.

4.            QUADRATIC EQUATIONS

[60 periods for
chapters 1to 4]
 

Factorisation Method of solving a Quadratic; To solve ax²+bx+c=0; Nature of the Roots of ax²+bx+c=0; Relation between the Roots and Co-efficients of the Quadratic Equation; Formation of Quadratic Equation when the roots are given; Word problems based on Quadratic Equation; Factorisation of ax²+bx+c=0; Graph of Quadratic Polynomials; Observations.

             5.            TRIGONOMETRY

Trigonometrical Identities; Triginimetrical Rations and their co-functions; Solution of simple Trigonometrical Equations (0^o<p>90^o); Heights and Distances; Clinometer and Trigonomitrical Tables.

   6.            SIMILARITY

Similarly; Similar polygons; Similar Triangles; Internal and External Division of a line segment.

             7.            PYTHAGORAS THEOREM

Pythagoras Theorem and converse of Pythagoras Theorem.

             8.            CIRCLES

Circles; Some Terms related to Circles; Circles passing through points; Tangents; Tangents from external point and the Circles touching each other.

             9.            GEOMETRICAL CONSTRUCTIONS

Ideas of Geometrical Construction; Construction of triangle; Construction of quadrilateral; Construction of tangent of a circle.

             10.       STATISTICS

Measure of central tendency (measures of Locations); The weighted Arithmetic Mean; Short-cut Method of finding the weighted A.M.; Median, Merits and Demerits of the A.M.; Geometrical and Harmonic Means; Mode; Measure of Location; Vital Statistics; Mortality Rate; Standardised Death rate; Index Numbers; Construction of Index Numbers.

             11.       COMPUTING

Flowchart involving Decision Boxes land Loops; Miscellaneous Algorithms and Flowcharts.

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

               Subject: Mathematics; Class: X; Time: 3 hours; Marks=100

     1.  Weightage to Objectives: 

     2.   Weightage to Forms of Questions: 

 3.             Weightage to Content 

 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), U (Understanding), A (Application), S (Skill), E (Essay Type), SA (Short answer Type), VSA (Very Short Answer Type), O (Objective Type).

N.B. :  For objective type question only the letter corresponding to the correct answer should be written.