Mec Maths Syllabus d5k48

Mathematics IA [ Top ] Revised Syllabus Intermediate I Year Mathematics Ia (Algebra, Vector Algebra & Trigonometry) Paper I A – Algebra:

65 Periods

1

Functions of Mappings

2

Surds 6

3

Logs 6

4

Mathematical Induction

9

14

VECTOR ALGEBRA:

5

Addition of Vectors 24

6

Multiplication of Vectors

Trigonometry:

7

25

60 Periods

Graphs & Periodic Functions )

(Trigonometric ratios of Compound angles ) (Multiple & Sub-multiple angles ) ( Transformations

9

8

Trigonometric Equations 16

9

Inverse Trigonometric functions 5

10

Hyperbolic functions

5

11

Properties of triangles

10

12

Heights and distances in single plane 7

13

Complex Numbers 6

14

De-movires Theorem

15

Trignometric expansions 3

5

Intermediate Mathematics –1a (Algebra, Vector Algebra & Trignometry) : 10 Periods

S. No Topics/Chapter

Sub-topics/Sections/Sub-sections

Periods of Instructions 1 Functions or Mappings A. Definitions of one-one, onto, bijection functions, Identity and constant functions Equality of two functions 9 periods B. Definitions of Inverse function, composite Function and Inverse of composite Function Theorems with proofs

F:A->B, g:B->C are bijective functions, then gof:A->C is also a bijection. Let A & B be two sets. If f:A->B is a Bijective then f –1 :B-A is also a bijective function If f:A->B and g:B->C are two Bijective functions then (gof) -1 =f -1 -1og -1 -1.

If f:A->B and g:B->C are two Bijective functions then (gof) -1 =f -1 -1og -1 -1. If f:A->B is a function and IA: A->A, IB: IB: B->2B are identity functions then foIA= f=IBof If f: A->B is a bijective function Then / f -1 = IA, fof –1 = IB If f:A->B, g:B->Cand h:C->D are any 3 functions then ho(gof) = (hog) of or composition of functions is associative

C. Definition of real valued function

Definition of domain, Range Algebra of real valued functions

2

Surds Evaluating Surds of the form

Cube root of the surds of the form

Rationalizing factors (upto 3rd degree) 3

Logarithms Definitions Introduction of common

logarithms

6 periods

Theorems:

log mn=log m+log n log (m/n) = log m – log n log m k = Klog m log a m = log b m . log a b Nature of Logarithms through graphs, Logarithms functions Types of Logarithms 4

Mathematical Induction

Principle of Mathematical Induction;

Theorem of Principle of finite Mathematical Induction Application of Mathematical Induction S n, S n2, S n3 etc., x-y devides x”-y” for all positive integral values of n and other divisibility problems

6 Periods

Vector Algebra

14 Periods

Addition Of Vector

Introduction of Vector as an ordered triad of real numbers- Representation of a vector as a directed line segment – Free and localized Vectors. Classification of Vectors – Collinear or parallel, like, unlike vectors, Co-initial vectors, coplanar and non-coplanar vectors, position vector, unit vector etc., Addition of vectors – parallelogram and triangle laws – Properties of

additions . Multiplication of Vector by Scalar Angle between two Non-Zero vectors. Vector of the points of division – Concurrence of Medians of a Triangle by Vector Method Linear combination of Vectors – linearly dependent and independent vectors Components of Vector in three dimension – Direction consines, modulus of a vector, Right and Left hand systems – Orthogonal triad of Vectors. Vector equation of line and plane in parametric from co linearity of three points and co planarity of four points. Multiplication Of Vectors Definition of the Scalar or dot product of two vectors its geometrical representation and Orthogonal projection of Properties of Scalar product – Commutative, and distributive laws – condition for perpendicularity of two vectors a, b are perpendicular vectors, Then a.b = o. Analytic expressions for scalar product in of i, j, k, angle between the two vectors. Some identities such as (a+b) 2 etc. Proof by Vector Method of angle in a semi-circle is a right angle laws of cosines and projection formula in a triangle Concurrency of the altitudes and perpendicular bisectors of sides of a triangle = cos A cos B + sin A sin B formal form – Angle between two planes. Vector equation of a plane in the normal form of two types: Vector equation of sphere, angle between two planes. Vector or Cross product of two vectors – Non-commutative vector product is distribution over addition Vector product among i, j, k, sine or the angle between two Vectors, Unit vector perpendicular to a given pair of Vectors

Vector area of a parallelogram and a triangle – Proofs by vector method (i) sin rule

Triple Products – Scalar triple product and its geometric interpretation. Co planarity of three vectors and deductions volume of a tetrahedron. Vector area of a plane in different parts, skew lines – simple problems. Vector triple product and its results. Product of Four vectors – Scalar and vector product of Four vectors

Trigonometry

Topics/Chapter

Sub-topics/Sections/Sub-sections

Periods of Instructions Graph & Periodicity

Definition of Trigonometric functions

with the help of unit circle

3 periods Particular values - Variation of sinq , cos ? ,tanq ? , Variation 3 periods in values as changes periodicity and extreme values, trigonometric ratio of any angle

Graphs y=sin ? , Y=cos ? , y=tan ? Trigonometric ratios of compound angles compound

Trigonometric Ratios of

angles such as Summation Formulae Sin(A+B), Cos(A+B), Tan (A+B)

5 periods Trigonometric ratios of Multiple and submultiples Angles Triogonometric ratios of 2A, 3A and A/2 (Multiple and submultiple Angles angles

4 periods Transformations and Identities Transformation from sum to products Transformation from products to sums

4 periods

Trigonometric Equations Trigonometric Equations Solving simple Trigonometric Equations Inverse of all the six Trigonometric functions, domains, ranges-graphs. Solving simple Equations involving Inverse trigonometric functions

5 periods

Hyperbolic functions the series

Meaning of e, exponential of

Definitions Domain and Range of Hyperbolic and Inverse Hyperbolic functions Addition formulae of Hyperbolic functions Sinh(x±y), Cosh(x±y) etc.,

3 periods Properties of triangles triangle.

Relation between the sides and angles of an

Half angle formulae and area of a triangle Incircle and ex-circle of a triangle

10 periods Heights & Distances

Angles of Elevation and Depression

Problems involving one plane

10 periods Complex Numbers Complex number as an ordered pair of real numbers. Representation in the form of a+ib, real and imaginary part equality of Complex Numbers Fundamental operations on Complex Numbers. Conjugate Complex Numbers Modulus and amplitude of a Complex Numbers Geometrical Representation of a complex number, Argand Plane and Argand diagram

6 periods Demovieris Theorem rational index.

Demovier's theorem for integral index and for

nth root of unity and its geometrial representation. Cube roots of unity Trigonometric Expansions

Expansion of Trigonometric functions,

Sin n ? , Cos n ? as series, expansion of Tann n ? and Cos n ? Expressing Sinnq and Cosq in of Sines and Cosines of multiples of ?

7 periods

Mathematics IB [ Top ] Revised Syllabus Intermediate I Year Mathematics Ib (Coordinate Geometry And Calculus)

Coordinate Geometry Dimensions: 65 Periods) Locus 4 Translation and rotation of axes 5 Straight lines

20

Pair of Straight lines

20

Dimensional; Coordinates 8 Direction cosines and ratios

Calculus:

8

Functions, Limits and Continuity

16

Derivatives, first order and second order derivatives Applications of derivatives Partial differentiation

16

20

8

Co-Ordinate Geometry – 2D

Locus Definition of locus Equation of locus Illustrations Translation & Rotation of axes

Translation of axes

Rotation of axes Illustrations Straight line General equation of a straight line and Forms of equation of a straight line slope intercept form Intercepts form Point-slope form Two point form Normal form xCosx+ySinx=p Symmetric form x-x 1 /sinq = y-y 1 /sinq = r To reduce the general equation into different forms Point of intersection of two straight lines Family of straight lines ing through the point of intersection of two given lines. Pair of straight lines origin

ax 2 +2hxy+by 2 =0 a pair of line through the

Angle between the lines ax 2 +2hyx+by 2 =0 conditions for coincidence perpendicularities Bi-sector of the angles between the lines L 1 =0, L 2 =0

Combined equation of the bisectors of the angles between the lines ax 2 +2hxy+by 2 =0

If the general equation of the second degree in x & y i.e. ax 2 +2nxy+by 2 +2gx+2fy+c=0 represents a pair of straight lines then

abc+2fgh-af 2 -bg 2 - ch 2 =0, h 2 >ab, g 2 >ac and f 2 >bc Converse of 4.5 without proof.

If S=ax 2 +2hxy+by 2 +2gx+2fy+c=0 represents a pair of straight lines then ax 2 +2hxy+by 2 =0 represents the line through the origin, parallel to the above lines. Angle between the lines S=0 condition for these line to be (I) Parallel (ii) Perpendicular Point of intersection of the lines S=0 Homogenization of the second degree equation with a first degree equation in x and y Co-Ordinate Geometry – 3D Co-ordinates Co-ordinate planes – Co-ordinates of a point – Distance between two points in space. To find the Co-ordinates of a point which divides the of two points

(x, y, z), (x1 y1 z1) internally in the ratio m:n – centroid of a triangle and

tetrahedron Direction cosines and ratios the cosines l 2 +m 2 +n 2 =1

Direction cosines of a line, relation between

Direction cosines of a line, to find the direction cosines when direction ratios are given

Calculus Functions, Limits and Continuity Function, Domain and Range of Continuity Function-Algebraic, Trigonometric,

Inverse Trigonometric, Hyperbolic, Step function and construction of graphs of logx, e l, lxl, (x)

Concepts of intervals and neighborhood Limits – Definition of right hand limit, left hand limit, limit. Limits of f+g, f/g, fog (without proof) Standard limits

(Limits 3,4, and 5 without proof) Continuity – Definition and simple illustration Differentiation

Introduction – Definition

Differentiation of a function at a point and on an Interval – Derivative of a function – Differentiation of sum, difference, product and quotient of functions. Differentiation of algebraic, circular, exponential, logarithmic functions.

Derivatives of composite, implicit, parametric, inverse circular, hyperbolic

and inverse hyperbolic functions.

Logarithmic differentiation, Derivative of a function with respect of another function. Derivatives of first and second order Application of Derivative

Infinitesimal – Differentials

Errors and approximations Geometrical interpretation of a derivative Equations of tangent, normal sub tangent, sub-normal at a point Lengths of tangent, normal sub-tangent, sub-normal at a point. Angle between two curves, orthogonally Derivative as a rate measurer Increasing and decreasing functions Maxima and minima Partial Differentiation

Partial derivatives - First and second orders only

Homogeneous functions – Euler's theorem on homogeneous functions – functions – simple applications.