# Andhra Pradesh Board Math Syllabus for Class 12

## Andhra Pradesh Board Syllabus for Class 12 Math

course structure
class-12

math

ALGEBRA, PROBABILITY: (125 Periods)
2) Theory of Equations 12 Periods
3) Matrices 24 Periods
4) Permutations and Combinations 18 Periods
5) Binomial Theorem 16 Periods
6) Partial fractions 6 Periods
7) Exponential and Logarithemic series 6 Periods

PROBABILITY:
8) Probability 18 Periods
9) Random variable and distributions 12 Periods
Total: 125 Periods

1.1 Quadratic Expressions, Equations in one Variable, Ex-treme Values – Changes in sign and
Magnitude – Qua-dratic Inequation.

2: THEORY OF EQUATIONS: 12 PERIODS
2.1 The relation between the roots and coefficients in an equation
2.2 Solving the equation when two or more roots of it are connected by certain relations
2.3 Equations with real coefficients, imaginary roots occur in conjugate pairs and its
consequences.
2.4 Transformation of equations, Reciprocal equations

3: MATRICES: 24 PERIODS
3.1 Definition - Types of Matrices – Equality, Addition, Com-mutative and associative, Properties
3.2 Scalar Multiplication of a Matrix – Additive inverse and identity. Multiplication of Matrices –
Non-commutativity – Associative and distributive laws of multiplication
3.3 Transpose of Matrix-Properties Symmetric and skew Symmetric Matrices.
Transpose of a Matrix Properties:
i) (A T ) T = A
ii) (KA)T = KA T
iii) (A+B)T = (A T + B T)
iv) (AB)T = B T A T
Symmetric and skew symmetric Matrices
3.4 Determinant of a Matrix, Singular, Non-singular Matri-ces, Minor, Co-factor of an element in
the Matrix – Prop-erties of determinants
3.5 Adjoint of a Matrix, Inverse of a Matrix Properties
i) A -1 = Adj A/det A
ii) (AB) -1 = B -1 A -1
iii) (A T ) -1 = (A -1 ) + T
3.6 Solution of simultaneous linear equation in two and three variables by Crammer’s rule, Matrix
inversion method
and Gauss – Jordan method, Consistency and in-con-sistency of simultaneous equations.
NOTE: In the treatment, upto 3x3 determinants and matrices should be considered.

4. PERMUTATIONS & COMBINATIONS:18 PERIODS
4.1 Definition of linear and circular permutations
4.2 To find the number of permutations of n dissimilar things taken ‘r’ at a time.
4.3 To prove nP r =(n-1)P r + r (n-1) p r-1 from the first prin-ciples
4.4 To find number of Permutations of n Dissimilar Things taken ‘r’ at a time when repetion of
Things is allowed any number of times.
4.5 To find number of circular Permutations of /n/ Different things taken all at a time.
4.6 To find the number of Permutations of ‘n’ things taken at a time when some of them are alike
and the rest are dissimilar
4.7 To find the number of combinations of ‘n’ dissimilar things taken 'r' at a time
4.8 To prove
i) If nc r = nc s then n=r+s or r=s
ii) Nc r + nc r -1 = (n+1) cr

5. BINOMIAL THEOREM: 16 PERIODS
5.1 Binomial theorem for positive Integral Index, Binomial coefficients and simple results on them,
Numerically greatest term.
5.2 Binomial Theorem for rational Index (statement only) Important particular cases of Binomial
Expansion.
5.3 Approximations using Binomial Theorem

6. PARTIAL FRACTIONS: 6 PERIODS
Resolving f(x)/g(x) into Partial fractions when g(x) contains:
6.1 Non-repeated linear factors
6.2 contains repeated and non repeated linear fractions only.
6.3 g(x) contains non-repeated and non-repeated irreduc-ible factors only.
6.4 g(x) contains repeated and non-repeated irreducible fac-tors only.
(Note: Number factors of g(x) should not exceed 4)

7. EXPONENTIAL AND
LOGARITHEMIC SERIES: 6 PERIODS
7.1 le x l Expansion for real x
7.2 log (1+x) expansion, condition on x
(Note: Statements of the results and very simple problems such as finding the general term
should only be given)

8: PROBABILITY: 30 PERIODS
8.1 Random experiment, random event, elementary events, exhaustive events, mutually
exclusive events
8.2 Classical definition – relative frequency approach – sample space, sample events, Addition
theorem on Probability
8.3 Dependent and independent events, multiplication theorem, Baye’s theorem

9. RANDOM VARIABLES AND DISTRIBUTIONS:
9.1 Random variables, Distributive functions, probability dis-tributive functions, Mean variance of
a random variable
9.2 Theoretical desecrate distributions like Binomial, poisson distribution – Mean and variance of
above distributions (without proof)

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