X-MATRIC MATHS Blue Print

S.No.	Chapter Name	Marks
1.	Number Work	25
2.	Mensuration	24
3.	Set Language	21
4.	Consumer Arithmetic	17
5.	Algebra	33
6.	Graphs	20
> >	Total Marks	140

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       MATHEMATICS - II

S.No.	Chapter Name	Marks
1.	Matrices	17
2.	Theoretical Geometry	26
3.	Co-ordinate Geometry	33
4.	Trigonometry	28
5.	Statistics	16
6.	Practical Geometry	20
> >	Total Marks	140

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X-Matric Formula Algebra

ALGEBRA

Remainder theorem.

If a polynomial P(x) of degree ≥ 1 over the set of real numbers
R is divided by x-a where a є R then the remainder is P(a) .

Factor theorem

If P(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number then

1. (x-a) is a factor of P(x) if P(a) = 0

2. P(a) = 0 if (x-a) is a factor of P (x).

Quadratic Equation

1. General quadratic Equation is

ax² + bx + c = 0, where a, b, c are real and a ≠ 0.

2. Roots
x = (-b +√ b²-4ac) /2a

3. If a and b are the roots then the required equation is

x² - (a+b) x + (ab)=0

4. Sum of the Roots (a+b) = –b / a

5. Product of the Roots (ab) = c / a

Discriminant Δ = b2 - 4ac	Nature of Roots
Δ > 0 but not a perfect square Δ > 0 and a perfect square Δ = 0 Δ <>	Real, unequal and irrational Real, unequal and rational Real and equal Unreal

SET LANGUAGE

Operations on Sets
1. Union of sets : A U B = {x / x є A or x є B or x є A and x є B }
Note:
A U A = A
A n A = A
A n A’= {}
A U A’= U
2. Intersection of sets: A n B = {x / x є A and x є B }
Properties of set difference
1. Set difference is not commutative A – B ≠ B – A
2. Set difference is not associative A– (B – C) ≠ (A – B) – C
Distributive Property
1. Union is distributed over intersection A U (B n C) = (A U B ) n (AU C)
2. Intersection is distributed over union A n ( B U C) = (A n B) U (A n C)
DE Morgan’s Laws
1. Regarding complementation
(i) (A U B)’ = A’ n B’
(ii) (A n B)’ = A’ U B’
2. Regarding set difference
(i) A – (B U C) = (A – B) n (A – C)
(ii) A – (B n C) = (A – B) U (A – C)
♦ n(A U B) = n (A) + n (B) – n(A n B) if A n B ≠ { }
♦ n(A U B) = n (A) + n (B) if A n B = { }

• n(A U B U C) = n (A) + n (B) + n (C)–n(A n B)–n(B n C)–n(A n C) + n(A n B n C)