Class 10 Standard Mathematics Notes
1. Real Numbers
Euclid's Division Lemma: a = bq + r
Fundamental Theorem of Arithmetic: Every number >1 is either prime or can be factored uniquely.
LCM and HCF using prime factorization.
Decimal expansion: Terminating (denominator = 2^m 5^n), Non-terminating otherwise.
2. Polynomials
Degree: Highest power of variable.
Zeroes of a polynomial: f(x) = 0
Sum = -b/a, Product = c/a (for quadratic)
Factor and Remainder Theorem.
3. Pair of Linear Equations
General form: ax + by + c = 0
Solution methods: Graphical, Substitution, Elimination, Cross-multiplication
Types: Consistent, Inconsistent, Dependent
4. Quadratic Equations
Standard form: ax + bx + c = 0
Discriminant D = b - 4ac
Roots: x = (-b D) / 2a
5. Arithmetic Progression
nth term: a + (n-1)d
Sum of n terms: Sn = n/2[2a + (n-1)d]
6. Triangles
Similarity: AAA, SSS, SAS
Pythagoras: a + b = c
Area ratio = (side ratio)
7. Coordinate Geometry
Distance: [(x2-x1) + (y2-y1)]
Midpoint: ((x1+x2)/2, (y1+y2)/2)
1. Real Numbers
Euclid's Division Lemma: a = bq + r
Fundamental Theorem of Arithmetic: Every number >1 is either prime or can be factored uniquely.
LCM and HCF using prime factorization.
Decimal expansion: Terminating (denominator = 2^m 5^n), Non-terminating otherwise.
2. Polynomials
Degree: Highest power of variable.
Zeroes of a polynomial: f(x) = 0
Sum = -b/a, Product = c/a (for quadratic)
Factor and Remainder Theorem.
3. Pair of Linear Equations
General form: ax + by + c = 0
Solution methods: Graphical, Substitution, Elimination, Cross-multiplication
Types: Consistent, Inconsistent, Dependent
4. Quadratic Equations
Standard form: ax + bx + c = 0
Discriminant D = b - 4ac
Roots: x = (-b D) / 2a
5. Arithmetic Progression
nth term: a + (n-1)d
Sum of n terms: Sn = n/2[2a + (n-1)d]
6. Triangles
Similarity: AAA, SSS, SAS
Pythagoras: a + b = c
Area ratio = (side ratio)
7. Coordinate Geometry
Distance: [(x2-x1) + (y2-y1)]
Midpoint: ((x1+x2)/2, (y1+y2)/2)
