GRADE 10 MATHEMATICS NOTES
1. REAL NUMBERS
Euclid’s Division Lemma: a = bq + r, where 0 ≤ r < b
HCF and LCM relation: HCF × LCM = Product of two numbers
2. POLYNOMIALS
Polynomial: An expression of variables and constants.
Zero of polynomial: Value of x where polynomial = 0
3. PAIR OF LINEAR EQUATIONS
Standard form: ax + by + c = 0
Methods: Substitution, Elimination, Graphical
4. QUADRATIC EQUATIONS
Standard form: ax² + bx + c = 0
Formula: x = [-b ± √(b² – 4ac)] / 2a
5. ARITHMETIC PROGRESSIONS (AP)
General term: an = a + (n – 1)d
Sum: Sn = n/2 [2a + (n – 1)d]
6. TRIANGLES
Pythagoras theorem: (Hypotenuse)² = (Base)² + (Height)²
Similarity of triangles
7. COORDINATE GEOMETRY
Distance formula: √[(x2-x1)² + (y2-y1)²]
Midpoint formula: [(x1+x2)/2 , (y1+y2)/2]
8. TRIGONOMETRY
sinθ = Perpendicular / Hypotenuse
cosθ = Base / Hypotenuse
tanθ = Perpendicular / Base
9. CIRCLES
Tangent: A line touching the circle at one point
Two tangents from external point are equal
10. MENSURATION
Area of circle = πr²
Surface area of sphere = 4πr²
Volume of sphere = 4/3 πr³
11. STATISTICS
Mean = (Sum of observations) / (Number of observations)
12. PROBABILITY
1. REAL NUMBERS
Euclid’s Division Lemma: a = bq + r, where 0 ≤ r < b
HCF and LCM relation: HCF × LCM = Product of two numbers
2. POLYNOMIALS
Polynomial: An expression of variables and constants.
Zero of polynomial: Value of x where polynomial = 0
3. PAIR OF LINEAR EQUATIONS
Standard form: ax + by + c = 0
Methods: Substitution, Elimination, Graphical
4. QUADRATIC EQUATIONS
Standard form: ax² + bx + c = 0
Formula: x = [-b ± √(b² – 4ac)] / 2a
5. ARITHMETIC PROGRESSIONS (AP)
General term: an = a + (n – 1)d
Sum: Sn = n/2 [2a + (n – 1)d]
6. TRIANGLES
Pythagoras theorem: (Hypotenuse)² = (Base)² + (Height)²
Similarity of triangles
7. COORDINATE GEOMETRY
Distance formula: √[(x2-x1)² + (y2-y1)²]
Midpoint formula: [(x1+x2)/2 , (y1+y2)/2]
8. TRIGONOMETRY
sinθ = Perpendicular / Hypotenuse
cosθ = Base / Hypotenuse
tanθ = Perpendicular / Base
9. CIRCLES
Tangent: A line touching the circle at one point
Two tangents from external point are equal
10. MENSURATION
Area of circle = πr²
Surface area of sphere = 4πr²
Volume of sphere = 4/3 πr³
11. STATISTICS
Mean = (Sum of observations) / (Number of observations)
12. PROBABILITY
