Keep this beside you while you revise. It covers the core Class 10 Maths formulas for CBSE and Kerala State (SSLC). From the faculty at Veda Topper International, Irinjalakuda.
Algebra — identities
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- a² − b² = (a + b)(a − b)
- (a + b)³ = a³ + 3a²b + 3ab² + b³
- (a − b)³ = a³ − 3a²b + 3ab² − b³
- a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²)
Quadratic equations ax² + bx + c = 0
- Roots: x = [ −b ± √(b² − 4ac) ] / 2a
- Discriminant: D = b² − 4ac (D>0 real & distinct, D=0 equal, D<0 no real roots)
- Sum of roots = −b/a; Product of roots = c/a
Arithmetic Progression (AP)
- nth term: aₙ = a + (n − 1)d
- Sum of n terms: Sₙ = n/2 [ 2a + (n − 1)d ] = n/2 (a + l)
Coordinate geometry
- Distance: √[ (x₂ − x₁)² + (y₂ − y₁)² ]
- Midpoint: ( (x₁ + x₂)/2 , (y₁ + y₂)/2 )
- Section formula: ( (mx₂ + nx₁)/(m + n) , (my₂ + ny₁)/(m + n) )
Trigonometry
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ
- tanθ = sinθ/cosθ; cotθ = cosθ/sinθ
- Standard angles (0°,30°,45°,60°,90°): sin = 0, ½, 1/√2, √3/2, 1
Mensuration (surface area & volume)
- Circle: area = πr², circumference = 2πr
- Sphere: volume = 4⁄3 πr³, surface = 4πr²
- Hemisphere: volume = 2⁄3 πr³, CSA = 2πr², TSA = 3πr²
- Cylinder: volume = πr²h, CSA = 2πrh, TSA = 2πr(r + h)
- Cone: volume = 1⁄3 πr²h, CSA = πrl, slant l = √(r² + h²)
Statistics & probability
- Mean (grouped) = Σfx / Σf
- Mode = l + [ (f₁ − f₀) / (2f₁ − f₀ − f₂) ] × h
- Median = l + [ (n/2 − cf) / f ] × h
- Probability of an event: P(E) = favourable outcomes / total outcomes
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