📚 Class 10 Science Notes

🌡️ Temperature Converter

Fahrenheit (°F)

Celsius (°C)

Kelvin (K)

°C = (°F − 32) × 5/9 | K = °C + 273.15

📏 Length Converter

Metres (m)

Centimetres (cm)

Kilometres (km)

Miles (mi)

⚖️ Mass Converter

Grams (g)

Kilograms (kg)

Pounds (lb)

Milligrams (mg)

🚀 Speed Converter

m/s

km/h

mph

📐 Area Converter

m²

cm²

km²

hectares

Real Numbers

Euclid's Division Lemma: a = bq + r, 0 ≤ r < b
HCF × LCM = Product of two numbers
√2, √3, √5 are irrational numbers

Polynomials

Sum of zeros α+β = −b/a
Product of zeros αβ = c/a
Quadratic: ax² + bx + c = 0
Discriminant D = b² − 4ac

Quadratic Equations

x = (−b ± √(b²−4ac)) / 2a
D > 0 → two distinct real roots
D = 0 → two equal roots
D < 0 → no real roots

Arithmetic Progressions

n-th term: aₙ = a + (n−1)d
Sum: Sₙ = n/2 [2a + (n−1)d]
Sₙ = n/2 (a + l), l = last term
Common difference d = aₙ − aₙ₋₁

Triangles & Similarity

Basic Proportionality Theorem (Thales): DE ∥ BC → AD/DB = AE/EC
AA / SSS / SAS similarity criteria
Ratio of areas = (ratio of sides)²
Pythagoras: AC² = AB² + BC²

Coordinate Geometry

Distance = √[(x₂−x₁)² + (y₂−y₁)²]
Mid-point = ((x₁+x₂)/2 , (y₁+y₂)/2)
Section formula: ((mx₂+nx₁)/(m+n) , (my₂+ny₁)/(m+n))
Area of Δ = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|

Trigonometry

sin θ = P/H, cos θ = B/H, tan θ = P/B
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
sin(90°−θ) = cos θ, tan(90°−θ) = cot θ

Circles

Tangent ⊥ Radius at point of contact
Two tangents from ext. point are equal
Angle in semicircle = 90°
Tangent-Secant: PA² = PB × PC

Areas Related to Circles

Area of circle = πr²
Circumference = 2πr
Area of sector = (θ/360) × πr²
Length of arc = (θ/360) × 2πr
Area of segment = Area of sector − Area of Δ

Surface Areas & Volumes

Cube: SA = 6a², V = a³
Cuboid: SA = 2(lb+bh+hl), V = lbh
Cylinder: CSA = 2πrh, TSA = 2πr(r+h), V = πr²h
Cone: CSA = πrl, TSA = πr(r+l), V = ⅓πr²h, l = √(r²+h²)
Sphere: SA = 4πr², V = 4/3 πr³
Hemisphere: CSA = 2πr², TSA = 3πr², V = 2/3 πr³

Statistics

Mean (Direct): x̄ = Σfxᵢ / Σf
Mean (Assumed Mean): x̄ = a + Σfdᵢ / Σf
Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h
Median = l + [(n/2 − cf)/f] × h

Probability

P(E) = Number of favourable outcomes / Total outcomes
0 ≤ P(E) ≤ 1
P(E) + P(Ē) = 1
P(impossible event) = 0
P(sure event) = 1

Home

Real Numbers

Polynomials

Quadratic Equations

Arithmetic Progressions

Triangles & Similarity

Coordinate Geometry

Trigonometry

Circles

Areas Related to Circles

Surface Areas & Volumes

Statistics

Probability

Light — Reflection

Light — Refraction

Electricity

Magnetic Effects of Current

Sources of Energy

Chemical Reactions

Acids, Bases & Salts

Metals & Non-Metals

Carbon & Its Compounds

Periodic Classification

Life Processes

Control & Coordination

Reproduction

Heredity & Evolution

Our Environment

Natural Resources