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Useful, no-nonsense resources for students — made by teachers with 12+ years of experience.

📐 Maths formula sheet ⌨️ Typing test 🧠 Computer GK quiz ⚡ Shortcut keys 📚 Official books & papers

📐 Class 10 Maths — all important formulas

NCERT / CBSE / HPBOSE Class 10. Revise these before every test.

Real Numbers

HCF × LCM = product of two numbers (a × b)
Euclid's division lemma: a = bq + r, 0 ≤ r < b

Polynomials

Quadratic ax² + bx + c: sum of zeroes α+β = −b/a, product αβ = c/a
Cubic: α+β+γ = −b/a, αβ+βγ+γα = c/a, αβγ = −d/a

Pair of Linear Equations

a₁/a₂ ≠ b₁/b₂ → unique solution
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → no solution
a₁/a₂ = b₁/b₂ = c₁/c₂ → infinitely many solutions

Quadratic Equations

x = [−b ± √(b² − 4ac)] / 2a
Discriminant D = b² − 4ac: D>0 two real roots, D=0 equal roots, D<0 no real roots

Arithmetic Progressions

nth term: aₙ = a + (n − 1)d
Sum: Sₙ = n/2 [2a + (n − 1)d] = n/2 (a + l)

Triangles

Pythagoras: (hypotenuse)² = (base)² + (perpendicular)²
Similar triangles: ratio of areas = square of ratio of corresponding sides

Coordinate Geometry

Distance = √[(x₂−x₁)² + (y₂−y₁)²]
Section formula: ((m x₂ + n x₁)/(m+n), (m y₂ + n y₁)/(m+n))
Mid-point: ((x₁+x₂)/2, (y₁+y₂)/2)

Trigonometry

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
tanθ = sinθ/cosθ; sin30° = 1/2, cos60° = 1/2, tan45° = 1, sin60° = √3/2

Circles

Tangent ⟂ radius at the point of contact
Tangents from an external point are equal in length

Areas Related to Circles

Circumference = 2πr, Area = πr²
Area of sector = (θ/360) × πr²
Length of arc = (θ/360) × 2πr

Surface Areas & Volumes

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

Statistics

Mean (direct) = Σfx / Σf
Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h
Median = l + [(n/2 − cf)/f] × h
Empirical: 3 Median = Mode + 2 Mean

Probability

P(E) = favourable outcomes / total outcomes
P(E) + P(not E) = 1, 0 ≤ P(E) ≤ 1

⌨️ Typing speed test (60 seconds)

Type the text below as fast and accurately as you can. The timer starts with your first key.

Learning is a treasure that will follow its owner everywhere. Practice every day, stay curious and never be afraid to ask questions. Small steps taken daily lead to big success. A good typist keeps the eyes on the screen and the fingers on the home row keys.

⏱ 60s⚡ 0 WPM🎯 100% accuracy

Govt. typing tests usually need 30–40 WPM. Our typing course gets you there step by step.

⚡ Keyboard shortcuts every student should know

⌨️ Windows

Keys	Action
`Win + D`	Show desktop
`Win + E`	Open File Explorer
`Alt + Tab`	Switch windows
`Win + L`	Lock PC
`Win + Shift + S`	Screenshot (snip)
`Ctrl + Shift + Esc`	Task Manager

⌨️ Everywhere

Keys	Action
`Ctrl + C / X / V`	Copy / Cut / Paste
`Ctrl + Z / Y`	Undo / Redo
`Ctrl + A`	Select all
`Ctrl + S`	Save
`Ctrl + P`	Print
`Ctrl + F`	Find

⌨️ MS Word

Keys	Action
`Ctrl + B / I / U`	Bold / Italic / Underline
`Ctrl + E / L / R / J`	Centre / Left / Right / Justify
`Ctrl + Enter`	Page break
`Shift + F3`	Change case
`Ctrl + ] / [`	Increase / decrease font
`F7`	Spelling & grammar