School Level Maths Formulas Handbook (1st–10th)

Class 1–3 Basics

• Addition: a + b
• Subtraction: a – b
• Multiplication: a × b
• Division: a ÷ b

Fractions

• Equivalent Fractions: multiply/divide numerator and denominator by same number
• Add fractions: a/b + c/b = (a+c)/b
• Multiply fractions: (a/b)(c/d) = ac/bd
• Divide fractions: (a/b) ÷ (c/d) = ad/bc

Decimals & Percentages

• Percentage = (Part/Whole) × 100
• Discount = Marked Price – Selling Price
• Profit = SP – CP
• Loss = CP – SP
• Profit % = (Profit/CP) × 100
• Loss % = (Loss/CP) × 100

Ratio & Proportion

• Ratio = a:b
• Proportion: a:b = c:d => ad = bc

Average

• Average = Sum of observations / Number of observations

Simple Interest

• SI = (P × R × T) / 100
• Amount = P + SI

Compound Interest

• Amount = P(1 + R/100)^n
• CI = Amount – Principal

Algebra Basics

• a + a = 2a
• a × a = a^2
• a^m × a^n = a^(m+n)
• a^m / a^n = a^(m-n)

Algebraic Identities

• (a+b)^2 = a^2 + 2ab + b^2
• (a-b)^2 = a^2 – 2ab + b^2
• a^2 – b^2 = (a-b)(a+b)
• (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
• (a-b)^3 = a^3 – 3a^2b + 3ab^2 – b^3

Linear Equations

• ax + b = c => x = (c-b)/a

Quadratic Equations

• ax^2 + bx + c = 0
• x = (-b ± √(b^2 – 4ac)) / 2a

Geometry: Perimeter & Area

• Rectangle Perimeter = 2(l+b)
• Rectangle Area = l × b
• Square Perimeter = 4a
• Square Area = a^2
• Triangle Area = (1/2) × b × h
• Parallelogram Area = b × h
• Circle Circumference = 2πr
• Circle Area = πr^2

Mensuration: Surface Area & Volume

• Cube TSA = 6a^2
• Cube Volume = a^3
• Cuboid TSA = 2(lb + bh + hl)
• Cuboid Volume = lbh
• Cylinder CSA = 2πrh
• Cylinder TSA = 2πr(r+h)
• Cylinder Volume = πr^2h
• Cone CSA = πrl
• Cone Volume = (1/3)πr^2h
• Sphere Surface Area = 4πr^2
• Sphere Volume = (4/3)πr^3

Coordinate Geometry

• Distance = √((x2-x1)^2 + (y2-y1)^2)
• Midpoint = ((x1+x2)/2, (y1+y2)/2)

Trigonometry

• sin θ = Opp/Hyp
• cos θ = Adj/Hyp
• tan θ = Opp/Adj
• tan θ = sin θ / cos θ
• sin^2 θ + cos^2 θ = 1

Statistics

• Mean = Sum / Number of values
• Median = Middle value
• Mode = Most frequent value

Probability

• Probability = Favorable outcomes / Total outcomes

Useful Values

• π ≈ 3.14 or 22/7
• √2 ≈ 1.414
• √3 ≈ 1.732

It includes:

• Basic arithmetic
• Fractions, decimals, percentages
• Profit & loss, SI & CI
• Algebra identities & equations
• Geometry formulas
• Mensuration formulas
• Coordinate geometry
• Trigonometry
• Statistics & probability

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