Math Formulas for Class 6–10 — Free Searchable Reference

(a + b)² Identity

Gr 7–10Algebra

(a + b)² = a² + 2ab + b²

Square of sum of two terms. Multiply out (a+b)(a+b) to get three terms.

இரண்டு உறுப்புகளின் கூட்டலின் வர்க்கம்.

(a − b)² Identity

Gr 7–10Algebra

(a − b)² = a² − 2ab + b²

Square of difference of two terms.

இரண்டு உறுப்புகளின் கழித்தலின் வர்க்கம்.

Difference of Squares

Gr 8–10Algebra

(a + b)(a − b) = a² − b²

Product of sum and difference equals difference of squares. Very useful for mental multiplication.

கூட்டல் மற்றும் கழித்தலின் பெருக்கம், வர்க்கங்களின் வித்தியாசத்திற்கு சமம்.

(a + b)³ Identity

Gr 9–10Algebra

(a + b)³ = a³ + 3a²b + 3ab² + b³

Cube of sum. Expand by multiplying (a+b)² × (a+b).

(a − b)³ Identity

Gr 9–10Algebra

(a − b)³ = a³ − 3a²b + 3ab² − b³

Cube of difference.

Sum of Cubes

Gr 9–10Algebra

a³ + b³ = (a + b)(a² − ab + b²)

Factorisation formula for sum of two cubes.

Difference of Cubes

Gr 9–10Algebra

a³ − b³ = (a − b)(a² + ab + b²)

Factorisation formula for difference of two cubes.

Quadratic Formula

Gr 9–10Algebra

x = (−b ± √(b² − 4ac)) / 2a

Solves any quadratic equation ax² + bx + c = 0. The expression b² − 4ac is called the discriminant.

ax² + bx + c = 0 என்ற எந்த இருபடி சமன்பாட்டையும் தீர்க்கும் சூத்திரம்.

Sum & Product of Roots

Gr 9–10Algebra

α + β = −b/a | αβ = c/a

For ax² + bx + c = 0 with roots α and β: their sum is −b/a and product is c/a.

Area of Triangle

Gr 6–10Geometry

Area = ½ × base × height

Half of base times perpendicular height. Works for any triangle.

அடி × உயரம் ÷ 2. எந்த முக்கோணத்திற்கும் செல்லும்.

Heron's Formula

Gr 9–10Geometry

A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2

Finds triangle area using only the three side lengths. s is the semi-perimeter.

மூன்று பக்க அளவுகளை மட்டும் பயன்படுத்தி முக்கோண பரப்பை கண்டறிய.

Pythagorean Theorem

Gr 7–10Geometry

a² + b² = c²

In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

செங்கோண முக்கோணத்தில், கர்ணத்தின் வர்க்கம் = மற்ற இரு பக்கங்களின் வர்க்கங்களின் கூட்டல்.

Area of Circle

Gr 6–10Geometry

A = πr²

Area of a circle where r is the radius and π ≈ 3.14159.

r ஆரம், π ≈ 3.14. வட்டத்தின் உள்ளே உள்ள பரப்பு.

Circumference of Circle

Gr 6–10Geometry

C = 2πr = πd

The perimeter of a circle. d is the diameter (d = 2r).

வட்டத்தின் சுற்றளவு. d = விட்டம் = 2r.

Area of Rectangle

Gr 6–8Geometry

Area = length × width

Perimeter = 2(l + w)

Area is length times width. Perimeter is the total distance around.

Area of Parallelogram

Gr 7–9Geometry

Area = base × height

Same as rectangle — base times perpendicular height (not the slant side).

Area of Trapezium

Gr 8–10Geometry

Area = ½ × (a + b) × h

a and b are the parallel sides, h is the perpendicular height between them.

Interior Angles of Polygon

Gr 7–10Geometry

Sum = (n − 2) × 180°

Each interior angle (regular) = (n−2)×180° / n

n is the number of sides. A triangle (n=3) → 180°. A quadrilateral (n=4) → 360°.

Cube

Gr 7–9Mensuration

Volume = a³ | Surface Area = 6a²

a is the side length. All faces are equal squares.

a = பக்க நீளம். அனைத்து முகங்களும் சம சதுரங்கள்.

Cuboid (Rectangular Prism)

Gr 7–9Mensuration

Volume = l × w × h | SA = 2(lw + lh + wh)

l = length, w = width, h = height.

Cylinder

Gr 8–10Mensuration

Volume = πr²h | Lateral SA = 2πrh | Total SA = 2πr(r + h)

r = radius of circular base, h = height.

Cone

Gr 9–10Mensuration

Volume = ⅓πr²h | Slant l = √(r² + h²) | Lateral SA = πrl

r = base radius, h = vertical height, l = slant height.

Sphere

Gr 9–10Mensuration

Volume = (4/3)πr³ | Surface Area = 4πr²

r = radius of the sphere.

Hemisphere

Gr 9–10Mensuration

Volume = (2/3)πr³ | Curved SA = 2πr² | Total SA = 3πr²

Half of a sphere. Total SA includes the flat circular base.

Percentage

Gr 6–10Arithmetic

P% of X = (P ÷ 100) × X

% = (Part ÷ Whole) × 100

Find any percentage of a number, or convert a fraction into a percentage.

ஒரு எண்ணின் சதவீதம் கண்டறிய, அல்லது பின்னத்தை சதவீதமாக மாற்ற.

Profit & Loss

Gr 7–9Arithmetic

Profit = SP − CP | Profit% = (Profit ÷ CP) × 100

Loss = CP − SP | Loss% = (Loss ÷ CP) × 100

CP = Cost Price, SP = Selling Price. Percentage is always over CP.

Simple Interest

Gr 7–9Arithmetic

SI = (P × R × T) / 100

Amount A = P + SI

P = Principal, R = Rate (% per year), T = Time (years).

P = அசல், R = வட்டி விகிதம் (%), T = காலம் (ஆண்டு).

Compound Interest

Gr 8–10Arithmetic

A = P(1 + R/100)ⁿ | CI = A − P

P = Principal, R = Rate %, n = number of periods. Interest earns interest.

Ratio & Proportion

Gr 6–9Arithmetic

a : b = c : d ⟺ ad = bc

Unitary method: find unit value first, then scale

If a/b = c/d, cross multiplication gives ad = bc (product of extremes = product of means).

Speed, Distance, Time

Gr 7–9Arithmetic

Speed = Distance ÷ Time

Distance = Speed × Time | Time = Distance ÷ Speed

The DST triangle: cover the unknown to get the formula for it.

Average (Mean)

Gr 6–9Arithmetic

Average = Sum of all values ÷ Number of values

Divide the total by how many items there are.

LCM & HCF Relationship

Gr 6–8Arithmetic

LCM × HCF = Product of the two numbers

For any two numbers a and b: LCM(a,b) × HCF(a,b) = a × b.

Basic Trig Ratios

Gr 9–10Trigonometry

sin θ = Opp/Hyp | cos θ = Adj/Hyp | tan θ = Opp/Adj

SOH–CAH–TOA. In a right-angled triangle relative to angle θ.

செங்கோண முக்கோணத்தில் θ கோணத்தை பொருத்த விகிதங்கள்.

Pythagorean Identity

Gr 10Trigonometry

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ | 1 + cot²θ = cosec²θ

Fundamental identity linking sin and cos. Follows directly from Pythagoras.

Standard Angle Values

Gr 9–10Trigonometry

sin 0°=0, 30°=½, 45°=1/√2, 60°=√3/2, 90°=1

cos 0°=1, 30°=√3/2, 45°=1/√2, 60°=½, 90°=0

Memorise these values — they appear in almost every trig problem. tan 45°=1, tan 60°=√3.

tan in terms of sin & cos

Gr 9–10Trigonometry

tan θ = sin θ / cos θ

Tangent can always be written as sine divided by cosine.

Mean (Arithmetic Average)

Gr 7–10Statistics

x̄ = (Σxᵢ) / n

Sum all values and divide by the count n. x̄ (x-bar) denotes the mean.

Median

Gr 7–10Statistics

Odd n: middle value | Even n: average of two middle values

Sort the data first. The middle value (or average of two middle values) is the median.

Mode

Gr 7–9Statistics

Mode = most frequently occurring value

The value that appears most often. A dataset can have more than one mode.

Range

Gr 6–9Statistics

Range = Maximum − Minimum

Measures the spread of data. Larger range = more spread out.

Mean of Grouped Data

Gr 9–10Statistics

x̄ = Σ(fᵢ × xᵢ) / Σfᵢ

fᵢ = frequency of each class, xᵢ = midpoint of each class interval.

Math Formula Explorer

(a + b)² Identity

(a − b)² Identity

Difference of Squares

(a + b)³ Identity

(a − b)³ Identity

Sum of Cubes

Difference of Cubes

Quadratic Formula

Sum & Product of Roots

Area of Triangle

Heron's Formula

Pythagorean Theorem

Area of Circle

Circumference of Circle

Area of Rectangle

Area of Parallelogram

Area of Trapezium

Interior Angles of Polygon

Cube

Cuboid (Rectangular Prism)

Cylinder

Cone

Sphere

Hemisphere

Percentage

Profit & Loss

Simple Interest

Compound Interest

Ratio & Proportion

Speed, Distance, Time

Average (Mean)

LCM & HCF Relationship

Basic Trig Ratios

Pythagorean Identity

Standard Angle Values

tan in terms of sin & cos

Mean (Arithmetic Average)

Median

Mode

Range

Mean of Grouped Data

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