NCERT Formula Library

Formula Library

Real NCERT formulas linked directly to their chapter — every entry opens the same verified page students see while learning that chapter.

Mathematics

272 formulas

1 week = 7 days

Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday

Months in a Year

1 year = 12 months = 365 days (or 366 in a leap year)

January to December

Numbers from Ten to Twenty

10 + ones digit = teen number

Numbers 11-19 are called "teen" numbers

Numbers from Ten to Twenty

Any 2-digit number = (tens × 10) + ones

13 = (1×10) + 3 = 10+3 = 13

Whole - Part = Remaining Part

You cannot subtract a bigger number from a smaller number in Class 1

Subtraction Fact

If a + b = c, then c - b = a

Since 3+4=7, we know 7-4=3 and 7-3=4

Numbers from One to Nine

Count each object once and only once

Always count from left to right or top to bottom to avoid missing any

Part + Part = Whole

The order does not matter: 3+4 = 4+3 = 7

Any number + 0 = that number

Zero is the identity for addition

Change Calculation

Change = Amount Given - Cost

Cost ₹7, gave ₹10, change = ₹10 - ₹7 = ₹3

Paise to Rupees

100 paise = ₹1

250 paise = ₹2 and 50 paise

Euclid Division Lemma

a = bq + r, 0 ≤ r < b

Used repeatedly to find HCF.

HCF-LCM Relationship

HCF(a, b) × LCM(a, b) = a × b

For 12 and 18: 6 × 36 = 12 × 18 = 216

Terminating Decimal Test

If q = 2^m × 5^n in lowest form, then p/q terminates

3/40 terminates because 40 = 2^3 × 5

For x² - 5x + 6, sum of zeroes = 5

Product of Zeroes

For x² - 5x + 6, product of zeroes = 6

α + β + γ = -b/a

For ax³ + bx² + cx + d, sum of zeroes depends on coefficient of x²

Pair of Linear Equations in Two Variables

Unique Solution Condition

a₁/a₂ ≠ b₁/b₂

If ratios of x and y coefficients differ, the lines intersect once

Pair of Linear Equations in Two Variables

Infinite Solutions Condition

a₁/a₂ = b₁/b₂ = c₁/c₂

Both equations represent the same line

Pair of Linear Equations in Two Variables

No Solution Condition

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Both lines are parallel and distinct

Quadratic Equations

ax² + bx + c = 0, a ≠ 0

2x² - 7x + 3 = 0 is in standard form

Quadratic Equations

Quadratic Formula

x = [-b ± √(b² - 4ac)] / 2a

For x² - 5x + 6 = 0, roots are 2 and 3

Quadratic Equations

For x² + 2x + 1, D = 0 so the roots are equal

Arithmetic Progressions

aₙ = a + (n - 1)d

If a = 3 and d = 4, then a₅ = 3 + 4×4 = 19

Arithmetic Progressions

Sum of First n Terms

Sₙ = n/2 [2a + (n - 1)d]

For a = 2, d = 3, n = 4: S₄ = 4/2[4 + 9] = 26

Arithmetic Progressions

Sum Using Last Term

Sₙ = n/2 (a + l)

If first term is 5, last term is 25 and n = 5, sum = 75

Area Ratio of Similar Triangles

Ar(ΔABC) / Ar(ΔPQR) = (AB / PQ)²

If corresponding sides are in ratio 2:3, areas are in ratio 4:9

Pythagoras Theorem

a² + b² = c²

For sides 3, 4, 5: 3² + 4² = 5²

Basic Proportionality Idea

If a line is parallel to one side of a triangle, it divides the other two sides proportionally

Useful in many textbook proofs

Coordinate Geometry

Distance Formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance between (1,2) and (4,6) is 5

Coordinate Geometry

Midpoint Formula

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Midpoint of (2,4) and (6,8) is (4,6)

Coordinate Geometry

Internal Section Formula

P = ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n))

Used when one point divides a segment in m:n

Introduction to Trigonometry

sin θ = P/H, cos θ = B/H, tan θ = P/B

In a 3-4-5 triangle with angle opposite 3, sin θ = 3/5

Introduction to Trigonometry

sin²θ + cos²θ = 1

If sin θ = 3/5, then cos θ = 4/5

Introduction to Trigonometry

Derived Identity

1 + tan²θ = sec²θ

If tan θ = 3/4, then sec²θ = 25/16

Some Applications of Trigonometry

Angle of Elevation Model

tan θ = height / horizontal distance

If θ = 45° and distance = 20 m, height = 20 m

Some Applications of Trigonometry

Angle of Depression Link

Angle of depression from the top equals the corresponding angle of elevation from below

This equality helps convert many observation problems

Radius-Tangent Property

Radius at the point of contact ⟂ tangent

If PT is tangent at T and OT is radius, then OT ⟂ PT

Equal Tangent Lengths

If tangents from P touch the circle at A and B, then PA = PB

Areas Related to Circles

If r = 7 cm, area = 49π cm²

Areas Related to Circles

If r = 7 cm, circumference = 14π cm

Areas Related to Circles

Area = (θ/360) × πr²

If θ = 90° and r = 14 cm, area = 49π cm²

Surface Areas and Volumes

Volume of Cylinder

For r = 3 cm, h = 10 cm, volume = 90π cm³

Surface Areas and Volumes

Volume of Sphere

For r = 3 cm, volume = 36π cm³

Surface Areas and Volumes

TSA of Cylinder

TSA = 2πr(h + r)

For r = 2 cm and h = 5 cm, TSA = 28π cm²

Mean = Σfx / Σf

Multiply each class mark by frequency and divide by total frequency

Mode = l + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h

Use the modal class and neighbouring frequencies

Median = l + [(N/2 - cf) / f] × h

Find the median class using cumulative frequency first

Basic Probability

P(E) = n(E) / n(S)

If 3 outcomes are favourable out of 8 total, probability = 3/8

Complement Rule

P(E) + P(not E) = 1

If P(E) = 0.35, then P(not E) = 0.65

Binomial Theorem

(a+b)ⁿ = Σ ⁿCr aⁿ⁻ʳ bʳ

(a+b)ⁿ = Σ ⁿCr aⁿ⁻ʳ bʳ

Complex Numbers and Quadratic Equations

Complex Numbers and Quadratic Equations

|z| = √(a²+b²)

|z| = √(a²+b²)

Complex Numbers and Quadratic Equations

Quadratic formula

Quadratic formula

Circle: x²+y²=r²

Circle: x²+y²=r²

Parabola: y²=4ax

Parabola: y²=4ax

Ellipse: x²/a²+y²/b²=1

Ellipse: x²/a²+y²/b²=1

Limits and Derivatives

d/dx(xⁿ) = nxⁿ⁻¹

d/dx(xⁿ) = nxⁿ⁻¹

Limits and Derivatives

d/dx(sin x) = cos x

d/dx(sin x) = cos x

Limits and Derivatives

d/dx(eˣ) = eˣ

d/dx(eˣ) = eˣ

Permutations and Combinations

ⁿPr = n!/(n-r)!

ⁿPr = n!/(n-r)!

Permutations and Combinations

ⁿCr = n!/r!(n-r)!

ⁿCr = n!/r!(n-r)!

Sequences and Series

Sum of AP = n/2(2a+(n-1)d)

Sum of AP = n/2(2a+(n-1)d)

Sequences and Series

Sum of GP = a(rⁿ-1)/(r-1)

Sum of GP = a(rⁿ-1)/(r-1)

Trigonometric Functions

Fundamental Identity

sin²θ + cos²θ = 1

Most important — used in almost every problem

Trigonometric Functions

sin(A+B) = sinAcosB + cosAsinB cos(A+B) = cosAcosB - sinAsinB

sin75° = sin(45°+30°) = (1/√2)(√3/2)+(1/√2)(1/2) = (√3+1)/(2√2)

Trigonometric Functions

sin2A = 2sinAcosA cos2A = cos²A - sin²A = 1-2sin²A

sin60°=sin(2×30°)=2×sin30°×cos30°=2×(1/2)×(√3/2)=√3/2 ✓

Trigonometric Functions

2sinAcosB = sin(A+B) + sin(A-B)

2sin75°cos15° = sin90°+sin60° = 1+√3/2

Application of Derivatives

Slope of Tangent

m = dy/dx|_(x₁,y₁) = f'(x₁)

y=x³-2x at (1,-1): m=3x²-2|_{x=1}=3-2=1. Tangent: y+1=1(x-1)→y=x-2

Application of Derivatives

Equation of Normal

y - y₁ = (-1/m)(x - x₁) where m = f'(x₁)

At (1,-1) with m=1: Normal: y+1=-1(x-1)→y=-x

Application of Derivatives

2nd Derivative Test

f'(x₀)=0 AND f''(x₀)<0 → local max | f''(x₀)>0 → local min

f(x)=x²-4x+3: f'=2x-4=0→x=2. f''=2>0 → local min at x=2, f(2)=-1

Application of Derivatives

Use chain rule: dV/dt = dV/dr × dr/dt

Sphere: V=4πr³/3 → dV/dt=4πr²×dr/dt. Given dr/dt=2cm/s at r=5: dV/dt=4π×25×2=200π cm³/s

|A| = a(ei-fh) - b(di-fg) + c(dh-eg)

|A| = a(ei-fh) - b(di-fg) + c(dh-eg)

A⁻¹ = adj(A)/|A|

A⁻¹ = adj(A)/|A|

Differential Equations

dy/dx = f(x)g(y)

dy/dx = f(x)g(y)

Differential Equations

∫xⁿdx = xⁿ⁺¹/(n+1)

∫xⁿdx = xⁿ⁺¹/(n+1)

∫sin x dx = -cos x

∫sin x dx = -cos x

Inverse Trigonometric Functions

sin⁻¹(-x) = -sin⁻¹x

sin⁻¹(-x) = -sin⁻¹x

Inverse Trigonometric Functions

sin⁻¹x + cos⁻¹x = π/2

sin⁻¹x + cos⁻¹x = π/2

Conditional Probability

P(A|B) = P(A∩B) / P(B)

P(A∩B)=0.12, P(B)=0.4: P(A|B)=0.12/0.4=0.3

P(Aᵢ|B) = P(Aᵢ)P(B|Aᵢ) / Σ P(Aⱼ)P(B|Aⱼ)

Classic problem: factory machines producing defective items

Binomial Distribution

P(X=r) = ⁿCᵣ pʳ qⁿ⁻ʳ | Mean=np | Variance=npq

Coin tossed 5 times: P(3 heads)=⁵C₃×(1/2)³×(1/2)²=10/32=5/16

Total Probability

P(B) = Σᵢ P(B|Aᵢ)×P(Aᵢ)

Used when event B can happen via multiple paths A₁, A₂, A₃...

Three Dimensional Geometry

l²+m²+n² = 1

l²+m²+n² = 1

Three Dimensional Geometry

Distance of point from plane

Distance of point from plane

a·b = |a||b|cosθ

a·b = |a||b|cosθ

|a×b| = |a||b|sinθ

|a×b| = |a||b|sinθ

Counting in Groups

Multiplication as Repeated Addition

a × b = a + a + a... (b times)

Or: 3×5 = 3+3+3+3+3 = 15 (three added five times). Both give 15!

Counting in Groups

Commutative Property

a × b = b × a

4 × 6 = 6 × 4 = 24

What is Long, What is Round?

Shape Properties Summary

Cube: 6 faces, 12 edges, 8 vertices | Cuboid: 6 faces, 12 edges, 8 vertices | Cone: 2 faces, 1 edge, 1 vertex | Cylinder: 3 faces, 2 edges, 0 vertices

A die is a cube — count: 6 faces (each face has numbers 1-6), 12 edges, 8 corners

1 litre (L) = 1000 millilitres (mL)

Large amounts use kilolitres (kL): 1 kL = 1000 L

Counting in Tens

2-digit number = Tens digit × 10 + Ones digit × 1

This is called expanded notation

Counting in Tens

Place value = Face value × Position value

In 73: place value of 7 = 7×10 = 70; place value of 3 = 3×1 = 3

Tens and Hundreds

Expanded Form (3-digit)

3-digit number = H×100 + T×10 + O×1

H=hundreds digit, T=tens digit, O=ones digit

Tens and Hundreds

10 tens = 1 hundred

10 groups of 10 = 100

How Much Can You Carry?

Standard Weight Units

kg = kilogram, g = gram

Column Subtraction

Subtract ones first, then tens (borrow if top < bottom)

54-28: ones=4<8 so borrow; 14-8=6; tens=(5-1)-2=2; answer=26

Checking Subtraction

Answer + Subtracted number = Original number

54-28=26; check: 26+28=54 ✓

Column Addition

Add ones first, then tens (carry if sum ≥ 10)

47+35: ones=7+5=12(write 2,carry 1); tens=4+3+1=8; answer=82

Unit Conversion

km = kilometre: 1 km = 1000 m (for long distances like roads)

Unit conversion

10 mm = 1 cm | 100 cm = 1 m | 1000 m = 1 km

Convert from larger to smaller unit: multiply. Smaller to larger: divide.

Perimeter of Rectangle

P = 2 × (length + breadth)

Rectangle 8 cm × 5 cm: P = 2×(8+5) = 2×13 = 26 cm

Perimeter of Square

Square side = 7 cm: P = 4×7 = 28 cm

Fun with Numbers

Expanded Form (4-digit)

Th×1000 + H×100 + T×10 + O×1

Th=thousands, H=hundreds, T=tens, O=ones

Column Addition

Add ones first, then tens, then hundreds

Carry means a group of 10 is moved to the next higher place value

Column Subtraction

Subtract ones first, then tens, then hundreds

503 - 248 = 255 (3<8: borrow; 13-8=5; 0-1-4: borrow; 10-5=5; 5-1-2=2)

Who is Heavier?

Scientific unit of mass is kilogram (kg)

How Many Times?

a × b = a added b times

Also: 6×4 = 4×6 = 24 (commutative)

How Many Times?

Any number × 0 = 0

How Many Times?

Any number × 1 = that number

Time Conversion

60 seconds = 1 minute | 60 minutes = 1 hour | 24 hours = 1 day | 7 days = 1 week | 52 weeks = 1 year

2 hours = 2×60 = 120 minutes | 3 days = 3×24 = 72 hours

Dividend ÷ Divisor = Quotient

24 ÷ 6 = 4 (24 is dividend, 6 is divisor, 4 is quotient)

Division-Multiplication Relationship

If a ÷ b = c, then b × c = a

If 15 ÷ 3 = 5, then 3 × 5 = 15

Any number ÷ 1 = same number

Fields and Fences

Perimeter of Rectangle

P = 2 × (l + b)

l=length, b=breadth

Fields and Fences

Perimeter of Square

Fields and Fences

Area of Rectangle

Rectangle 8m × 5m: A = 8×5 = 40 sq m

Fields and Fences

A = s × s = s²

Square with side 6cm: A = 6×6 = 36 sq cm

Building with Bricks

Multiplicand × Multiplier = Product

23 × 14 = 322 (23 is multiplicand, 14 is multiplier, 322 is product)

Building with Bricks

Multiply by Powers of 10

N × 10 = N with one extra 0 | N × 100 = N with two extra 0s

56 × 1000 = 56,000

Halves and Quarters

Fraction = Numerator / Denominator

In 3/8: numerator=3, denominator=8, meaning 3 parts out of 8 equal parts

Halves and Quarters

Finding Fraction of a Number

p/q of N = N ÷ q × p

3/4 of 20 = 20÷4×3 = 5×3 = 15

24-hour conversion

PM time (except noon): 24-hr = 12-hr + 12

3:00 PM = 3+12 = 15:00 | 8:30 PM = 8:30+12 = 20:30

Time difference

End time - Start time = Duration

15:45 - 11:20 = 4 h 25 min

A Trip to Bhopal

Actual distance = Map distance × Scale factor

Map distance 5 cm, scale 1 cm = 50 km → Actual = 5×50 = 250 km

Shapes and Angles

Angle Sum of Triangle

∠A + ∠B + ∠C = 180°

If two angles are 60° and 70°, third angle = 180-60-70 = 50°

Shapes and Angles

Angle Sum of Quadrilateral

Sum of all 4 angles = 360°

If three angles are 90°, 90°, 80°, fourth angle = 360-260 = 100°

Shapes and Angles

Area of Rectangle

Area = length × breadth

Room 5m × 4m: Area = 5×4 = 20 m²

Shapes and Angles

Area = side × side = side²

Square with side 6 cm: Area = 6² = 36 cm²

How Many Squares?

Area of Rectangle

Area unit is always "squared" (cm², m², km²)

How Many Squares?

7 cm × 7 cm = 49 cm²

Parts and Wholes

Equivalent Fractions

a/b = (a×n)/(b×n) for any non-zero n

3/4 = 6/8 = 9/12 (multiply by 2, then 3)

Parts and Wholes

Adding Fractions (same denom)

a/c + b/c = (a+b)/c

3/7 + 2/7 = 5/7

Parts and Wholes

Adding Fractions (different denom)

a/b + c/d = (a×d + c×b)/(b×d)

1/3 + 1/4 = (4+3)/12 = 7/12

Indian Number System

1 crore = 100 lakh | 1 lakh = 100 thousand | 1 thousand = 10 hundred

2,75,48,923 = 2 crore 75 lakh 48 thousand 9 hundred 23

If digit to the right is ≥ 5: round up | < 5: round down

Round 7,349 to nearest hundred: look at tens digit (4 < 5) → 7,300

Be My Multiple, I'll be Your Factor

HCF × LCM Relationship

HCF × LCM = Product of two numbers

For 12 and 18: HCF=6, LCM=36. Check: 6×36 = 216 = 12×18 ✓

Be My Multiple, I'll be Your Factor

Finding HCF (Division Method)

Divide larger by smaller; replace larger with remainder; repeat till remainder = 0

HCF(18,12): 18÷12=1 R6; 12÷6=2 R0; HCF=6

Can You See the Pattern?

F(n) = F(n-1) + F(n-2)

Starting values: F(1)=1, F(2)=1

Can You See the Pattern?

Magic Sum Formula

Magic sum of n×n square using 1 to n² = n(n²+1)/2

3×3 square: 3×(9+1)/2 = 3×5 = 15

Mapping Your Way

Speed-Distance-Time Triangle

S = D/T | D = S×T | T = D/S

Speed = 60 km/h, Time = 2.5 h → Distance = 60×2.5 = 150 km

Boxes and Sketches

Volume of Cuboid

V = l × b × h

4 cm × 3 cm × 5 cm = 60 cm³

Boxes and Sketches

6 cm cube: V = 6³ = 216 cm³

Boxes and Sketches

Surface Area of Cube

5 cm cube: SA = 6×25 = 150 cm²

Tenths and Hundredths

Decimal to Fraction

Move denominator as power of 10 based on decimal places

0.7 = 7/10; 0.45 = 45/100; 0.125 = 125/1000

Tenths and Hundredths

Comparing Decimals

Compare whole part first; if equal compare tenth; if equal compare hundredth

3.45 vs 3.52: whole equal; tenths 4<5; so 3.45 < 3.52

Area and its Boundary

Area of Rectangle

l=length, b=breadth

Area and its Boundary

Area and its Boundary

Perimeter of Rectangle

l=12cm, b=7cm: P=2×(12+7)=2×19=38 cm

Knowing Our Numbers

Place Value = Face Value × Position Value

Position values: 1, 10, 100, 1000...

Knowing Our Numbers

Estimation (nearest 10)

If units ≥ 5: add 10, units=0. If units < 5: units=0

67 → 70, 54 → 50, 85 → 90

Knowing Our Numbers

Large Number Formula

1 crore = 100 lakhs = 10 million

2.5 crore = 25 million = 25,000,000

Playing with Numbers

HCF × LCM Relation

HCF(a,b) × LCM(a,b) = a × b

HCF(4,6)=2, LCM(4,6)=12. Check: 2×12=24=4×6 ✓

Playing with Numbers

Divisibility by 3

Sum of all digits divisible by 3

783: 7+8+3=18, 18÷3=6. So 783 is divisible by 3 ✓

Playing with Numbers

Divisibility by 9

Sum of all digits divisible by 9

5832: 5+8+3+2=18, 18÷9=2. So 5832 divisible by 9 ✓

Commutative Property

a + b = b + a | a × b = b × a

7+3=3+7=10, 4×6=6×4=24

Associative Property

(a+b)+c = a+(b+c) | (a×b)×c = a×(b×c)

(2+3)+4 = 2+(3+4) = 9

Distributive Property

a × (b + c) = a×b + a×c

Most useful property for mental math

Understanding Elementary Shapes

Complementary Angles

a + b = 90° (they complement each other)

Complement of 35° = 90-35 = 55°

Understanding Elementary Shapes

Supplementary Angles

a + b = 180° (they supplement each other)

Supplement of 110° = 180-110 = 70°

Understanding Elementary Shapes

Euler's Formula for 3D shapes

Faces + Vertices - Edges = 2

Cube: 6+8-12=2 ✓, Tetrahedron: 4+4-6=2 ✓

Basic Geometrical Ideas

Sum of angles in triangle

∠A + ∠B + ∠C = 180°

If two angles are 60° and 70°, third angle = 180-60-70 = 50°

Basic Geometrical Ideas

Sum of angles in quadrilateral

∠A + ∠B + ∠C + ∠D = 360°

If three angles are 90°, 90°, 100°: fourth = 360-280 = 80°

Basic Geometrical Ideas

Diameter and Radius

d = 2r | r = d/2

r=5cm → d=10cm. d=14cm → r=7cm

Matchstick Pattern (triangles)

n triangles require (2n+1) matchsticks

4 triangles: 2×4+1 = 9 matchsticks

Perimeter using variable

Square with side l: Perimeter = 4l

l=5cm: P=4×5=20cm. l=x cm: P=4x cm

Decimal Place Values

...Hundreds | Tens | Ones . Tenths | Hundredths | Thousandths...

5.374: 5 = ones, 3 = tenths, 7 = hundredths, 4 = thousandths

Fraction to Decimal

Divide numerator by denominator

3/4 = 3÷4 = 0.75. 1/8 = 0.125. 1/3 = 0.333...

Money Conversion

₹1 = 100 paise. So ₹p.q means p rupees q paise

₹7.05 = 7 rupees 5 paise = 705 paise

Additive Inverse

a + (-a) = 0, so additive inverse of a is -a

Additive inverse of 7 is -7. Of -12 is 12. Of 0 is 0.

Integer Subtraction

a - b = a + (-b)

5 - (-3) = 5 + 3 = 8. (-4) - (-7) = (-4) + 7 = 3

Sign Rules for Addition

+×+ = +, -×- = +, +×- = -, -×+ = -

(+7)×(+3)=+21, (-7)×(-3)=+21, (+7)×(-3)=-21

Mean = Sum of all values / Number of values

Data: 12, 18, 15, 20, 10. Sum=75, n=5. Mean=75/5=15

Every 5th mark crosses previous 4 (like a gate)

HH HH HH | = 11 items

Equivalent Fractions

a/b = (a×n)/(b×n) for any n≠0

2/3 = 4/6 = 6/9 = 10/15

Converting Mixed to Improper

a(b/c) = (a×c + b)/c

2¾ = (2×4+3)/4 = 11/4

Adding Fractions (different denom)

a/b + c/d = (ad+bc)/bd

1/3 + 1/4 = (4+3)/12 = 7/12

Perimeter of Rectangle

l=length, b=breadth

Perimeter of Square

Area of Rectangle

l=8cm, b=5cm → A=8×5=40 cm²

A = s × s = s²

Side=7cm → A=7²=49 cm²

Ratio and Proportion

Ratio in simplest form

a:b = a/HCF(a,b) : b/HCF(a,b)

24:36 → HCF=12 → 2:3

Ratio and Proportion

Proportion Test

a:b::c:d if and only if a×d = b×c

3:4::6:8 → 3×8=24, 4×6=24 ✓ In proportion

Lines of symmetry

Regular polygon with n sides has n lines of symmetry

Equilateral triangle (n=3): 3 lines. Square (n=4): 4 lines. Regular hexagon (n=6): 6 lines

Lines and Angles

Complementary angles: a + b = 90°

Complementary angles: a + b = 90°

Lines and Angles

Supplementary angles: a + b = 180°

Supplementary angles: a + b = 180°

Lines and Angles

Vertically opposite angles are equal

Vertically opposite angles are equal

Exponents and Powers

aᵐ × aⁿ = aᵐ⁺ⁿ

aᵐ × aⁿ = aᵐ⁺ⁿ

Exponents and Powers

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

aᵐ ÷ aⁿ = aᵐ⁻ⁿ

Exponents and Powers

(aᵐ)ⁿ = aᵐⁿ

(aᵐ)ⁿ = aᵐⁿ

Exponents and Powers

(+)×(+)=+, (−)×(−)=+, (+)×(−)=−, (−)×(+)=-

(−5)×(+3)=−15, (−4)×(−7)=+28

|a| = a if a≥0, |a| = −a if a<0

|−8|=8, |+6|=6, |0|=0

Mean = Sum of all observations / Total number

Data: 4,7,8,9,2. Sum=30, n=5. Mean=6

P(event) = Number of favourable outcomes / Total outcomes

P(head) = 1/2. P(ace from deck) = 4/52 = 1/13

Perimeter and Area

Area of Triangle

A = ½ × b × h

h is perpendicular height, not slant

Perimeter and Area

Area of Parallelogram

b=8cm, h=5cm: A = 8×5 = 40 cm²

Perimeter and Area

Circumference of Circle

r=7cm: C = 2×22/7×7 = 44 cm

Perimeter and Area

r=7cm: A = 22/7×49 = 154 cm²

Perimeter and Area

Area of Semi-circle

r=7: A = 154/2 = 77 cm²

Fractions and Decimals

Fraction multiplication

a/b × c/d = ac/bd

2/3 × 3/4 = 6/12 = 1/2

Fractions and Decimals

Fraction division (reciprocal)

a/b ÷ c/d = a/b × d/c

2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Simple Equations

Linear Equation

ax + b = c → x = (c - b) / a

Simple Equations

Transposition Rule

If ax + b = c, then ax = c - b (b moves to RHS with -ve sign)

2x + 7 = 15 → 2x = 15-7 = 8 → x = 4

Simple Equations

Substitute x back in original equation → LHS must equal RHS

x=5 in 3x+4=19: 3(5)+4=15+4=19 ✓

Triangles and Its Properties

Angle sum in triangle

∠A + ∠B + ∠C = 180°

Angles 50°, 70°: third = 180-120 = 60°

Triangles and Its Properties

Exterior angle theorem

Exterior angle = sum of opposite interior angles

Interior angles 65° and 75°: exterior angle = 65+75 = 140°

Triangles and Its Properties

Pythagoras theorem

c² = a² + b²

c is hypotenuse (opposite to right angle)

Comparing Quantities

x% of y = (x/100) × y

Very commonly used in daily life

Comparing Quantities

Profit% = (Profit / CP) × 100 = (SP-CP)/CP × 100

CP=₹200, SP=₹250: Profit=₹50, Profit%=50/200×100=25%

Comparing Quantities

Loss% = (Loss / CP) × 100

CP=₹500, SP=₹400: Loss=₹100, Loss%=20%

Comparing Quantities

Simple Interest

SI = P × R × T / 100

Amount = P + SI

Comparing Quantities

Find SP from Profit%

SP = CP × (100 + Profit%) / 100

CP=₹800, Profit%=25: SP=800×125/100=₹1000

Rational Numbers

a/b where b ≠ 0

a/b where b ≠ 0

Rational Numbers

Visualising Solid Shapes

Euler's formula: F + V - E = 2

Euler's formula: F + V - E = 2

P(E) = Favourable outcomes / Total outcomes

P(E) = Favourable outcomes / Total outcomes

Exponents and Powers

a⁻ⁿ = 1/aⁿ

a⁻ⁿ = 1/aⁿ

Exponents and Powers

aᵐ × aⁿ = aᵐ⁺ⁿ

aᵐ × aⁿ = aᵐ⁺ⁿ

Exponents and Powers

aᵐ/aⁿ = aᵐ⁻ⁿ

aᵐ/aⁿ = aᵐ⁻ⁿ

Exponents and Powers

(aᵐ)ⁿ = aᵐⁿ

(aᵐ)ⁿ = aᵐⁿ

Linear Equations in One Variable

Consecutive integers formula

n, n+1, n+2 (consecutive). n, n+2, n+4 (consecutive odd/even)

Sum of 4 consecutive integers = 4n+6. If =54: n=12, so 12,13,14,15

Rational Numbers

Standard Form of Rational Number

p/q where HCF(p,q)=1 and q>0

-6/4 in standard form: divide by HCF(6,4)=2 → -3/2

Rational Numbers

Multiplicative Inverse

Reciprocal of p/q = q/p

Reciprocal of 3/7 = 7/3. Reciprocal of -5/8 = -8/5

Comparing Quantities

SP = MP - Discount = MP × (100-Discount%)/100

MP=₹800, Disc=25%: SP=800×75/100=₹600

Comparing Quantities

GST Calculation

Amount paid = SP + (GST% × SP)/100 = SP×(100+GST%)/100

SP=₹2000, GST=18%: Amount=2000×118/100=₹2360

Comparing Quantities

Compound Interest

A = P(1 + R/100)ⁿ | CI = A - P

n = number of years (or periods)

Comparing Quantities

SI vs CI Difference

CI - SI = P(R/100)² (for 2 years)

P=₹5000, R=10%: CI-SI=5000×0.01=₹50

Area of Trapezium

A = ½ × (a + b) × h

a,b are parallel sides; h is perpendicular height

TSA = 2(lb + bh + lh)

l=5, b=3, h=4: TSA=2(15+12+20)=94 cm²

V = l × b × h

l=5, b=3, h=4: V=60 cm³

r=7, h=10: CSA=2×22/7×7×10=440 cm²

Cylinder Volume

1000 cm³ = 1 litre

a²-b² = (a+b)(a-b)

a²-b² = (a+b)(a-b)

a²+2ab+b² = (a+b)²

a²+2ab+b² = (a+b)²

Cubes and Cube Roots

Cube of a number

n³ = n × n × n

5³=125, 10³=1000, (-3)³=-27

Cubes and Cube Roots

∛n = m means m³ = n

∛125=5 because 5³=125. ∛(-125)=-5

Algebraic Expressions and Identities

(a+b)² Identity

(a+b)^2 = a^2 + 2ab + b^2

(x+5)² = x²+10x+25. (2+3)²=4+12+9=25=5² ✓

Algebraic Expressions and Identities

(a-b)² Identity

(a-b)^2 = a^2 - 2ab + b^2

(x-4)² = x²-8x+16

Algebraic Expressions and Identities

Difference of squares

(a+b)(a-b) = a^2 - b^2

(x+7)(x-7)=x²-49. 103×97=(100)²-3²=9991

Direct and Inverse Proportions

Direct: x/y = k (constant)

Direct: x/y = k (constant)

Direct and Inverse Proportions

Inverse: x × y = k

Inverse: x × y = k

Squares and Square Roots

√(a × b) = √a × √b

√(a × b) = √a × √b

Squares and Square Roots

(a+b)² = a²+2ab+b²

(a+b)² = a²+2ab+b²

Squares and Square Roots

(a-b)² = a²-2ab+b²

(a-b)² = a²-2ab+b²

Understanding Quadrilaterals

Sum of angles of quadrilateral = 360°

Sum of angles of quadrilateral = 360°

Understanding Quadrilaterals

Opposite angles of parallelogram are equal

Opposite angles of parallelogram are equal

Visualising Solid Shapes

Euler's formula: F + V - E = 2

Euler's formula: F + V - E = 2

Areas of Parallelograms and Triangles

Area = base × height

Area = base × height

Areas of Parallelograms and Triangles

Area of triangle = ½ × b × h

Area of triangle = ½ × b × h

Heron's Formula

Heron's Formula

Area = √[s(s-a)(s-b)(s-c)]

Area = √[s(s-a)(s-b)(s-c)]

Linear Equations in Two Variables

ax + by + c = 0

ax + by + c = 0

Lines and Angles

Angle sum = 180°

Angle sum = 180°

Lines and Angles

Vertically opposite angles are equal

Vertically opposite angles are equal

Rationalising Factor

Multiply by conjugate: (a+√b)(a-√b) = a²-b

Rationalise 1/(√2+1): multiply by (√2-1)/(√2-1) = (√2-1)/(2-1) = √2-1

Laws of Exponents

aᵐ × aⁿ = aᵐ⁺ⁿ | aᵐ/aⁿ = aᵐ⁻ⁿ | (aᵐ)ⁿ = aᵐⁿ

2³ × 2⁴ = 2⁷ = 128 | 3⁵/3² = 3³ = 27

a^(1/n) = ⁿ√a | a^(m/n) = ⁿ√(aᵐ)

8^(1/3) = ∛8 = 2 | 27^(2/3) = (∛27)² = 3² = 9

(a+b)² = a²+2ab+b² (a-b)² = a²-2ab+b² (a+b)(a-b) = a²-b²

(x+3)² = x²+6x+9 | (2x-5)(2x+5) = 4x²-25

Cubic Identities

(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)

(x+2)³ = x³+6x²+12x+8

Special: a³+b³+c³

If a+b+c=0, then a³+b³+c³ = 3abc

If x+y+z=0, then x³+y³+z³ = 3xyz

P(E) = n(favorable outcomes)/n(total outcomes)

P(E) = n(favorable outcomes)/n(total outcomes)

Mode = most frequent value

Mode = most frequent value

Surface Areas and Volumes

CSA=2πrh | TSA=2πr(r+h) | V=πr²h

π ≈ 22/7 ≈ 3.14159

Surface Areas and Volumes

l=√(r²+h²) | CSA=πrl | TSA=πr(r+l) | V=⅓πr²h

r=3, h=4: l=5, V=⅓×π×9×4≈37.7 cm³

Surface Areas and Volumes

SA=4πr² | V=4/3 πr³

r=6cm: SA=4π×36≈452.4 cm² | V=4/3×π×216≈904.8 cm³

Surface Areas and Volumes

CSA=2πr² | TSA=3πr² | V=2/3 πr³

r=7: TSA=3×22/7×49=462 cm²

Science

58 formulas

Acids, Bases and Salts

Acids, Bases and Salts

Acids, Bases and Salts

pH = 7 = neutral

pH = 7 = neutral

V = IR (V=voltage, I=current, R=resistance)

V=12V, R=4Ω: I=V/R=12/4=3A

Series Resistance

R_total = R₁ + R₂ + R₃

3Ω + 5Ω + 2Ω = 10Ω

Parallel Resistance

1/R_eq = 1/R₁ + 1/R₂ + 1/R₃

6Ω and 3Ω in parallel: 1/R=1/6+1/3=1/2 → R=2Ω

Electrical Power

P = VI = I²R = V²/R

I=2A, R=5Ω: P=I²R=4×5=20W

Electrical Energy

E = P × t = VIt

1000W heater for 2 hours: E=1000×7200=7,200,000 J = 2 kWh

Heating Effect (Joule)

I=3A, R=10Ω, t=60s: H=9×10×60=5400 J

Light — Reflection and Refraction

1/v + 1/u = 1/f

1/v + 1/u = 1/f

Light — Reflection and Refraction

Light — Reflection and Refraction

n = sin i/sin r

n = sin i/sin r

Light — Reflection and Refraction

P = 1/f (in metres)

P = 1/f (in metres)

Components of Food

Iodine Test for Starch

Food + Iodine solution → Blue-black colour = starch present

Rice: blue-black (starch present). Onion: no colour change (no starch)

Motion and Measurement of Distances

Unit Conversions

1 km = 1000 m = 100,000 cm = 10,00,000 mm

Your height 160cm = 1.6m = 0.0016km

Motion and Measurement of Distances

1 hour = 60 minutes = 3600 seconds

2.5 hours = 150 minutes = 9000 seconds

Getting to Know Plants

Photosynthesis Equation

CO₂ + H₂O + Sunlight → Glucose + O₂

Chlorophyll in leaves captures sunlight energy

Light, Shadows and Reflections

Law of Reflection

Angle of incidence = Angle of reflection

Light hits mirror at 40° → reflects at 40° (both measured from normal)

Temperature Conversion

F = (9/5)C + 32 | C = (F-32) × 5/9

Normal body temperature

Kelvin to Celsius

0°C = 273K (freezing of water). -273°C = 0K (absolute zero)

Acids, Bases and Salts

Acid + Base → Salt + Water

HCl + NaOH → NaCl + H₂O (table salt + water)

Acids, Bases and Salts

pH 0-6: acid (lower = stronger). pH 7: neutral. pH 8-14: base (higher = stronger)

Battery acid: pH 1. Lemon: pH 2. Blood: pH 7.4. Baking soda: pH 9. Drain cleaner: pH 14

Respiration in Organisms

Glucose + Oxygen → CO₂ + Water + Energy

Glucose + Oxygen → CO₂ + Water + Energy

Respiration in Organisms

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + Energy

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + Energy

Nutrition in Plants

Photosynthesis Equation

6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂

Occurs in chloroplasts of leaf cells

Physical and Chemical Changes

Rusting (simplified)

Iron + Oxygen + Water → Iron Oxide (rust)

4Fe + 3O₂ + 6H₂O → 4Fe(OH)₃ → Fe₂O₃ (rust)

Motion and Time

Speed = Distance / Time

Motion and Time

Unit Conversion

1 km/h = 5/18 m/s | 1 m/s = 18/5 km/h = 3.6 km/h

72 km/h = 72×5/18 = 20 m/s

Motion and Time

Pendulum Time Period

T = 2π√(L/g)

T depends only on length L, not mass

Motion and Time

Distance from Graph

Distance = Speed × Time = Area under speed-time graph

Speed=40m/s for 5s: Distance=40×5=200m

Microorganisms: Friend and Foe

Pasteurization Temperature

Milk heated to 70°C for 15 seconds OR 63°C for 30 minutes

Developed by Louis Pasteur in 1864

Metals and Non-metals

Reactivity Series (decreasing)

K > Na > Ca > Mg > Al > Zn > Fe > Pb > H > Cu > Ag > Au

More reactive metal displaces less reactive from solution

Law of Reflection

Angle of incidence (i) = Angle of reflection (r)

Light hits mirror at 35°: reflects at 35°

Speed and Refractive Index

n = c/v (refractive index = speed in vacuum / speed in medium)

Glass n≈1.5: light slows to c/1.5 = 2×10⁸ m/s

Combustion and Flame

Calorific value = Energy released per kg of fuel

Calorific value = Energy released per kg of fuel

Force and Pressure

Pressure = Force / Area

Pressure = Force / Area

Force and Pressure

Speed = Distance / Time (like all speed)

Speed varies with temperature and medium

Echo Minimum Distance

Minimum distance = (Speed of sound × 0.1s) / 2 = 17.15 m

Human ear cannot distinguish sounds less than 0.1s apart

Frequency and Pitch

Higher frequency → Higher pitch (shriller sound)

Whistle: ~3000 Hz (high pitch). Bass drum: ~50-100 Hz (low pitch)

Atoms and Molecules

Law of conservation of mass

Law of conservation of mass

Atoms and Molecules

Law of constant proportions

Law of constant proportions

F = Gm₁m₂/r²

F = Gm₁m₂/r²

Car travels 120 km in 2h: v = 120/2 = 60 km/h

1st Equation of Motion

u=initial velocity, v=final velocity, a=acceleration, t=time

2nd Equation of Motion

s = ut + ½at²

u=0, a=10, t=5: s=0+½×10×25=125m

3rd Equation of Motion

v² = u² + 2as

u=0, a=10, s=20: v²=400, v=20m/s

Average Velocity (uniform acc)

v_avg = (u+v)/2

u=10, v=30: avg=20 m/s

Force and Laws of Motion

Newton's Second Law

F = ma = Δp/Δt

F in Newtons, m in kg, a in m/s²

Force and Laws of Motion

Truck: 5000kg×20m/s = 100,000 kg⋅m/s | Ball: 0.1kg×30m/s = 3 kg⋅m/s

Force and Laws of Motion

Impulse = F × t = Δp = m(v-u)

Bat hits ball: F=500N for 0.02s → Impulse=10 N⋅s

Force and Laws of Motion

Conservation of Momentum

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

2kg at 5m/s hits 3kg at rest: 10=2v₁+3v₂. If stick: v=(10)/5=2 m/s

Work and Energy

Work and Energy

Work and Energy

Work and Energy

Physics

61 formulas

Universal Gravitation

F = Gm₁m₂/r²

G = 6.674×10⁻¹¹ N⋅m²/kg²

M=6×10²⁴kg, R=6.4×10⁶m: g=6.67×10⁻¹¹×6×10²⁴/(6.4×10⁶)² ≈ 9.8 m/s²

g_h = g(R/(R+h))² ≈ g(1-2h/R) for h<<R

At h=R: g_h = g/4. At h=2R: g_h = g/9

Orbital Velocity

v_o = √(GM/r) = √(gR²/r)

Near Earth surface (r≈R): v_o = √(9.8×6.4×10⁶) ≈ 7920 m/s ≈ 7.9 km/s

Escape Velocity

v_e = √(2GM/R) = √(2gR) = √2 × v_o

v_e = √(2×9.8×6.4×10⁶) ≈ 11,200 m/s ≈ 11.2 km/s

Kepler's 3rd Law

T² ∝ r³ → T₁²/T₂² = r₁³/r₂³

Earth: T=1yr, r=1AU. Mars: r=1.52AU → T²=1.52³=3.51 → T=1.88 years

Motion in a Plane

Range = u²sin2θ/g

Range = u²sin2θ/g

Motion in a Plane

Maximum height = u²sin²θ/2g

Maximum height = u²sin²θ/2g

Motion in a Plane

Time of flight = 2usinθ/g

Time of flight = 2usinθ/g

Motion in a Straight Line

1st Equation of Motion

u=initial velocity, v=final velocity

Motion in a Straight Line

2nd Equation of Motion

s = ut + ½at²

u=0, a=10, t=3: s=0+½×10×9=45 m

Motion in a Straight Line

3rd Equation of Motion

v² = u² + 2as

u=0, a=10, s=20: v²=400, v=20 m/s

Motion in a Straight Line

Distance in nth second

sₙ = u + a(2n-1)/2

Distance in the nth second (not total)

Motion in a Straight Line

Average Velocity

v_avg = (u+v)/2 [only for uniform acceleration]

u=10, v=30: avg=20 m/s

T = 2π√(l/g)

T = 2π√(l/g)

T = 2π√(m/k)

T = 2π√(m/k)

System of Particles and Rotational Motion

System of Particles and Rotational Motion

System of Particles and Rotational Motion

Work, Energy and Power

W = F·d·cosθ

W = F·d·cosθ

Work, Energy and Power

Work, Energy and Power

Alternating Current

Vrms = V₀/√2

Vrms = V₀/√2

Alternating Current

Z = √(R²+X²)

Z = √(R²+X²)

Alternating Current

P = VrmsIrms cosφ

P = VrmsIrms cosφ

rn = 0.529n² Å

rn = 0.529n² Å

En = -13.6/n² eV

En = -13.6/n² eV

Current Electricity

Current Electricity

Current Electricity

Kirchhoff: ΣI=0, ΣV=0

Kirchhoff: ΣI=0, ΣV=0

Dual Nature of Radiation and Matter

Dual Nature of Radiation and Matter

KEmax = hν - W₀

KEmax = hν - W₀

Dual Nature of Radiation and Matter

Electric Charges and Fields

F = kq₁q₂/r² = q₁q₂/(4πε₀r²)

k = 9×10⁹ N⋅m²/C²

Electric Charges and Fields

E = F/q₀ = kq/r² (point charge)

q₀ is positive test charge

Electric Charges and Fields

φ = ∮E⃗⋅dA⃗ = Q_enc/ε₀

Charge Q inside sphere of any radius: φ = Q/ε₀ (same for any closed surface!)

Electric Charges and Fields

Field due to Line Charge

E = λ/(2πε₀r)

λ=1μC/m, r=0.1m: E=10⁻⁶/(2π×8.85×10⁻¹²×0.1)=1.8×10⁵ N/C

Electromagnetic Induction

Electromagnetic Induction

Electromagnetic Induction

Electrostatic Potential and Capacitance

Electrostatic Potential and Capacitance

Electrostatic Potential and Capacitance

Electrostatic Potential and Capacitance

Series: 1/C = 1/C₁+1/C₂

Series: 1/C = 1/C₁+1/C₂

Moving Charges and Magnetism

Moving Charges and Magnetism

B = μ₀I/2πr (wire)

B = μ₀I/2πr (wire)

Moving Charges and Magnetism

B = μ₀nI (solenoid)

B = μ₀nI (solenoid)

ΔE = Δm × c²

ΔE = Δm × c²

Mirror: 1/v+1/u=1/f

Mirror: 1/v+1/u=1/f

Lens: 1/v-1/u=1/f

Lens: 1/v-1/u=1/f

n = sin i/sin r

n = sin i/sin r

YDSE Fringe Width

β = distance between consecutive bright (or dark) fringes

Path Difference

Bright: Δ=nλ (n=0,±1,±2...) | Dark: Δ=(2n+1)λ/2

For 3rd bright fringe: Δ=3λ. For 2nd dark: Δ=3λ/2

Intensity Pattern

I = 4I₀cos²(δ/2) where δ = phase difference = 2πΔ/λ

At bright fringe: δ=0,2π: I=4I₀ (maximum)

tan(θ_B) = n (refractive index)

Glass n=1.5: θ_B=arctan(1.5)=56.3°

Chemistry

10 formulas

Equilibrium Constant

Kc = [C]^c[D]^d / [A]^a[B]^b

Only include aqueous and gaseous species; not pure solids/liquids

Kp and Kc Relation

Kp = Kc(RT)^Δn

N₂+3H₂⇌2NH₃: Δn=2-4=-2, so Kp=Kc(RT)⁻²

pH = -log[H⁺] | [H⁺][OH⁻] = 10⁻¹⁴ at 25°C

[H⁺]=10⁻³: pH=3 (acidic). [H⁺]=10⁻¹¹: pH=11 (basic)

Henderson-Hasselbalch

pH = pKa + log([A⁻]/[HA])

Used for buffer pH calculation

Some Basic Concepts of Chemistry

Some Basic Concepts of Chemistry

Mole = 6.022×10²³ particles

Mole = 6.022×10²³ particles

Chemical Kinetics

Rate = k[A]ᵐ[B]ⁿ

Rate = k[A]ᵐ[B]ⁿ

Chemical Kinetics

k = Ae^(-Ea/RT)

k = Ae^(-Ea/RT)

Electrochemistry

Electrochemistry

E = E° - (RT/nF)lnQ

E = E° - (RT/nF)lnQ

Biology

3 formulas

Molecular Basis of Inheritance

Chargaff's Rule

%A = %T | %G = %C | %A+%T+%G+%C = 100%

If A=30%: T=30%, G+C=40%, so G=C=20%

Molecular Basis of Inheritance

Number of Codons

4³ = 64 codons total. 61 sense + 3 stop codons

20 amino acids coded by 61 codons — most amino acids have multiple codons (degenerate code)

Molecular Basis of Inheritance

Replication time

Human DNA: ~3×10⁹ base pairs replicated in ~8 hours

Rate ≈ 100 base pairs/second at each replication fork

Accountancy

18 formulas

Bank Reconciliation Statement

Balance as per cash book ± Adjustments = Balance as per passbook

Balance as per cash book ± Adjustments = Balance as per passbook

Depreciation, Provisions and Reserves

SLM = (Cost - Residual Value) / Useful life

SLM = (Cost - Residual Value) / Useful life

Depreciation, Provisions and Reserves

WDV = Book value × Rate%

WDV = Book value × Rate%

Financial Statements — I

Gross Profit = Net Sales - Cost of goods sold

Gross Profit = Net Sales - Cost of goods sold

Financial Statements — I

Net Profit = Gross Profit - Indirect Expenses

Net Profit = Gross Profit - Indirect Expenses

Recording of Transactions — I

Assets = Liabilities + Capital

Assets = Liabilities + Capital

Recording of Transactions — I

Debit = Credit (in balanced accounts)

Debit = Credit (in balanced accounts)

Accounting for Partnership

P&L Appropriation = Net Profit - Interest on Capital - Salary + Interest on Drawings

P&L Appropriation = Net Profit - Interest on Capital - Salary + Interest on Drawings

Accounting for Share Capital

Securities Premium = Issue price - Face value

Securities Premium = Issue price - Face value

Accounting for Share Capital

Capital Reserve = Proceeds from re-issue of forfeited shares

Capital Reserve = Proceeds from re-issue of forfeited shares

Accounting Ratios

Current ratio = CA/CL

Current ratio = CA/CL

Accounting Ratios

Quick ratio = (CA-Inventory)/CL

Quick ratio = (CA-Inventory)/CL

Accounting Ratios

Gross profit ratio = GP/Net Sales × 100

Gross profit ratio = GP/Net Sales × 100

Accounting Ratios

Net profit ratio = NP/Net Sales × 100

Net profit ratio = NP/Net Sales × 100

Accounting Ratios

Return on equity = NP/Shareholders' equity × 100

Return on equity = NP/Shareholders' equity × 100

Dissolution of Partnership

Realisation account closes with profit/loss on realisation

Realisation account closes with profit/loss on realisation

Reconstitution of Partnership

Goodwill = Super profit × Years of purchase

Goodwill = Super profit × Years of purchase

Reconstitution of Partnership

Gaining ratio = New ratio - Old ratio

Gaining ratio = New ratio - Old ratio

Business Studies

3 formulas

Maslow's hierarchy of needs

Maslow's hierarchy of needs

Financial Management

Trading on equity

Trading on equity

Financial Management

EPS = PAT / Number of shares

EPS = PAT / Number of shares

Economics

22 formulas

r = Σdx·dy / √(Σdx² × Σdy²)

r = Σdx·dy / √(Σdx² × Σdy²)

Measures of Central Tendency

Measures of Central Tendency

Median = L + (N/2 - CF)/f × h

Median = L + (N/2 - CF)/f × h

Measures of Dispersion

SD = √(Σfd²/N)

SD = √(Σfd²/N)

Measures of Dispersion

CV = (SD/Mean) × 100

CV = (SD/Mean) × 100

Determination of Income and Employment

Income = Consumption + Saving

Income = Consumption + Saving

Determination of Income and Employment

Determination of Income and Employment

Determination of Income and Employment

Determination of Income and Employment

Multiplier = 1/(1-MPC)

Multiplier = 1/(1-MPC)

Government Budget and the Economy

Fiscal deficit = Total expenditure - Revenue receipts - Non-debt capital receipts

Fiscal deficit = Total expenditure - Revenue receipts - Non-debt capital receipts

Government Budget and the Economy

Primary deficit = Fiscal deficit - Interest payments

Primary deficit = Fiscal deficit - Interest payments

National Income Accounting

GDP = C + I + G + (X-M)

GDP = C + I + G + (X-M)

National Income Accounting

NNP = GNP - Depreciation

NNP = GNP - Depreciation

National Income Accounting

National income = NNP - Indirect taxes + Subsidies

National income = NNP - Indirect taxes + Subsidies

Production and Costs

Production and Costs

Production and Costs

The Theory of the Firm Under Perfect Competition

Profit = TR - TC

Profit = TR - TC

The Theory of the Firm Under Perfect Competition

MR = MC (equilibrium)

MR = MC (equilibrium)

Theory of Consumer Behaviour

MUx/Px = MUy/Py (Cardinal)

MUx/Px = MUy/Py (Cardinal)

Theory of Consumer Behaviour

MRSxy = Px/Py (Ordinal)

MRSxy = Px/Py (Ordinal)