The Formula Book

Physics Math Chemistry

Click Any of the Tabs Above To View Formulae Of Subjects. Here is a guide:

Green Formulae are Normal formulae good to Know and Many May Come on a Paper Red Signifies that the Formula is very Important and is Likely to be Asked in an Examination Yellow Means that formulae are Not Super Important to Remember, Come back to These Later

Algebraic Identities and Law's of indices

2.5

(a + b)^{2} = a^{2} + b^{2} + 2 a b

Algebric Indentity #1

2.5

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

Algebraic Identity #2

2.5

a^{2} - b^{2} = (a + b) \cdot (a - b)

Algebraic Identity #3

2.5

x^{n} \cdot x^{m} = x^{m + n}

Used for Multiplying Indices

2.5

\frac{x^{n}}{x^{m}} = x^{m -- n}

Used for Dividing Indices

2.5

{(x^{n}) m}^{} = x^{n \cdot m}

Used of solving indices with two exponents

2.5

\frac{y}{x^{m}} = \frac{y^{m}}{x^{m}}

used for indices with a fraction

2.5

x^{- m} = \frac{1}{x^{m}}

used for indices with negative exponents

2.5

x^{\frac{m}{n}} = \sqrt[n]{x^{m}}

Used if any number has a fraction as an exponent

x

avg = sum of all elements/number of elements

finding average

12.5

Q2 = median

value of Q2

Shape Chapters

7.1

P = 2 \cdot (L + B)

Used to calculate perimeter of rectangle.

7.1

P = 4*s

Used to calculate perimeter of square.

7.1

C = πd or 2πr

Used to calculate perimeter of circle

7.1

A = s²

Used to calculate area of square

7.1

A = L*B

Used to calculate area of rectangle

7.1

A = (1/2)*bh

Used to calculate area of triangle

7.1

A = πr²

Used to calculate area of circle

7.2

V = L \cdot B \cdot H

Used to calculate volume of cuboid

7.1

V = s³

Used to calculate volume of cube

7.1

V = π r^{2} h

Used to calculate volume of cylinder

7.1

V = A of cross section * height

Used to calculate volume of any regular 3d shape

7.1

A = \frac{a + b}{2} \cdot h

Used to calculate area of trapezium.

7.1

A = Θ/360 * πr²

Used to calculate area of a sector

7.1

C = Θ/360 * 2πr

Used to calculate arc length

7.1

V = (1/3) 𝜋r^2h

Used to calculate volume of cone

7.1

SA = 4πr^2

Used to calculate surface area of sphere

7.1

V = (4/3)πr^3

Used to calculate volume of sphere

11.1

a² +b² = c²

Pythagoras theorem, used to calculate various sides of a right angles triangle

11.3

Scale factor(Area) = scale factor (length)²

Used to calculate scale factor of Areas.

11.3

Scale factor(vol) = scale factor(length)³

Used to calculate scale factor of volumes.

15.2

sin(θ) = O/H

Trigonometric formula which is used to calculate angle using opposite and hypotenuse

15.2

cos(θ) = A/H

Trigonometric formula which is used to calculate angle using Adjacent and hypotenuse

15.2

tan(θ) = O/A

Trigonometric formula which is used to calculate angle using opposite and Adjacent

15.3

sin^2θ + cos^2θ = 1

Trigonometric formula which gives a product of 1

15.5

sin(θ) = sin(180 - θ)

Alternative sine formula

15.5

cos(θ) = -cos(180 - θ)

Alternative cosine formula

15.5

cos(θ) = cos(360-θ)

Alternative cosine formula which has positive value

15.5

tan(θ) = tan(180 + θ)

Alternative Tangent formula

15.6

a/sinA = b/sinB = c/sinC

Used to calculate sides and angles of a triangle

15.6

a^{2} = b^{2} + c^{2} - 2 b c \cdot \cos (A)

Cosine Ratio

15.6

(main side)² = (other sides)² - 2(other sides) *Cos(main angle)

simplifies cosine ratios, main side is the side you want to use, main angle is the angle opposite to the side you want to find, if you learn to use this there is no need to remember the above 3 formulas

15.7

A = \frac{1}{2} \cdot a \cdot b \cdot C

Using to calculate area of triangle when height is not given

15.7

Area = (1/2)*(given sides) * sin(given angle)

simplifies the above 3 formulas, if you learn to use this no need to remember the above formulas

19.4

The angle in a semi circle is a right angle

circle theorem #1

19.4

The angle between the tangent and radius is 90 degrees

circle theorem #2

19.4

The angle at the center of a circle is twice the angle at the circumference

circle theorem #3

19.4

angles in the same segment are equal

circle theorem #4

19.4

The opposite angles of a cyclic quadrilateral add up to 180 degrees

circle theorem #5

19.4

Each exterior angle of a cyclic quadrilateral is equal to the interior angle opposite to it

Circle theorem #6

19.4

Angle subtended by the diameter on the circumference is 90 degrees

Circle theorem #7

19.4

The angle between the tangent and the chord is equal to the angle in alternate segment

Alternate segment theorem

21.4

\frac{Δ_{y}}{/} = gradient = speed

used to find the speed in a distance time graph

21.6

F = K * D

Formula used to solve direct proportionality problems

21.6

F = K * 1/D

Formula used to solve inverse proportionality problems

Sequences

9.1

An = A1 + (n - 1)D

Used to find nth term of a sequence

Graph and Quadric Chapters

10.1

m = (y2 - y1)/(x2 - x1)

Used to find gradient

10.2

y = mx + c

A formula that links gradient and c interception, this is the standard formula and should be used for graphing

10.2

{(a + b)}^{2} = a^{2} + b^{2} + 2 \cdot a \cdot b

Used to square a binomial with operation +

10.2

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

Used to square a binomial with operation -

12.1

Mean = \frac{\sum_{x}}{\sum_{f}}

Used to calculate mean

12.1

Median = fi/2

Used to calculate the middle number

12.1

Range = highest - lowest

Used to calculate the range

12.5

Q1 = (1/4) * (n+1)

Finding lower quartile

12.5

Q3 = (3/4) * (n+1)

Finding upper quartile

12.5

IQR = Q3 - Q1

Used to calculate inter quartile range

14.5

\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Used to solve quadratic equations

18.1

x = \frac{- b}{2 a}

Used to find the x intercept of the turning point of a parabola

18.1

a x^{2} + b x + c = 0

used to find the x intercept of a parabola by making the y value as 0, in the equation

18.2

y = \frac{a}{x} + q

general formula for hyperbola

18.1

a x^{2} + b x + c

general formula for parabola

18.5

y = a^x

general formula for exponential graphs

18.5

y = x^3

general formula for cubic graphs

18.7

if y = x, dy/dx or f'(x) = 0

derivation for a numerical value such as 5

18.7

if y = nx, dy/dx or f'(x) = n

derivation for a variable to the power 1, such as 5x

18.7

if y = nx^a, dy/dx or f'(x) = anx^(n - 1)

derivation for a variable to the power higher then 1, such as 5x2

20.1

fd = f/cw

Used to calculate the frequency density

20.1

P = pn/100

Used to find the position of a percentile

Measurements and Conversions

13.1

1 km = 10 hm

Used to convert km to hm

13.1

1 hm = 100 decameter

Used to convert hm to decameter

13.1

1 decameter = 10 m

Used to convert decameter to m

13.1

1 m = 10 dm

Used to convert m = dm

13.1

1 dm = 10 cm

Used to convert dm = cm

13.1

1 cm = 10 mm

Used to convert cm = mm

13.1

1000 kg = 1t

Used to convert kg to t

Finance related chapters

17.2

I = PRT/100

Used to find the simple interest

17.1

Net Income = Gross Income - Deductions

Used to calculate the net income

17.2

HP = Deposit + (number of installments + amount per installment)

Used to calculate the hire purchase (HP)

17.2

V = P(1 + r/100)^n

Used to calculate compound interest

17.3

P = SP - CP

Used to calculate the profit

17.3

L = CP - SP

Used to calculate loss

17.3

p% = P/CP * 100%

Used to calculate percentage profit

17.3

l% = L/CP * 100%

Used to calculate percentage loss

Terms

S.I Unit

mass

kg

volume

m(eter³) or cm³

distance

m(eters)

time

s(econds)

speed

m/s

acceleration

m/s²

g

10 m/s²

momentum

kg m/s

Density

ƥ (rho)

weight

N(ewtons)

Force

N(ewtons)

velocity

+m/s or -m/s

pressure

(p)ascals

work

J(oules)

power

W(atts)

energy

J(oules)

kelvin

K

Celsius

*C

Specific heat capacity

J/kg *c

Specific latent heat of fusion

J/kg

Specific heat capacity

J/kg

Frequency

Hz

wavelength

ƛ or m(eters)

Formulae's

1.4

density = mass / volume

density formula

2.1

speed = distance / time

speed formula

2.1

speed = velocity (just value)

2.1

acceleration = ∆ velocity / ∆ time

acceleration formula

2.1

Force = mass * acceleration

formula of force

2.9

weight = mass * g

formula of weight

2.11

momentum = mass * velocity

formula of momentum

2.12

impulse = force * time

formula of impulse

2.12

impulse = ∆ change in momentum

formula of impulse

2.11

resultant force = ∆ change in momentum [or impulse] / ∆ time taken

resultant force formula

x

(final velocity)² = (initial velocity)² + 2*(acceleration * displacement)

formula of (final velocity)²

x

displacement = (initial velocity * time) + (acceleration*time²)/2

displacement formula

x

final velocity = initial velocity + (acceleration * time)

formula of final velocity

3.1

moment = perpendicular distance * force

formula of moment

3.4

load of spring = spring constant * extension

formula of load of spring

3.5

pressure = force / area

pressure formula

3.6

liquid pressure = density * g * depth

formula of liquid pressure

3.8

pressure 1 * volume 1 == pressure*2 * volume 2

formula of pressure 1 * volume 1

4.1

work = distance * Force

formula of work

4.3

G.P.E = mass * g * height from ground

formula of g.p.e

4.3

kinetic energy = (1/2)*mass*velocity²

kinetic energy formula

4.4

power = work done / ∆ time taken

power formula

4.4

power = energy transferred / ∆ time taken

power formula

4.4

efficiency = useful work / total energy input

efficiency formula

4.4

efficiency = useful energy / total energy

efficiency formula

4.4

efficiency = useful power / total power

efficiency formula

5.1

energy transfer = mass * L

formula of energy transfer

5.2

kelvin = degrees Celsius + 273

formula of kelvin from Celsius scale

5.9

energy transfer = mass * S.H.C * ∆ temp

formula of energy transfer

6.1

speed of wave = frequency * wavelength

formula of speed of wave

6.4

speed of echo sound = (2 * distance to wall)/(echo time)

formula to find the speed of an echo

6.4

speed of sound = (distance traveled)/(time taken)

formula to find the speed of sound

7.6

n = \frac{sin i}{sin r}

formula to calculate the refractive index of a medium, n is the refractive index, I is the angle of incidence and r is the angle of refraction

7.6

\sin (c) = \frac{1}{n}

formula to calculate the critical angle on a medium, c is the critical angle and n is the refractive index

8.4

I = Q/T

formula to calculate current from charge and time, I is current, Q is charge and T is time

8.5

V = W/Q

formula to calculate voltage from work done and charge, V is voltage, W is work done and Q is charge

8.6

R = V/I

ohm's law, R is resistance, V is voltage and A is current

8.7

V = I⋅R

ohm's law, R is resistance, V is voltage and A is current

8.7

I = V/R

ohm's law, R is resistance, V is voltage and A is current

8.8

R = ρ * L/A

formula to calculate resistance from the resistivity of the material

8.8

\frac{R_{a} A_{a}}{L_{a}} = \frac{R_{b} A_{b}}{L_{b}}

formula used to calculate the resistance of another wire from another wire with the same resistivity

8.1

R = R_{1} + R_{2} + R_{n}

formula used to calculate the total resistance of a series circuit

8.1

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{n}}

formula use to calculate the total resistance of a parallel circuit

8.12

P = V⋅I

formula used to calculate the electrical power of a circuit

8.12

E = V⋅I⋅T

formula used to calculate the energy transferred in a circuit, E is the energy transferred, I is the current and t is the time taken.

9.10

Vs/Vp = Ns/Np

formula used to calculate the number of coils present in the primary and secondary circuit from the input and output voltage

9.11

Vp⋅Ip = Vs⋅Is

formula used to calculate the amount of current reduced and the voltage increased, by knowing the power

Physics Laws

2.6

Newton's first law of motion

If no external force is acting on it, an object will -if stationary, remain stationary -if moving, keep moving at a steady speed in a straight line

2.7

Newton's second law of motion

F = ma, this relationship between force, mass and acceleration is sometimes called newton's second law of motion

2.1

Newton's third law of motion

every reaction has an equally likely opposite reaction

2.12

Law of conservation of momentum

When two or more objects act on each other, their total momentum remains constant, provided no external forces are acting

3.1

Principle of moments

If an object is in equilibrium: the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about that points

3.4

Hooke's law

A material obeys hooke's law if, beneath it's elastic limit, the extension is proportional to the load

3.8

Boyle's law

P1V1 = P2V2, if pressure is halved, then volume is doubled, if pressure is doubled, then volume is halved

4.2

law of conservation of energy

Energy can be stored or transferred, but it cannot be created or destroyed

7.2

laws of reflection

1) The angle of incidence is equal to the angle of reflection 2) the incident ray, the reflected raw, and the normal all lie in the same place

7.6

Snell's law

the sines of the two angles are always in proportion, sin(i)/sin(r)

8.7

Ohm's law

The current in a circuit is always proportional to the pd, V = IR

9.3

Right hand grip rule

A rule used to find the field direction produced by a current

9.5

Fleming's left hand rule

A rule used to find the direction of force

9.7

Faraday's law of electromagnetic induction

The emf induced in a conductor is proportional to the rate at which magnetic field lines are cut by the conductor

9.8

Lenz's law

An induced current always flows in a direction such that it opposes the charge which produced it

9.8

Fleming's right hand rule

a rule used to find the direction of induced current

Convex Lens

Object Position

Properties

∞

Focus

At 2F

2F^-

F - 2F

beyond 2F^-

F

∞

F - Optical Center

F-2F

Concave Lens

Object Position

Properties

∞

F^-

∞ - Optical Center

Optical Center - F^-

Constant Values

5.1

1 mole (1 mol)

6.02 x 1023

5.3

R.T.P (room temperature and pressure)

20*C \& 1 atmosphere

5.3

volume of gas at R.T.P

24dm³

Formulae

5.1

moles = mass/mass of 1 mole

finding the number of moles

5.1

mass of 1 mole = Mr or Ar

Very important formula of finding the how much mass one mole has

5.3

volume of gas at rtp = 24dm³ * number of moles

volumes of gas for any amount of moles

5.3

number of moles in x volume = volume/24dm³

no need to learn this formulas if the above formula is learnt

5.4

concentration = amount(mol/g) / volume

concentration formula

5.4

volume = amount / concentration

no need to this formula and the one below if the above formula is learnt

5.4

amount = concentration * volume

^

5.6

multiplier = Mr / empirical mass molecular formula = multiplier * empirical formula

finding the molecular formula from empirical mass

5.7

%yield = mass of product / theoretical mass

finding the percentage yield

5.8

%purity = pure mass / impure mass

finding the percentage purity, too much logic for the marks these are worth, the hardest formula to apply

8.3

enthalpy (∆H) = bond break energy - bond making energy

enthalpy, the total energy change during a reaction

18.6

(Retention Factor) Rf = distance from origin to dot / distance from origin to solvent front

retention factor, using a table can tell you what element/compound you will deal with

The Reactivity Series

Potassium

Sodium

Lithium

Calcium

Magnesium

Aluminum

Carbon

Zinc

Iron

Hydrogen

Copper

Silver

Gold

Platinum

Ways to change Equilibrium

Favours

Temperature

Endothermic Reaction

Pressure

The Side with lowest amount of molecules

Concentration

Side with more concentration

Catalyst

Both Forward and Reverse Reactions

Process

Catalyst Used And Product

Conditions

Haber's Process

Iron (Fe) is Catalyst Ammonia is produced

450 Degrees C 200 Atmospheres

Contact Process

Vanadium PentOxide is the Catalyst Produces Sulfuric Acid

450 Degrees C2 Atmospheres

Indicator

Colour in Acid

Colour in Bases

Litmus

Red

Blue

Methyl Orange

Red

Yellow

Thymolphthalein

Colourless

Blue

Phenolphthalein

Colourless

Pink

Ion or type of compound

Acid or Base

Metal Oxide

Base (except aluminum oxide and zinc oxide)

Non Metal Oxide

Acid

Hydroxide

Base

Carbonate

Base

Nitrate

Non Determinable

Type of compound

Typical Acid Reaction

Metals

Acid + Metal → Salt + Hydrogen

Bases

Acid + Base → Salt + Water

Carbonates

Acid + Carbonate → Salt + Carbon Dioxide + Water

Ammonia

Ammonia + Acid → Ammonium Salt (NO WATER OR GAS FORMS)

Soluble

Insoluble

Sodium Salts

No Exceptions

Potassium Salts

No Exceptions

Ammonium Salts

No Exceptions

Halides

Except halides of silver and lead

Sulfates

Except: Calcium Barium Lead sulfate

Except: Sodium Potassium Ammonium

Carbonates

Grp

Trend

Sequence

I & II

Reactivity

increases

I & II

Density

increases

I & II

Melting point

increases

VII

Reactivity

decreases

VII

Density

increases

VII

Boiling point

increases

VII

Colour

darkness increases

Gas

Test

Properties

Ammonia

HeatHold Damp Red Litmus Paper over itPaper Turns Blue

Colourless Alkaline Gas Strong Sharp Smell

Hydrogen

Collect in a TubeHold a lighted splint to itSqueaky Pop is heard

Colourless When Lit, Reacts Vigorously with Oxygen

Oxygen

Collect OxygenHold glowing splint to itSplint Immediately bursts into flame

Colourless Fuel Burns Easier in it

Chlorine

Hold Damp Litmus Paper in a fume cupboardPaper turns white

Poisonous Can Bleach Dyes

Sulfur Dioxide

Get solution of Potassium Manganate(VII) Add a Little amount of dilute Hydrochloric Acid Soak A piece of filter paper in the now acidified Potassium Manganate(VII) Place filter paper in the gas (S0₂) Paper becomes colourless from purple

Colourless Poisonous Acidic gas Chocking smell

Cation Flame Test

Colour

Lithium

Red

Sodium

Yellow

Potassium

Lilac

Calcium

Orange-Red

Barium

Light Green

Copper (II)

Blue-Green

Cation Test

Procedure and Result

Ammonium

Add - dil. NaOH (aq) 

Heat Gently

Ammonia Released ( Turns damp Blue Litmus to red )

Iron (||)

Add - dil • Ammonia (aq) to one portion

Add - dil • NaOH (aq) to the other potion

Pale Green Precipitate will form

Iron (|||)

Divide into 2 portions
Add - dil • Ammonia (aq) to one portion
Add - dil • NaOH (aq) to the other potion

Reddish Brown Precipitate will form

Zinc

Divide into 2 portions

Add - dil • NaOH (aq) to one portion
Add - dil • Ammonia (aq) to the other potion

White Precipitate forms
Adding more makes solution colourless

Aluminum

Divide into 2 portions

Add - dil • NaOH (aq) to one portion
White Precipitate forms
Adding more makes it colourless

Add - dil • Ammonia (aq) to the other potion
White Precipitate forms
Adding more has no effect

Calcium

Divide into 2 portions

Add - dil • NaOH (aq) to one portion
White Precipitate forms
Adding more has no effect

Add - dil • Ammonia (aq) to the other potion
No Precipitate, or very slight white precipitate is formed
Adding more has no effect

Anion

Tests

Halide

To a small amount of solution, add an equal volume of dilute nitric acid Add aqueous silver nitrate, which is insoluble If halide is present, precipitate forms Chlorine is white Bromine is Creme Iodine is Pale-Yellow

Sulphate

To a small amount of solution, add an equal volume of dilute nitric acid Add barium nitrate solution, which is insoluble White Precipitate is formed if sulphate is present SO4^2- + Ba^2+ -> BaSO4

Sulfite

To a small amount of solution, add an equal volume of dilute acidified potassium permanganate (purple) Solution turns colourless

Carbonate

To a small amount of solution, add an equal volume of dilute Hydrochloric acid A gas will be produced (Carbon Dioxide) It turns limewater milky

Nitrate

To a small amount of solution (or solid), add little aqueous Sodium Hydroxide Add small pieces of Aluminum foil Heat Gently A gas is given off (Ammonia) Expose this gas with Damp red litmus paper Paper turns blue