IAL ATLAS · Formula Database

The Formula
Atlas.

A structured formula reference for Pearson Edexcel International A Level Mathematics, Physics, Chemistry and Biology. Find formulas by subject, unit and topic without digging through notes.

Mathematics
Pure Mathematics · Mechanics · Statistics
Pure Mathematics 1
P1 · WMA11
Algebra
Index Laws
aᵐaⁿ = aᵐ⁺ⁿ
aᵐ/aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
a⁰ = 1
Quadratic Formula
x = (−b ± √(b² − 4ac)) / 2a
Discriminant
Δ = b² − 4ac
Δ > 0: two real roots · Δ = 0: repeated root · Δ < 0: no real roots
Completing the Square
ax² + bx + c = a(x + b/2a)² + c − b²/4a
Arithmetic Sequence
uₙ = a + (n−1)d
Arithmetic Series
Sₙ = n/2 [2a + (n−1)d]
Sₙ = n/2(a + l)
Geometric Sequence
uₙ = arⁿ⁻¹
Geometric Series
Sₙ = a(1−rⁿ)/(1−r)
Infinite Geometric Series
S∞ = a/(1−r)
Valid when |r| < 1.
Coordinate Geometry
Gradient
m = (y₂−y₁)/(x₂−x₁)
Straight Line
y − y₁ = m(x − x₁)
y = mx + c
Distance Between Two Points
d = √[(x₂−x₁)² + (y₂−y₁)²]
Midpoint
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Circle
(x−a)² + (y−b)² = r²
Trigonometry
Basic Identities
sin²θ + cos²θ = 1
tanθ = sinθ/cosθ
Sine Rule
a/sin A = b/sin B = c/sin C
Cosine Rule
a² = b² + c² − 2bc cos A
Area of Triangle
Area = 1/2 ab sin C
Differentiation
Power Rule
d/dx(xⁿ) = nxⁿ⁻¹
Constant Multiple
d/dx[af(x)] = af′(x)
Stationary Point
dy/dx = 0
Second Derivative
d²y/dx² > 0 → minimum
d²y/dx² < 0 → maximum
Integration
Power Rule
∫xⁿ dx = xⁿ⁺¹/(n+1) + C
n ≠ −1
Area Under a Curve
Area = ∫ᵃᵇ y dx
Definite Integral
∫ᵃᵇ f(x)dx = F(b) − F(a)
Pure Mathematics 2
P2 · WMA12
Indices & Logarithms
Logarithm Laws
logₐ(xy) = logₐx + logₐy
logₐ(x/y) = logₐx − logₐy
logₐ(xⁿ) = n logₐx
Change of Base
logₐx = log_bx / log_ba
Exponential Definition
aˣ = eˣˡⁿᵃ
Binomial Expansion
Binomial Coefficient
(n choose r) = n!/[r!(n−r)!]
Binomial Expansion
(a+b)ⁿ = Σ [nCr aⁿ⁻ʳ bʳ]
Differentiation
Exponential
d/dx(eˣ) = eˣ
Logarithm
d/dx(ln x) = 1/x
Chain Rule
dy/dx = dy/du × du/dx
Product Rule
d(uv)/dx = u dv/dx + v du/dx
Integration
Exponential
∫eˣ dx = eˣ + C
1/x
∫1/x dx = ln|x| + C
Integration by Substitution
∫f(g(x))g′(x)dx = ∫f(u)du
Trigonometric Identities
Double Angle
sin 2x = 2 sin x cos x
cos 2x = cos²x − sin²x
cos 2x = 2cos²x − 1
cos 2x = 1 − 2sin²x
Addition Formulae
sin(A±B)=sinA cosB ± cosA sinB
cos(A±B)=cosA cosB ∓ sinA sinB
Pure Mathematics 3
P3 · WMA13
Functions
Composite Function
(fg)(x) = f(g(x))
Inverse Function
f⁻¹(f(x)) = x
f(f⁻¹(x)) = x
Numerical Methods
Newton-Raphson Method
xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ)
Iteration
xₙ₊₁ = g(xₙ)
Differentiation
Quotient Rule
d(u/v)/dx = [v du/dx − u dv/dx]/v²
Implicit Differentiation
dy/dx obtained by differentiating both sides with respect to x
Integration
Integration by Parts
∫u dv = uv − ∫v du
Area Between Curves
Area = ∫(upper − lower) dx
Trigonometry
R-form
a cos x + b sin x = R cos(x−α)
R = √(a²+b²)
tan α = b/a
Pure Mathematics 4
P4 · WMA14
Vectors
Magnitude
|a| = √(a₁²+a₂²+a₃²)
Unit Vector
â = a/|a|
Scalar Product
a·b = |a||b|cosθ
a·b = a₁b₁+a₂b₂+a₃b₃
Angle Between Vectors
cosθ = (a·b)/(|a||b|)
Differential Equations
Separable Form
dy/dx = f(x)g(y)
∫dy/g(y) = ∫f(x)dx
First Order Linear Form
dy/dx + Py = Q
Parametric Equations
Gradient
dy/dx = (dy/dt)/(dx/dt)
Second Derivative
d²y/dx² = [d/dt(dy/dx)]/(dx/dt)
Mechanics 1
M1 · WME01
SUVAT
Equation 1
v = u + at
Equation 2
s = ut + 1/2 at²
Equation 3
s = vt − 1/2 at²
Equation 4
v² = u² + 2as
Equation 5
s = 1/2(u+v)t
Forces
Newton's Second Law
F = ma
Weight
W = mg
Momentum
p = mv
Impulse
Impulse = Ft = Δp
Work Done
W = Fs cosθ
Kinetic Energy
KE = 1/2 mv²
Gravitational Potential Energy
GPE = mgh
Power
P = W/t
P = Fv
Projectiles
Horizontal Component
uₓ = u cosθ
Vertical Component
uᵧ = u sinθ
Horizontal Motion
x = u cosθ · t
Vertical Motion
y = u sinθ · t − 1/2 gt²
Coefficient of Friction
F ≤ μR
Mechanics 2
M2 · WME02
Momentum & Collisions
Conservation of Momentum
Total momentum before = Total momentum after
Coefficient of Restitution
e = relative speed of separation / relative speed of approach
Impulse
Impulse = ∫F dt = Δp
Circular Motion
Angular Speed
ω = v/r
Centripetal Acceleration
a = v²/r = rω²
Centripetal Force
F = mv²/r = mrω²
Centre of Mass
Centre of Mass Coordinate
x̄ = Σmx / Σm
ȳ = Σmy / Σm
Moments
Moment of a Force
Moment = Force × perpendicular distance
Equilibrium
ΣF = 0
ΣMoment = 0
Statistics 1
S1 · WST01
Sampling & Data
Sample Mean
x̄ = Σx/n
Frequency Mean
x̄ = Σfx/Σf
Estimated Mean from Grouped Data
x̄ ≈ Σfm/Σf
m = class midpoint.
Measures of Dispersion
Variance
s² = Σ(x−x̄)²/n
Alternative Variance Formula
s² = Σx²/n − x̄²
Frequency Variance
s² = Σfx²/Σf − x̄²
Standard Deviation
s = √s²
Range
Range = maximum − minimum
Interquartile Range
IQR = Q₃ − Q₁
Probability
Complement
P(A′) = 1 − P(A)
Addition Rule
P(A∪B) = P(A)+P(B)−P(A∩B)
Independent Events
P(A∩B) = P(A)P(B)
Conditional Probability
P(A|B) = P(A∩B)/P(B)
Correlation & Regression
Product Moment Correlation Coefficient
r = [nΣxy − ΣxΣy] / √[(nΣx²−(Σx)²)(nΣy²−(Σy)²)]
Regression Line of y on x
y = a + bx
Regression Gradient
b = Sxy/Sxx
Regression Intercept
a = ȳ − bx̄
Histograms
Frequency Density
Frequency density = frequency / class width
Frequency from Histogram
Frequency = class width × frequency density
Statistics 2
S2 · WST02
Discrete Random Variables
Expected Value
E(X) = Σxp(x)
Variance
Var(X) = E(X²) − [E(X)]²
Binomial Distribution
Binomial Probability
P(X=r) = ⁿCᵣ pʳ(1−p)ⁿ⁻ʳ
Mean
E(X) = np
Variance
Var(X) = np(1−p)
Poisson Distribution
Poisson Probability
P(X=r) = e⁻λ λʳ/r!
Mean & Variance
E(X)=λ
Var(X)=λ
Normal Distribution
Standardisation
Z = (X−μ)/σ
Physics
Mechanics · Materials · Waves · Electricity · Fields · Particles · Cosmology
Unit 1 · Mechanics & Materials
WPH11
Motion
Speed
speed = distance/time
Acceleration
a = Δv/Δt
SUVAT
v = u + at
s = ut + 1/2at²
v² = u² + 2as
s = 1/2(u+v)t
Forces & Momentum
Newton's Second Law
F = ma
Momentum
p = mv
Impulse
FΔt = Δp
Moment
moment = Fd
Energy
Work Done
W = Fs cosθ
Kinetic Energy
Eₖ = 1/2mv²
Gravitational Potential Energy
ΔEₚ = mgΔh
Power
P = W/t
Materials
Density
ρ = m/V
Stress
stress = F/A
Strain
strain = ΔL/L
Young Modulus
E = stress/strain
Elastic Strain Energy
E = 1/2 FΔL
Unit 2 · Waves & Electricity
WPH12
Waves
Wave Equation
v = fλ
Frequency & Period
f = 1/T
Intensity
I = P/A
Refraction
n₁ sinθ₁ = n₂ sinθ₂
Refractive Index
n = c/v
Electricity
Charge
Q = It
Potential Difference
V = W/Q
Ohm's Law
V = IR
Electrical Power
P = IV
P = I²R
P = V²/R
Electrical Energy
E = VIt
Resistors in Series
Rtotal = R₁ + R₂ + ...
Resistors in Parallel
1/Rtotal = 1/R₁ + 1/R₂ + ...
Unit 4 · Further Mechanics, Fields & Particles
WPH14
Circular Motion
Angular Velocity
ω = 2πf = 2π/T
Centripetal Acceleration
a = v²/r = rω²
Centripetal Force
F = mv²/r
Electric Fields
Electric Field Strength
E = F/Q
Electric Force
F = kQq/r²
Electric Potential
V = kQ/r
Gravitational Fields
Newton's Law of Gravitation
F = GMm/r²
Gravitational Field Strength
g = GM/r²
Gravitational Potential
V = −GM/r
Particles
Mass-Energy
E = mc²
Photon Energy
E = hf
Photon Momentum
p = h/λ
Unit 5 · Thermodynamics, Radiation, Oscillations & Cosmology
WPH15
Thermal Physics
Specific Heat Capacity
ΔE = mcΔθ
Specific Latent Heat
ΔE = mL
Oscillations
Simple Harmonic Motion
a = −ω²x
Angular Frequency
ω = 2πf
SHM Period
T = 2π/ω
Radiation
Activity
A = λN
Radioactive Decay
N = N₀e⁻λt
Half-Life
t½ = ln2/λ
Cosmology
Hubble's Law
v = H₀d
Redshift
z = Δλ/λ
Chemistry
Structure · Bonding · Energetics · Rates · Equilibrium · Organic · Transition Metals
Unit 1 · Structure, Bonding & Intro Organic
WCH11
Amount of Substance
Moles from Mass
n = m/M
Concentration
c = n/V
Number of Particles
N = nNₐ
Molar Gas Volume
n = V/Vₘ
Atomic Structure
Relative Atomic Mass
Aᵣ = Σ(isotope mass × abundance)/Σabundance
Mass Spectrometry
m/z = mass-to-charge ratio
Bonding
Formal Charge
Formal charge = valence electrons − non-bonding electrons − 1/2 bonding electrons
Unit 2 · Energetics, Group Chemistry & Organic
WCH12
Energetics
Enthalpy Change
q = mcΔT
Molar Enthalpy Change
ΔH = −q/n
Bond Enthalpy
ΔH = Σ(bonds broken) − Σ(bonds formed)
Hess's Law
ΔHreaction = ΣΔHformation(products) − ΣΔHformation(reactants)
Gas Equation
Ideal Gas Equation
pV = nRT
Rates
Rate
rate = change in concentration / time
Unit 4 · Rates, Equilibrium & Further Organic
WCH14
Rates
Rate Equation
rate = k[A]ᵐ[B]ⁿ
Rate Constant
k = rate / ([A]ᵐ[B]ⁿ)
Equilibrium
Equilibrium Constant
Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ
Acids & Bases
pH
pH = −log₁₀[H⁺]
pOH
pOH = −log₁₀[OH⁻]
Water Ionic Product
Kᵥ = [H⁺][OH⁻]
Unit 5 · Transition Metals & Organic Nitrogen
WCH15
Electrochemistry
Charge
Q = It
Faraday Relationship
Q = n(e⁻)F
Cell Potential
E°cell = E°cathode − E°anode
Biology
Molecules · Cells · Transport · Energy · Environment · Genetics · Gene Technology
Unit 1 · Molecules, Diet, Transport & Health
WBI11
Magnification
Magnification
Magnification = image size / actual size
Actual Size
Actual size = image size / magnification
Biological Calculations
Percentage Change
% change = (change/original) × 100
Percentage Error
% error = (absolute uncertainty/value) × 100
Unit 2 · Cells, Development, Biodiversity & Conservation
WBI12
Cell Calculations
Surface Area to Volume Ratio
SA:V = surface area / volume
Population
Population Growth
growth rate = change in population / time
Unit 4 · Energy, Environment, Microbiology & Immunity
WBI14
Photosynthesis
Photosynthesis Equation
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
Respiration
Aerobic Respiration
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O
Respiratory Quotient
RQ = CO₂ produced / O₂ consumed
Microbiology
Population Growth
growth = final population − initial population
Unit 5 · Respiration, Internal Environment, Coordination & Gene Technology
WBI15
Genetics
Hardy-Weinberg
p + q = 1
p² + 2pq + q² = 1
Genetic Ratios
Probability of Independent Events
P(A and B) = P(A) × P(B)
Chi-Squared
χ² = Σ[(O−E)²/E]
Unit 6 · Practical Skills II
WBI16
Data Analysis
Percentage Difference
% difference = |A−B| / [(A+B)/2] × 100
Percentage Change
% change = [(final−initial)/initial] × 100
Rate
rate = change / time
No matching formula found.