CAIE O Level, IGCSE, AS & A Level Formula Library

Accounting Foundation Essential New

☆

Accounting Equation

Accounting equation

Core & Extended

Assets = Capital + Liabilities

Reveal formulaTest your memory first

Assetsresources owned Capitalowner’s claim Liabilitiesamounts owed

Exam tipEvery transaction keeps the equation balanced.

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Accounting Foundation Essential New

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Income Statement

Gross profit

Core & Extended

Gross profit = Revenue − Cost of sales

Reveal formulaTest your memory first

Revenuesales less returns inwards Cost of salescost of goods sold

Exam tipGross profit concerns trading goods before operating expenses.

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Accounting Foundation Essential New

☆

Income Statement

Profit for the year

Core & Extended

Profit = Gross profit + Other income − Expenses

Reveal formulaTest your memory first

Profitprofit for the year

Exam tipInclude all revenue and expense adjustments for the period.

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Accounting Standard Essential New

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Profitability Ratios

Gross margin

Core & Extended

gross margin = gross profitrevenue × 100%

Reveal formulaTest your memory first

gross profitrevenue − cost of sales revenuenet sales

Exam tipDo not confuse margin with mark-up: margin uses revenue as denominator.

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Accounting Standard Essential New

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Liquidity Ratios

Current ratio

Core & Extended

current ratio = current assetscurrent liabilities

Reveal formulaTest your memory first

current assetsshort-term assets current liabilitiesshort-term obligations

Exam tipUsually state as x : 1, not a percentage.

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Accounting Foundation Essential New

☆

Accounting Equation

Owner’s equity

Core & Extended

owner’s equity = assets − liabilities

Reveal formulaTest your memory first

assetsresources controlled by the business liabilitiesamounts owed

Exam tipOwner’s equity is the residual interest in the business.

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Accounting Standard Essential New

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Capital

Closing capital

Core & Extended

closing capital = opening capital + capital introduced + profit − drawings

Reveal formulaTest your memory first

capital introducedadditional owner investment drawingsowner withdrawals

Exam tipUse loss as a negative profit.

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Accounting Foundation Essential New

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Depreciation

Carrying amount

Core & Extended

carrying amount = cost − accumulated depreciation

Reveal formulaTest your memory first

costoriginal non-current asset cost accumulated depreciationtotal depreciation to date

Exam tipCarrying amount is also called net book value.

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Accounting Foundation Essential New

☆

Efficiency Ratios

Average inventory

Core & Extended

average inventory = opening inventory + closing inventory2

Reveal formulaTest your memory first

opening inventoryinventory at period start closing inventoryinventory at period end

Exam tipUse average inventory when both opening and closing figures are available.

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Accounting Standard Essential New

☆

Profitability Ratios

Capital employed

Core & Extended

capital employed = owner’s equity + non-current liabilities

Reveal formulaTest your memory first

owner’s equitycapital attributable to owner non-current liabilitieslong-term finance owed

Exam tipAn alternative is total assets minus current liabilities.

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Accounting Challenging Essential New

☆

Manufacturing Accounts

Cost of production

Core & Extended

cost of production = prime cost + factory overheads + opening work in progress − closing work in progress

Reveal formulaTest your memory first

WIPwork in progress

Exam tipAdjust factory cost for unfinished production at the beginning and end.

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Accounting Standard Essential New

☆

Analysis of Financial Statements

Return on capital employed

AS & A Level

ROCE = profit from operations / capital employed × 100%

Reveal formulaTest your memory first

profit from operationsoperating profit capital employedequity plus non-current liabilities

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Standard Essential New

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Analysis of Financial Statements

Inventory turnover

AS & A Level

inventory turnover = cost of sales / average inventory

Reveal formulaTest your memory first

average inventory(opening+closing inventory)/2

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Standard Essential New

☆

Analysis of Financial Statements

Gearing ratio

AS & A Level

gearing = non-current liabilities / capital employed × 100%

Reveal formulaTest your memory first

capital employedequity plus non-current liabilities

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Standard Essential New

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Analysis of Financial Statements

Earnings per share

A Level

EPS = profit attributable to ordinary shareholders / weighted average ordinary shares

Reveal formulaTest your memory first

EPSearnings per ordinary share

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Challenging Essential New

☆

Investment Appraisal

Net present value

A Level

NPV = Σ[cash flowₜ/(1+r)ᵗ] − initial investment

Reveal formulaTest your memory first

rdiscount rate ttime period cash flowₜnet cash flow in period t

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Standard Essential New

☆

Investment Appraisal

Accounting rate of return

A Level

ARR = average annual profit / average investment × 100%

Reveal formulaTest your memory first

average investmentcommonly (initial+residual value)/2

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Standard Essential New

☆

Cost and Management Accounting

Contribution per unit

AS & A Level

contribution per unit = selling price − variable cost per unit

Reveal formulaTest your memory first

contributionamount toward fixed costs and profit

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Standard Essential New

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Cost and Management Accounting

Break-even output

AS & A Level

break-even units = fixed costs / contribution per unit

Reveal formulaTest your memory first

fixed costscosts unchanged by output

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Foundation New

☆

Financial Statements

Capital

Core & Extended

Capital = Assets − Liabilities

Reveal formulaTest your memory first

Capitalowner’s equity Assetstotal assets Liabilitiestotal liabilities

Exam tipUse values at the same date.

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Accounting Foundation New

☆

Financial Statements

Working capital

Core & Extended

Working capital = Current assets − Current liabilities

Reveal formulaTest your memory first

Current assetsshort-term assets Current liabilitiesshort-term obligations

Exam tipPositive working capital does not automatically mean strong liquidity; consider composition.

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Accounting Foundation New

☆

Income Statement

Cost of sales

Core & Extended

Cost of sales = Opening inventory + Net purchases + Carriage inwards − Closing inventory

Reveal formulaTest your memory first

Net purchasespurchases − returns outwards

Exam tipCarriage inwards belongs in cost of sales; carriage outwards is an expense.

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Accounting Standard New

☆

Depreciation

Straight-line depreciation

Core & Extended

annual depreciation = cost − residual valueuseful life

Reveal formulaTest your memory first

costoriginal asset cost residual valueestimated disposal value useful lifeyears

Exam tipCharge the same annual amount over the asset’s useful life.

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Accounting Challenging New

☆

Depreciation

Reducing-balance depreciation

Core & Extended

depreciation = net book value × rate

Reveal formulaTest your memory first

net book valuecost − accumulated depreciation rateannual depreciation rate

Exam tipApply the percentage to the opening net book value each year.

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Accounting Standard New

☆

Adjustments

Provision for doubtful debts

Core & Extended

provision = trade receivables × rate

Reveal formulaTest your memory first

trade receivablesamount due from credit customers rateestimated doubtful percentage

Exam tipUse adjusted trade receivables after irrecoverable debts are removed.

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Accounting Standard New

☆

Profitability Ratios

Mark-up

Core & Extended

mark-up = gross profitcost of sales × 100%

Reveal formulaTest your memory first

gross profitrevenue − cost of sales cost of salescost of goods sold

Exam tipMark-up uses cost of sales as the denominator.

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Accounting Standard New

☆

Profitability Ratios

Profit margin

Core & Extended

profit margin = profit for the yearrevenue × 100%

Reveal formulaTest your memory first

profit for the yearnet profit revenuenet sales

Exam tipA fall may result from lower gross margin or higher expenses.

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Accounting Challenging New

☆

Profitability Ratios

Return on capital employed

Core & Extended

ROCE = net profit before interestcapital employed × 100%

Reveal formulaTest your memory first

capital employedissued shares + reserves + non-current liabilities

Exam tipUse profit before interest so returns are compared with all long-term finance.

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Accounting Challenging New

☆

Liquidity Ratios

Liquid (acid-test) ratio

Core & Extended

acid-test ratio = current assets − inventorycurrent liabilities

Reveal formulaTest your memory first

inventoryclosing inventory

Exam tipInventory is removed because it may not be quickly converted into cash.

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Accounting Standard New

☆

Efficiency Ratios

Rate of inventory turnover

Core & Extended

inventory turnover = cost of goods soldaverage inventory

Reveal formulaTest your memory first

average inventory(opening + closing inventory) ÷ 2

Exam tipA higher rate often means inventory is sold more quickly, but context matters.

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Accounting Standard New

☆

Efficiency Ratios

Trade receivables collection period

Core & Extended

receivables days = trade receivablescredit sales × 365

Reveal formulaTest your memory first

trade receivablesyear-end amount due credit salessales on credit

Exam tipCompare with the credit period offered to customers.

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Accounting Standard New

☆

Efficiency Ratios

Trade payables payment period

Core & Extended

payables days = trade payablescredit purchases × 365

Reveal formulaTest your memory first

trade payablesyear-end amount owed credit purchasespurchases on credit

Exam tipCompare with the credit period allowed by suppliers.

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Accounting Standard New

☆

Incomplete Records

Profit from capital changes

Core & Extended

profit = closing capital − opening capital + drawings − additional capital

Reveal formulaTest your memory first

drawingsowner withdrawals additional capitalnew capital introduced

Exam tipAdjust capital changes caused by drawings and fresh investment.

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Accounting Foundation New

☆

Income Statement

Net sales

Core & Extended

net sales = sales − returns inwards

Reveal formulaTest your memory first

returns inwardsgoods returned by customers

Exam tipReturns inwards reduce revenue.

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Accounting Foundation New

☆

Income Statement

Net purchases

Core & Extended

net purchases = purchases − returns outwards

Reveal formulaTest your memory first

returns outwardsgoods returned to suppliers

Exam tipCarriage inwards is added later when calculating cost of sales.

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Accounting Standard New

☆

Inventory

Cost of goods available for sale

Core & Extended

goods available = opening inventory + net purchases + carriage inwards

Reveal formulaTest your memory first

opening inventoryinventory at start carriage inwardscost of bringing purchases to the business

Exam tipInclude direct purchase costs such as carriage inwards.

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Accounting Standard New

☆

Inventory

Closing inventory from cost of sales

Core & Extended

closing inventory = goods available − cost of sales

Reveal formulaTest your memory first

goods availableopening inventory plus net purchase costs

Exam tipThis is a rearrangement of the cost-of-sales formula.

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Accounting Standard New

☆

Efficiency Ratios

Inventory holding period

Core & Extended

inventory days = average inventorycost of sales × 365

Reveal formulaTest your memory first

average inventoryaverage stock held cost of salescost of goods sold

Exam tipA lower number often indicates faster inventory movement, but context matters.

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Accounting Standard New

☆

Manufacturing Accounts

Prime cost

Core & Extended

prime cost = direct materials + direct labour + direct expenses

Reveal formulaTest your memory first

direct materialsmaterials traceable to production direct labourproduction wages traceable to units

Exam tipPrime cost contains only direct production costs.

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Accounting Standard New

☆

Analysis of Financial Statements

Dividend yield

A Level

dividend yield = dividend per share / market price per share × 100%

Reveal formulaTest your memory first

DPSdividend per share

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Challenging New

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Cost and Management Accounting

Material price variance

A Level

MPV = actual quantity × (standard price − actual price)

Reveal formulaTest your memory first

MPVmaterial price variance

Exam tipUse consistent units and identify every quantity before substituting.

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Accounting Challenging New

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Cost and Management Accounting

Material usage variance

A Level

MUV = standard price × (standard quantity − actual quantity)

Reveal formulaTest your memory first

MUVmaterial usage variance

Exam tipUse consistent units and identify every quantity before substituting.

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Additional Mathematics Standard Essential New

☆

Functions

Composite function

Extended

(f∘g)(x) = f(g(x))

Reveal formulaTest your memory first

f,gfunctions

Exam tipUse consistent units and identify every quantity before substituting.

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Additional Mathematics Standard Essential New

☆

Functions

Inverse function condition

Extended

f⁻¹(f(x)) = x

Reveal formulaTest your memory first

f⁻¹inverse function

Exam tipRestrict the domain when necessary so the function is one-to-one.

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Additional Mathematics Standard Essential New

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Coordinate Geometry

Circle equation

Extended

(x−a)²+(y−b)²=r²

Reveal formulaTest your memory first

a,bcentre rradius

Exam tipUse consistent units and identify every quantity before substituting.

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Additional Mathematics Standard Essential New

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Trigonometry

Sine addition formula

Extended

sin(A±B)=sinA cosB ± cosA sinB

Reveal formulaTest your memory first

A,Bangles

Exam tipUse consistent units and identify every quantity before substituting.

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Additional Mathematics Standard Essential New

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Trigonometry

Cosine addition formula

Extended

cos(A±B)=cosA cosB ∓ sinA sinB

Reveal formulaTest your memory first

A,Bangles

Exam tipUse consistent units and identify every quantity before substituting.

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Additional Mathematics Standard Essential New

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Differentiation

Product rule

Extended

d(uv)/dx = u(dv/dx)+v(du/dx)

Reveal formulaTest your memory first

u,vfunctions of x

Exam tipUse consistent units and identify every quantity before substituting.

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Additional Mathematics Standard Essential New

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Integration

Definite integral area

Extended

area = ∫ₐᵇ y dx

Reveal formulaTest your memory first

a,bx-limits ycurve equation

Exam tipAreas below the x-axis contribute negatively to the integral.

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Biology Standard Essential New

☆

Cell Structure

Magnification

AS & A Level

magnification = image size / actual size

Reveal formulaTest your memory first

image sizemeasured image dimension actual sizereal specimen dimension

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

☆

Gas Exchange and Respiration

Respiratory quotient

AS & A Level

RQ = CO₂ produced / O₂ consumed

Reveal formulaTest your memory first

RQrespiratory quotient CO₂carbon dioxide volume or moles O₂oxygen volume or moles

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

☆

Transport in Mammals

Cardiac output

AS & A Level

cardiac output = heart rate × stroke volume

Reveal formulaTest your memory first

heart ratebeats per minute stroke volumeblood per beat

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

☆

Water Relations

Water potential

AS & A Level

Ψ = Ψs + Ψp

Reveal formulaTest your memory first

Ψwater potential Ψssolute potential Ψppressure potential

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

☆

Ecology

Simpson diversity index

A Level

D = 1 − Σ[n(n−1)]/[N(N−1)]

Reveal formulaTest your memory first

nnumber of organisms of one species Ntotal organisms

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

☆

Genetics

Hardy–Weinberg allele equation

A Level

p + q = 1

Reveal formulaTest your memory first

pfrequency of one allele qfrequency of the other allele

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

☆

Genetics

Hardy–Weinberg genotype equation

A Level

p² + 2pq + q² = 1

Reveal formulaTest your memory first

p²homozygous dominant frequency 2pqheterozygous frequency q²homozygous recessive frequency

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

☆

Statistics

Chi-squared test

A Level

χ² = Σ(O−E)²/E

Reveal formulaTest your memory first

Oobserved frequency Eexpected frequency

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

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Practical Skills

Rate of a process

Core & Extended

rate = change / time

Reveal formulaTest your memory first

changemeasured change timetime interval

Exam tipUse consistent units and identify every quantity before substituting.

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Biology Standard Essential New

☆

Practical Skills

Percentage change

Core & Extended

percentage change = (new − original)/original × 100%

Reveal formulaTest your memory first

originalstarting value newfinal value

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

☆

Operations

Labour productivity

AS & A Level

labour productivity = output / number of employees

Reveal formulaTest your memory first

outputunits produced employeeslabour input

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

☆

Operations

Capacity utilisation

AS & A Level

capacity utilisation = actual output / maximum output × 100%

Reveal formulaTest your memory first

actual outputcurrent production maximum outputfull capacity

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

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Finance

Contribution

AS & A Level

contribution per unit = selling price − variable cost per unit

Reveal formulaTest your memory first

contributionamount toward fixed costs and profit

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

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Finance

Break-even output

AS & A Level

break-even output = fixed costs / contribution per unit

Reveal formulaTest your memory first

fixed costscosts independent of output

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

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Finance

Margin of safety

AS & A Level

margin of safety = actual output − break-even output

Reveal formulaTest your memory first

actual outputplanned or current sales

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

☆

Investment Appraisal

Payback period

A Level

payback = years before recovery + unrecovered amount / next year cash flow

Reveal formulaTest your memory first

unrecovered amountinvestment still outstanding

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

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Investment Appraisal

Accounting rate of return

A Level

ARR = average annual profit / initial investment × 100%

Reveal formulaTest your memory first

average annual profittotal net profit / project life

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

☆

Finance

Gross profit

Core & Extended

gross profit = revenue − cost of sales

Reveal formulaTest your memory first

revenuesales income cost of salesdirect cost of goods sold

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard Essential New

☆

Marketing

Market share

Core & Extended

market share = business sales / total market sales × 100%

Reveal formulaTest your memory first

business salessales of one firm market salesall firms combined

Exam tipUse consistent units and identify every quantity before substituting.

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Business Standard New

☆

Human Resources

Labour turnover

AS & A Level

labour turnover = employees leaving / average number employed × 100%

Reveal formulaTest your memory first

employees leavingdepartures in period

Exam tipUse consistent units and identify every quantity before substituting.

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Chemistry Foundation Essential New

☆

Stoichiometry

Moles from mass

Core & Extended

n = mM_r

Reveal formulaTest your memory first

namount of substance mmass Mᵣmolar mass

Exam tipUse grams with g/mol. For elements use Aᵣ instead of Mᵣ.

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Chemistry Standard Essential New

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Stoichiometry

Molar concentration

Core & Extended

c = nV

Reveal formulaTest your memory first

cconcentration namount of solute Vsolution volume

Exam tipConvert cm³ to dm³ by dividing by 1000.

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Chemistry Standard Essential New

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Stoichiometry

Percentage yield

Extended

percentage yield = actual yieldtheoretical yield × 100%

Reveal formulaTest your memory first

actual yieldmass actually obtained theoretical yieldmaximum calculated mass

Exam tipActual yield should not normally exceed theoretical yield.

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Chemistry Standard Essential New

☆

Stoichiometry

Weighted relative atomic mass

Extended

A_r = Σ(isotope mass × abundance)Σ abundance

Reveal formulaTest your memory first

Arrelative atomic mass

Exam tipAbundances may be percentages or simple ratios, but use them consistently.

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Chemistry Standard Essential New

☆

Stoichiometry

Stoichiometric mole ratio

Core & Extended

n(A)coefficient A = n(B)coefficient B

Reveal formulaTest your memory first

namount of substance

Exam tipUse coefficients from the balanced equation.

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Chemistry Standard Essential New

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Formulae

Molecular formula multiplier

Extended

multiplier = M_r of molecular formulaM_r of empirical formula

Reveal formulaTest your memory first

Mrrelative formula mass

Exam tipThe multiplier should be a whole number.

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☆

Stoichiometry

Percentage purity

Core & Extended

purity % = mass of pure substancemass of impure sample × 100%

Reveal formulaTest your memory first

pure massmass of desired substance

Exam tipThe pure mass is usually found from reaction data.

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Titration

Titration mole relationship

Extended

c₁V₁coefficient 1 = c₂V₂coefficient 2

Reveal formulaTest your memory first

cmolar concentration Vsolution volume

Exam tipConvert cm³ to dm³ unless both volumes cancel in a ratio.

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Experimental Techniques

Volume conversion

Core & Extended

V(dm³) = V(cm³)1000

Reveal formulaTest your memory first

Vvolume

Exam tipOne dm³ equals 1000 cm³.

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☆

Amounts of Substance

Ideal gas equation

AS & A Level

pV = nRT

Reveal formulaTest your memory first

ppressure Vvolume namount Rgas constant +1

Exam tipUse consistent units and identify every quantity before substituting.

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☆

Energetics

Enthalpy change from bond energies

AS & A Level

ΔH = ΣE(bonds broken) − ΣE(bonds formed)

Reveal formulaTest your memory first

ΔHreaction enthalpy Ebond energy

Exam tipUse consistent units and identify every quantity before substituting.

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☆

Kinetics

Rate of reaction

AS & A Level

rate = change in concentration / time

Reveal formulaTest your memory first

ratereaction rate concentrationamount per volume

Exam tipUse consistent units and identify every quantity before substituting.

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Kinetics

Arrhenius equation

A Level

k = Ae⁻ᴱᵃ/(RT)

Reveal formulaTest your memory first

krate constant Afrequency factor Eₐactivation energy Rgas constant +1

Exam tipUse consistent units and identify every quantity before substituting.

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Equilibria

Equilibrium constant Kc

A Level

Kc = product concentrations^coefficients / reactant concentrations^coefficients

Reveal formulaTest your memory first

Kcconcentration equilibrium constant [X]equilibrium concentration

Exam tipUse consistent units and identify every quantity before substituting.

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Equilibria

Equilibrium constant Kp

A Level

Kp = product partial pressures^coefficients / reactant partial pressures^coefficients

Reveal formulaTest your memory first

Kppressure equilibrium constant ppartial pressure

Exam tipUse consistent units and identify every quantity before substituting.

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Acid–Base Equilibria

pH definition

A Level

pH = −log₁₀[H⁺]

Reveal formulaTest your memory first

pHacidity scale [H⁺]hydrogen ion concentration

Exam tipUse consistent units and identify every quantity before substituting.

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☆

Acid–Base Equilibria

Ionic product of water

A Level

Kᵥ = [H⁺][OH⁻]

Reveal formulaTest your memory first

Kᵥionic product of water

Exam tipUse consistent units and identify every quantity before substituting.

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☆

Acid–Base Equilibria

Acid dissociation constant

A Level

Kₐ = [H⁺][A⁻]/[HA]

Reveal formulaTest your memory first

Kₐacid dissociation constant HAweak acid A⁻conjugate base

Exam tipUse consistent units and identify every quantity before substituting.

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Electrochemistry

Charge passed

A Level

Q = It

Reveal formulaTest your memory first

Qcharge Icurrent ttime

Exam tipUse consistent units and identify every quantity before substituting.

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Electrochemistry

Moles of electrons

A Level

n(e⁻) = Q/F

Reveal formulaTest your memory first

Qcharge FFaraday constant

Exam tipUse consistent units and identify every quantity before substituting.

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Electrochemistry

Standard cell potential

A Level

E°cell = E°cathode − E°anode

Reveal formulaTest your memory first

E°cellstandard cell potential

Exam tipUse consistent units and identify every quantity before substituting.

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Thermodynamics

Gibbs free energy

A Level

ΔG = ΔH − TΔS

Reveal formulaTest your memory first

ΔGGibbs change ΔHenthalpy change Ttemperature ΔSentropy change

Exam tipUse consistent units and identify every quantity before substituting.

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Analysis

Chromatography Rf value

AS & A Level

Rᶠ = distance moved by solute / distance moved by solvent front

Reveal formulaTest your memory first

Rᶠretention factor

Exam tipUse consistent units and identify every quantity before substituting.

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Stoichiometry

Relative atomic mass

Core & Extended

A_r = Σ(isotope mass × abundance)Σabundance

Reveal formulaTest your memory first

Aᵣrelative atomic mass abundancepercentage or proportion

Exam tipUse all abundances in the same form. If percentages total 100, divide by 100.

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☆

Stoichiometry

Relative formula mass

Core & Extended

M_r = ΣA_r

Reveal formulaTest your memory first

Mᵣrelative formula/molecular mass Aᵣrelative atomic mass

Exam tipMultiply each Aᵣ by its subscript before adding.

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Stoichiometry

Mass from moles

Core & Extended

m = nM_r

Reveal formulaTest your memory first

mmass namount Mᵣmolar mass

Exam tipFirst use the balanced equation to find the required mole ratio.

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☆

Stoichiometry

Number of particles

Extended

N = nN_A

Reveal formulaTest your memory first

Nnumber of particles namount NₐAvogadro constant

Exam tipState whether particles are atoms, molecules, ions or formula units.

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☆

Stoichiometry

Moles in solution

Core & Extended

n = cV

Reveal formulaTest your memory first

namount cconcentration Vvolume

Exam tipVolume must be in dm³ when concentration is mol/dm³.

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☆

Stoichiometry

Mass concentration

Core & Extended

concentration = mass of solutevolume of solution

Reveal formulaTest your memory first

massmass of dissolved solute volumevolume of solution

Exam tipDo not confuse g/dm³ with mol/dm³.

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☆

Stoichiometry

Gas volume at room conditions

Extended

V = 24n

Reveal formulaTest your memory first

Vgas volume at r.t.p. namount of gas

Exam tipAt room temperature and pressure, 1 mol gas occupies approximately 24 dm³.

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Stoichiometry

Atom economy

Extended

atom economy = M_r of desired producttotal M_r of all products × 100%

Reveal formulaTest your memory first

Mᵣrelative formula mass

Exam tipUse coefficients from the balanced equation when totaling product masses.

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☆

Stoichiometry

Percentage by mass

Extended

% by mass = mass of element in one moleM_r of compound × 100%

Reveal formulaTest your memory first

Mᵣrelative formula mass

Exam tipInclude the number of atoms of the element in the formula.

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Rates of Reaction

Average rate

Core & Extended

rate = change in quantitytime

Reveal formulaTest your memory first

quantitymass, volume, concentration or amount timetime interval

Exam tipState units from the measured quantity, e.g. cm³/s or g/s.

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☆

Experimental Techniques

Chromatography Rf value

Core & Extended

R_f = distance moved by substancedistance moved by solvent front

Reveal formulaTest your memory first

Rᶠretention factor distancemeasured from start line

Exam tipRᶠ is between 0 and 1 when measured correctly.

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☆

Energetics

Thermal energy change

Extended

q = mcΔT

Reveal formulaTest your memory first

qenergy transferred mmass of solution cspecific heat capacity ΔTtemperature change

Exam tipFor dilute aqueous solutions, c is often taken as 4.18 J/(g °C) when instructed.

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Energetics

Bond energy enthalpy change

Extended

ΔH = ΣE(bonds broken) − ΣE(bonds formed)

Reveal formulaTest your memory first

ΔHenthalpy change Ebond energy

Exam tipBreaking bonds absorbs energy; forming bonds releases energy.

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☆

Solutions

Dilution

Extended

c₁V₁ = c₂V₂

Reveal formulaTest your memory first

c₁initial concentration V₁initial volume c₂final concentration V₂final volume

Exam tipUse only for dilution where the amount of solute remains unchanged.

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Empirical Formula

Empirical formula steps

Extended

moles of each element = massA_r

Reveal formulaTest your memory first

massmass or percentage of element Aᵣrelative atomic mass

Exam tipDivide all mole values by the smallest, then convert to whole numbers.

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Stoichiometry

Reacting mass ratio

Extended

m(A)coefficient A × M_r(A) = m(B)coefficient B × M_r(B)

Reveal formulaTest your memory first

mmass Mrrelative formula mass

Exam tipThis combines moles = mass/Mr with the equation ratio.

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☆

Stoichiometry

Gas volume ratio

Core & Extended

V(A)coefficient A = V(B)coefficient B

Reveal formulaTest your memory first

Vgas volume at the same temperature and pressure

Exam tipGas volumes follow the equation ratio when conditions are the same.

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Hydrated Salts

Water of crystallisation

Extended

x = moles of H₂Omoles of anhydrous salt

Reveal formulaTest your memory first

xnumber of water molecules per formula unit

Exam tipUse mass lost on heating as the mass of water.

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☆

Solutions

Molar concentration from mass

Extended

c = mM_rV

Reveal formulaTest your memory first

cmolar concentration msolute mass Mrrelative formula mass Vsolution volume

Exam tipThis combines n = m/Mr and c = n/V.

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Acid–Base Equilibria

pKa definition

A Level

pKₐ = −log₁₀Kₐ

Reveal formulaTest your memory first

pKₐlogarithmic acid-strength measure Kₐacid dissociation constant

Exam tipUse consistent units and identify every quantity before substituting.

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Data Representation

Uncompressed bitmap size

AS & A Level

file size (bits) = width × height × colour depth

Reveal formulaTest your memory first

width,heightpixel dimensions colour depthbits per pixel

Exam tipUse consistent units and identify every quantity before substituting.

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Data Representation

Uncompressed sound size

AS & A Level

file size = sample rate × sample resolution × channels × duration

Reveal formulaTest your memory first

sample ratesamples per second resolutionbits per sample durationrecording time

Exam tipUse consistent units and identify every quantity before substituting.

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Communication

Data transfer time

AS & A Level

time = data size / transfer rate

Reveal formulaTest your memory first

timetransfer duration data sizeamount transferred transfer ratebits per second

Exam tipUse consistent units and identify every quantity before substituting.

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☆

Data Compression

Compression ratio

AS & A Level

compression ratio = original size / compressed size

Reveal formulaTest your memory first

original sizebefore compression compressed sizeafter compression

Exam tipUse consistent units and identify every quantity before substituting.

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☆

Data Representation

Image file size

Core & Extended

bits = pixels × colour depth

Reveal formulaTest your memory first

pixelswidth × height colour depthbits per pixel

Exam tipUse consistent units and identify every quantity before substituting.

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Communication

Transfer time

Core & Extended

time = file size / bit rate

Reveal formulaTest your memory first

file sizeamount of data bit ratetransfer speed

Exam tipUse consistent units and identify every quantity before substituting.

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☆

Hash Tables

Load factor

A Level

load factor = occupied slots / total slots

Reveal formulaTest your memory first

occupied slotsstored entries total slotstable capacity

Exam tipUse consistent units and identify every quantity before substituting.

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Processor Fundamentals

CPU execution time

A Level

CPU time = instruction count × CPI / clock rate

Reveal formulaTest your memory first

CPIaverage cycles per instruction clock ratecycles per second

Exam tipUse consistent units and identify every quantity before substituting.

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Elasticity

Price elasticity of demand

Core & Extended

PED = %Δ quantity demanded%Δ price

Reveal formulaTest your memory first

PEDprice elasticity of demand %Δpercentage change

Exam tipPED is usually negative because price and demand move oppositely; many questions use its absolute value.

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Firms and Production

Total revenue

Core & Extended

TR = P × Q

Reveal formulaTest your memory first

TRtotal revenue Pprice per unit Qquantity sold

Exam tipRevenue is not the same as profit because costs have not been deducted.

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Firms and Production

Total cost

Core & Extended

TC = TFC + TVC

Reveal formulaTest your memory first

TCtotal cost TFCtotal fixed cost TVCtotal variable cost

Exam tipFixed costs do not change with output in the short run.

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Firms and Production

Profit

Core & Extended

Profit = TR − TC

Reveal formulaTest your memory first

TRtotal revenue TCtotal cost

Exam tipIf total cost exceeds total revenue, the firm makes a loss.

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Macroeconomics

Inflation rate

Core & Extended

inflation = new CPI − old CPIold CPI × 100%

Reveal formulaTest your memory first

CPIconsumer price index

Exam tipA falling inflation rate still means prices are rising, just more slowly.

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Macroeconomics

Unemployment rate

Core & Extended

unemployment rate = unemployedlabour force × 100%

Reveal formulaTest your memory first

labour forceemployed + unemployed actively seeking work

Exam tipPeople outside the labour force are not counted as unemployed.

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Price Indices

Price index

Core & Extended

price index = current pricebase-year price × 100

Reveal formulaTest your memory first

base yearreference year with index 100

Exam tipAn index above 100 means the price is higher than in the base year.

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Price Indices

Weighted price index

Extended

weighted index = Σ(weight × price relative)Σ weights

Reveal formulaTest your memory first

weightrelative importance in household spending price relativecurrent price ÷ base price × 100

Exam tipItems with larger weights have a greater effect on the index.

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Macroeconomics

Real GDP

Extended

real GDP = nominal GDPGDP deflator × 100

Reveal formulaTest your memory first

nominal GDPGDP at current prices GDP deflatorprice index for domestic output

Exam tipReal GDP removes the effect of price changes.

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International Trade

Balance of trade

Core & Extended

balance of trade = value of visible exports − value of visible imports

Reveal formulaTest your memory first

exportsgoods sold abroad importsgoods bought from abroad

Exam tipA positive value is a trade surplus; a negative value is a trade deficit.

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Firms and Production

Market share

Core & Extended

market share = firm’s salestotal market sales × 100%

Reveal formulaTest your memory first

firm salessales of one business market salessales by all firms

Exam tipUse the same measurement for the numerator and denominator.

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Elasticity

Price elasticity of demand

AS & A Level

PED = %ΔQd / %ΔP

Reveal formulaTest your memory first

Qdquantity demanded Pprice

Exam tipUse consistent units and identify every quantity before substituting.

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Elasticity

Income elasticity of demand

AS & A Level

YED = %ΔQd / %ΔY

Reveal formulaTest your memory first

Yconsumer income

Exam tipUse consistent units and identify every quantity before substituting.

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Elasticity

Cross elasticity of demand

AS & A Level

XED = %ΔQd of X / %ΔP of Y

Reveal formulaTest your memory first

XEDcross elasticity

Exam tipUse consistent units and identify every quantity before substituting.

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International Trade

Terms of trade index

AS & A Level

terms of trade = export price index / import price index × 100

Reveal formulaTest your memory first

export price indexaverage export prices import price indexaverage import prices

Exam tipUse consistent units and identify every quantity before substituting.

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Macroeconomics

Simple Keynesian multiplier

A Level

k = 1/(1−MPC) = 1/MPS

Reveal formulaTest your memory first

kmultiplier MPCmarginal propensity to consume MPSmarginal propensity to save

Exam tipUse consistent units and identify every quantity before substituting.

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Macroeconomic Indicators

GDP deflator

AS & A Level

GDP deflator = nominal GDP / real GDP × 100

Reveal formulaTest your memory first

nominal GDPGDP at current prices real GDPGDP at constant prices

Exam tipUse consistent units and identify every quantity before substituting.

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Elasticity

Price elasticity of supply

Core & Extended

PES = %Δ quantity supplied%Δ price

Reveal formulaTest your memory first

PESprice elasticity of supply

Exam tipPES is normally positive because price and supply move in the same direction.

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Elasticity

Income elasticity of demand

Extended

YED = %Δ quantity demanded%Δ income

Reveal formulaTest your memory first

YEDincome elasticity of demand

Exam tipPositive YED indicates a normal good; negative YED indicates an inferior good.

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Elasticity

Cross elasticity of demand

Extended

XED = %Δ demand for X%Δ price of Y

Reveal formulaTest your memory first

XEDcross elasticity of demand

Exam tipPositive XED suggests substitutes; negative XED suggests complements.

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Firms and Production

Average revenue

Core & Extended

AR = TRQ

Reveal formulaTest your memory first

ARaverage revenue TRtotal revenue Qquantity

Exam tipFor a single-price firm, average revenue equals price.

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Firms and Production

Average cost

Core & Extended

AC = TCQ

Reveal formulaTest your memory first

ACaverage cost TCtotal cost Qoutput

Exam tipAverage cost may fall as output rises due to economies of scale.

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☆

Labour and Productivity

Labour productivity

Core & Extended

productivity = outputlabour input

Reveal formulaTest your memory first

outputunits produced labour inputworkers or worker-hours

Exam tipUse the labour-input measure stated in the question.

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Macroeconomics

Economic growth rate

Core & Extended

growth rate = new real GDP − old real GDPold real GDP × 100%

Reveal formulaTest your memory first

real GDPinflation-adjusted output

Exam tipUse real GDP, not nominal GDP, when measuring changes in output.

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Development

Real GDP per head

Core & Extended

real GDP per head = real GDPpopulation

Reveal formulaTest your memory first

real GDPinflation-adjusted national output populationnumber of people

Exam tipIt is an average and does not show income distribution or non-material living standards.

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International Trade

Terms of trade index

Extended

terms of trade = export price indeximport price index × 100

Reveal formulaTest your memory first

export price indexindex of export prices import price indexindex of import prices

Exam tipA rise is an improvement in the terms of trade, though its overall effect depends on elasticities and…

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Exchange Rates

Currency conversion

Core & Extended

domestic currency = foreign currency × exchange rate; foreign currency = domestic currency ÷ exchange rate

Reveal formulaTest your memory first

exchange ratedomestic currency units per 1 foreign currency unit

Exam tipFirst identify how the exchange rate is quoted. Multiply when converting foreign currency into domestic currency; divide for…

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Labour Markets

Real wage index

Extended

real wage index = money wage indexconsumer price index × 100

Reveal formulaTest your memory first

money wage indexnominal wage index CPIconsumer price index

Exam tipReal wages rise only when money wages rise faster than prices.

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Macroeconomics

GDP deflator

Extended

GDP deflator = nominal GDPreal GDP × 100

Reveal formulaTest your memory first

nominal GDPcurrent-price output real GDPconstant-price output

Exam tipThe base year has a deflator of 100.

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Government Finance

Government budget balance

Core & Extended

budget balance = government revenue − government expenditure

Reveal formulaTest your memory first

revenuetax and other government income expendituregovernment spending

Exam tipA negative result is a budget deficit.

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Population

Population growth rate

Extended

growth rate = births − deaths + net migrationpopulation × 100%

Reveal formulaTest your memory first

net migrationimmigration − emigration

Exam tipUse figures from the same time period.

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Labour Markets

Labour-force participation rate

Extended

participation rate = labour forceworking-age population × 100%

Reveal formulaTest your memory first

labour forceemployed plus unemployed people seeking work

Exam tipPeople outside the labour force are not counted as unemployed.

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Macroeconomics

Marginal propensities

A Level

MPC = ΔC/ΔY; MPS = ΔS/ΔY

Reveal formulaTest your memory first

Cconsumption Ssaving Yincome

Exam tipUse consistent units and identify every quantity before substituting.

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Macroeconomic Indicators

Real GDP per head

AS & A Level

real GDP per head = real GDP / population

Reveal formulaTest your memory first

real GDPinflation-adjusted output populationnumber of people

Exam tipUse consistent units and identify every quantity before substituting.

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Complex Numbers

Modulus of a complex number

AS & A Level

|z| = √(x² + y²)

Reveal formulaTest your memory first

zx+iy xreal part yimaginary part

Exam tipUse consistent units and identify every quantity before substituting.

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Complex Numbers

Euler form

AS & A Level

eⁱθ = cos θ + i sin θ

Reveal formulaTest your memory first

i√−1 θargument

Exam tipUse consistent units and identify every quantity before substituting.

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Complex Numbers

De Moivre theorem

AS & A Level

(cos θ + i sin θ)ⁿ = cos(nθ) + i sin(nθ)

Reveal formulaTest your memory first

ninteger power θangle

Exam tipUse consistent units and identify every quantity before substituting.

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Matrices

Inverse of a 2×2 matrix

AS & A Level

A⁻¹ = 1/(ad−bc) [[d,−b],[−c,a]]

Reveal formulaTest your memory first

ad−bcdeterminant of A

Exam tipThe inverse exists only when ad−bc ≠ 0.

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Matrices

Eigenvalue equation

AS & A Level

det(A − λI) = 0

Reveal formulaTest your memory first

Asquare matrix λeigenvalue Iidentity matrix

Exam tipUse consistent units and identify every quantity before substituting.

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Polar Coordinates

Area in polar coordinates

A Level

A = ½∫r² dθ

Reveal formulaTest your memory first

rpolar radius θpolar angle

Exam tipUse consistent units and identify every quantity before substituting.

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Further Mechanics

Elastic string tension

A Level

T = λx/l

Reveal formulaTest your memory first

Ttension λmodulus of elasticity xextension lnatural length

Exam tipUse consistent units and identify every quantity before substituting.

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Further Statistics

Chi-squared statistic

A Level

χ² = Σ(O−E)²/E

Reveal formulaTest your memory first

Oobserved frequency Eexpected frequency

Exam tipUse consistent units and identify every quantity before substituting.

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Matrices

Eigenvector relation

AS & A Level

Av = λv

Reveal formulaTest your memory first

veigenvector λcorresponding eigenvalue

Exam tipUse consistent units and identify every quantity before substituting.

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Hyperbolic Functions

Hyperbolic definitions

A Level

cosh x = (eˣ+e⁻ˣ)/2; sinh x = (eˣ−e⁻ˣ)/2

Reveal formulaTest your memory first

xreal variable

Exam tipUse consistent units and identify every quantity before substituting.

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Hyperbolic Functions

Hyperbolic identity

A Level

cosh²x − sinh²x = 1

Reveal formulaTest your memory first

xreal variable

Exam tipUse consistent units and identify every quantity before substituting.

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Further Mechanics

Projectile trajectory

A Level

y = x tan θ − gx²/(2V²cos²θ)

Reveal formulaTest your memory first

Vprojection speed θprojection angle ggravitational acceleration

Exam tipUse consistent units and identify every quantity before substituting.

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Further Mechanics

Elastic potential energy

A Level

E = λx²/(2l)

Reveal formulaTest your memory first

Eelastic energy λmodulus xextension lnatural length

Exam tipUse consistent units and identify every quantity before substituting.

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Number

Percentage change

Core & Extended

percentage change = changeoriginal value × 100%

Reveal formulaTest your memory first

changenew value − original value original valuestarting value

Exam tipThe denominator is always the original value.

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Algebra

Quadratic formula

Core & Extended

x = −b ± √(b² − 4ac)2a

Reveal formulaTest your memory first

a, b, ccoefficients in ax² + bx + c = 0 xsolution

Exam tipWrite the equation in the form ax² + bx + c = 0 first.

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Coordinate Geometry

Gradient

Core & Extended

m = y₂ − y₁x₂ − x₁

Reveal formulaTest your memory first

mgradient (x₁,y₁),(x₂,y₂)two points on the line

Exam tipKeep the subtraction order the same on top and bottom.

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Coordinate Geometry

Straight-line equation

Core & Extended

y = mx + c

Reveal formulaTest your memory first

mgradient cy-intercept

Exam tipc is the value of y when x = 0.

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Mensuration

Area of a circle

Core & Extended

A = πr²

Reveal formulaTest your memory first

Aarea rradius

Exam tipSquare the radius, not the diameter.

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Trigonometry

Pythagoras’ theorem

Core & Extended

a² + b² = c²

Reveal formulaTest your memory first

chypotenuse a, bother two sides

Exam tipc is always opposite the right angle.

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Trigonometry

Sine rule

Extended

asin A = bsin B = csin C

Reveal formulaTest your memory first

a, b, cside lengths A, B, Copposite angles

Exam tipPair each side with its opposite angle.

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Trigonometry

Cosine rule

Extended

a² = b² + c² − 2bc cos A

Reveal formulaTest your memory first

aside opposite A b, cother sides Aincluded/opposite angle

Exam tipUse for SSS or SAS data.

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Statistics

Mean

Core & Extended

mean = Σxn

Reveal formulaTest your memory first

Σxsum of all values nnumber of values

Exam tipInclude repeated values separately unless using frequencies.

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Percentages

Profit percentage

Core & Extended

profit % = profitcost price × 100%

Reveal formulaTest your memory first

profitselling price − cost price

Exam tipProfit percentage is based on cost price unless the question states otherwise.

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Percentages

Reverse percentage

Core & Extended

original = finalmultiplier

Reveal formulaTest your memory first

multiplier1 + rate for an increase, or 1 − rate for a decrease

Exam tipConvert the percentage change into a decimal multiplier first.

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Algebraic Identities

Difference of two squares

Core & Extended

a² − b² = (a − b)(a + b)

Reveal formulaTest your memory first

a, balgebraic terms

Exam tipThis works only for a subtraction of two perfect squares.

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Coordinate Geometry

Point–slope equation

Extended

y − y₁ = m(x − x₁)

Reveal formulaTest your memory first

mgradient (x1,y1)known point on the line

Exam tipThis is useful when a gradient and one point are given.

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Angles and Polygons

Interior angle of a regular polygon

Core & Extended

interior angle = (n − 2) × 180°n

Reveal formulaTest your memory first

nnumber of sides

Exam tipAll interior angles are equal only in a regular polygon.

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Mensuration

Total surface area of a cylinder

Core & Extended

A = 2πr² + 2πrh

Reveal formulaTest your memory first

rradius hheight

Exam tipThe two circular ends contribute 2πr².

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Statistics

Estimated mean from grouped data

Core & Extended

estimated mean = ΣfxΣf

Reveal formulaTest your memory first

ffrequency xclass midpoint

Exam tipUse class midpoints, so the result is an estimate.

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Statistics

Interquartile range

Core & Extended

IQR = Q₃ − Q₁

Reveal formulaTest your memory first

Q1lower quartile Q3upper quartile

Exam tipIQR describes the spread of the middle 50% of the data.

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Probability

General addition rule

Extended

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Reveal formulaTest your memory first

A ∪ BA or B A ∩ BA and B

Exam tipSubtract the overlap because it was counted twice.

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Probability

Expected frequency

Core & Extended

expected frequency = probability × number of trials

Reveal formulaTest your memory first

pprobability of the outcome nnumber of trials

Exam tipAn expected frequency does not have to be exactly what happens.

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Pure Mathematics

Arithmetic sequence nth term

AS & A Level

uₙ = a + (n − 1)d

Reveal formulaTest your memory first

uₙnth term afirst term dcommon difference nterm number

Exam tipUse when consecutive terms change by a constant difference.

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Pure Mathematics

Arithmetic series sum

AS & A Level

Sₙ = n/2[2a + (n − 1)d]

Reveal formulaTest your memory first

Sₙsum of first n terms afirst term dcommon difference nnumber of terms

Exam tipUse consistent units and identify every quantity before substituting.

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Pure Mathematics

Geometric sequence nth term

AS & A Level

uₙ = arⁿ⁻¹

Reveal formulaTest your memory first

uₙnth term afirst term rcommon ratio nterm number

Exam tipUse consistent units and identify every quantity before substituting.

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Pure Mathematics

Infinite geometric series

AS & A Level

S∞ = a/(1 − r), |r| < 1

Reveal formulaTest your memory first

S∞sum to infinity afirst term rcommon ratio

Exam tipUse consistent units and identify every quantity before substituting.

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Pure Mathematics

Binomial coefficient

AS & A Level

ⁿCᵣ = n!/[r!(n − r)!]

Reveal formulaTest your memory first

ntotal selections rnumber chosen !factorial

Exam tipUse consistent units and identify every quantity before substituting.

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Circular Measure

Arc length in radians

AS & A Level

s = rθ

Reveal formulaTest your memory first

sarc length rradius θangle in radians

Exam tipUse consistent units and identify every quantity before substituting.

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Circular Measure

Sector area in radians

AS & A Level

A = ½r²θ

Reveal formulaTest your memory first

Asector area rradius θangle in radians

Exam tipUse consistent units and identify every quantity before substituting.

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Coordinate Geometry

Circle equation

AS & A Level

(x − a)² + (y − b)² = r²

Reveal formulaTest your memory first

a,bcentre coordinates rradius

Exam tipUse consistent units and identify every quantity before substituting.

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Algebra

Quadratic discriminant

AS & A Level

Δ = b² − 4ac

Reveal formulaTest your memory first

Δdiscriminant a,b,ccoefficients of ax²+bx+c

Exam tipΔ>0 gives two real roots, Δ=0 one repeated root, Δ<0 no real roots.

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Differentiation

Power rule

AS & A Level

d(xⁿ)/dx = nxⁿ⁻¹

Reveal formulaTest your memory first

nconstant power xvariable

Exam tipUse consistent units and identify every quantity before substituting.

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Differentiation

Product rule

AS & A Level

d(uv)/dx = u(dv/dx) + v(du/dx)

Reveal formulaTest your memory first

u,vfunctions of x

Exam tipUse consistent units and identify every quantity before substituting.

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Differentiation

Chain rule

AS & A Level

dy/dx = (dy/du)(du/dx)

Reveal formulaTest your memory first

uintermediate variable ydependent variable

Exam tipUse consistent units and identify every quantity before substituting.

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Differentiation

Trigonometric derivatives

A Level

d(sin x)/dx = cos x; d(cos x)/dx = −sin x; d(tan x)/dx = sec²x

Reveal formulaTest your memory first

xangle in radians

Exam tipUse consistent units and identify every quantity before substituting.

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Integration

Power integration rule

AS & A Level

∫xⁿ dx = xⁿ⁺¹/(n+1) + C, n ≠ −1

Reveal formulaTest your memory first

nconstant power Cconstant of integration

Exam tipUse consistent units and identify every quantity before substituting.

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Numerical Methods

Newton–Raphson iteration

A Level

xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ)

Reveal formulaTest your memory first

xₙcurrent approximation xₙ₊₁next approximation

Exam tipUse consistent units and identify every quantity before substituting.

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Mechanics

Constant acceleration velocity

AS & A Level

v = u + at

Reveal formulaTest your memory first

uinitial velocity vfinal velocity aacceleration ttime

Exam tipUse consistent units and identify every quantity before substituting.

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Mechanics

Constant acceleration displacement

AS & A Level

s = ut + ½at²

Reveal formulaTest your memory first

sdisplacement uinitial velocity aacceleration ttime

Exam tipUse consistent units and identify every quantity before substituting.

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Mechanics

Force and acceleration

AS & A Level

F = ma

Reveal formulaTest your memory first

Fresultant force mmass aacceleration

Exam tipUse consistent units and identify every quantity before substituting.

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Mechanics

Impulse and momentum

AS & A Level

I = Ft = mv − mu

Reveal formulaTest your memory first

Iimpulse Fconstant force mmass u,vinitial and final velocity

Exam tipUse consistent units and identify every quantity before substituting.

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Probability & Statistics

Conditional probability

AS & A Level

P(A|B) = P(A∩B)/P(B)

Reveal formulaTest your memory first

P(A|B)probability of A given B P(A∩B)probability both occur

Exam tipUse consistent units and identify every quantity before substituting.

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Probability & Statistics

Binomial probability

AS & A Level

P(X=r) = ⁿCᵣpʳ(1−p)ⁿ⁻ʳ

Reveal formulaTest your memory first

nnumber of trials rsuccesses psuccess probability

Exam tipUse consistent units and identify every quantity before substituting.

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Probability & Statistics

Standard normal transformation

AS & A Level

z = (x − μ)/σ

Reveal formulaTest your memory first

zstandard score xobserved value μmean σstandard deviation

Exam tipUse consistent units and identify every quantity before substituting.

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Number

Simple interest

Core & Extended

I = PRT100

Reveal formulaTest your memory first

Iinterest Pprincipal Rannual rate Ttime

Exam tipSimple interest is calculated only on the original principal.

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Number

Compound growth or decay

Core & Extended

final = initial × (1 ± r)ⁿ

Reveal formulaTest your memory first

rrate as a decimal nnumber of periods

Exam tipUse + for growth and − for depreciation. Convert percentage to decimal.

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Ratio and Proportion

Direct proportion

Core & Extended

y = kx

Reveal formulaTest your memory first

kconstant of proportionality

Exam tipFor direct proportion, y/x is constant and the graph passes through the origin.

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Ratio and Proportion

Inverse proportion

Extended

y = kx

Reveal formulaTest your memory first

kconstant of proportionality

Exam tipFor inverse proportion, xy is constant.

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Algebra

Discriminant

Extended

D = b² − 4ac

Reveal formulaTest your memory first

Ddiscriminant a, b, cquadratic coefficients

Exam tipD > 0: two real roots; D = 0: one repeated root; D < 0: no real roots.

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Sequences

Arithmetic sequence nth term

Core & Extended

u_n = a + (n − 1)d

Reveal formulaTest your memory first

uₙnth term afirst term dcommon difference nterm number

Exam tipCheck that the difference between consecutive terms is constant.

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Sequences

Geometric sequence nth term

Extended

u_n = arⁿ⁻¹

Reveal formulaTest your memory first

uₙnth term afirst term rcommon ratio nterm number

Exam tipThe ratio between consecutive terms must be constant.

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Coordinate Geometry

Perpendicular gradients

Extended

m₁m₂ = −1

Reveal formulaTest your memory first

m₁, m₂gradients of perpendicular non-vertical lines

Exam tipThe perpendicular gradient is the negative reciprocal.

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Coordinate Geometry

Midpoint

Core & Extended

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Reveal formulaTest your memory first

Mmidpoint (x₁,y₁),(x₂,y₂)endpoints

Exam tipAverage the x-coordinates and y-coordinates separately.

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Coordinate Geometry

Distance between two points

Extended

d = √((x₂ − x₁)² + (y₂ − y₁)²)

Reveal formulaTest your memory first

ddistance (x₁,y₁),(x₂,y₂)points

Exam tipThis is Pythagoras’ theorem applied to horizontal and vertical changes.

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Angles and Polygons

Interior angle sum

Core & Extended

sum = (n − 2) × 180°

Reveal formulaTest your memory first

nnumber of sides

Exam tipThis gives the total of all interior angles of any polygon.

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Angles and Polygons

Exterior angle of a regular polygon

Core & Extended

exterior angle = 360°n

Reveal formulaTest your memory first

nnumber of sides

Exam tipOne exterior angle plus one interior angle equals 180° for a regular polygon.

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Mensuration

Area of a triangle

Core & Extended

A = ½bh

Reveal formulaTest your memory first

Aarea bbase hperpendicular height

Exam tipThe height must be perpendicular to the chosen base.

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Mensuration

Area of a parallelogram

Core & Extended

A = bh

Reveal formulaTest your memory first

Aarea bbase hperpendicular height

Exam tipDo not use the sloping side as the height unless it is perpendicular.

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Mensuration

Area of a trapezium

Core & Extended

A = ½(a + b)h

Reveal formulaTest your memory first

a, bparallel sides hperpendicular height

Exam tipOnly a and b are the parallel sides.

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Mensuration

Circumference of a circle

Core & Extended

C = 2πr = πd

Reveal formulaTest your memory first

Ccircumference rradius ddiameter

Exam tipDiameter = 2 × radius.

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Mensuration

Arc length

Extended

arc length = θ360° × 2πr

Reveal formulaTest your memory first

θcentral angle rradius

Exam tipUse the central angle of the sector.

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Mensuration

Area of a sector

Extended

sector area = θ360° × πr²

Reveal formulaTest your memory first

θcentral angle rradius

Exam tipA semicircle uses θ = 180°; a quarter-circle uses 90°.

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Mensuration

Volume of a prism

Core & Extended

V = Al

Reveal formulaTest your memory first

Vvolume Across-sectional area llength

Exam tipThe cross-section must be constant along the prism.

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Mensuration

Volume of a pyramid

Core & Extended

V = ⅓Ah

Reveal formulaTest your memory first

Vvolume Abase area hperpendicular height

Exam tipUse perpendicular height, not a sloping edge.

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Mensuration

Volume of a cylinder

Core & Extended

V = πr²h

Reveal formulaTest your memory first

Vvolume rradius hheight

Exam tipCylinder volume = circular cross-section × length.

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Mensuration

Curved surface area of a cylinder

Core & Extended

A = 2πrh

Reveal formulaTest your memory first

Acurved surface area rradius hheight

Exam tipTotal surface area also includes two circles: 2πr².

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Mensuration

Volume of a cone

Core & Extended

V = ⅓πr²h

Reveal formulaTest your memory first

Vvolume rradius hperpendicular height

Exam tipA cone has one-third the volume of a cylinder with the same base and height.

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Mensuration

Curved surface area of a cone

Core & Extended

A = πrl

Reveal formulaTest your memory first

Acurved surface area rradius lslant height

Exam tipUse slant height l, not vertical height h.

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Mensuration

Volume of a sphere

Core & Extended

V = 43πr³

Reveal formulaTest your memory first

Vvolume rradius

Exam tipUse 4/3 × π × r³. Do not confuse volume with surface area.

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Mensuration

Surface area of a sphere

Core & Extended

A = 4πr²

Reveal formulaTest your memory first

Asurface area rradius

Exam tipA hemisphere’s curved area is 2πr²; add πr² if the circular base is included.

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Trigonometry

Sine ratio

Core & Extended

sin θ = oppositehypotenuse

Reveal formulaTest your memory first

θangle

Exam tipUse only in a right-angled triangle. Label sides relative to θ.

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Trigonometry

Cosine ratio

Core & Extended

cos θ = adjacenthypotenuse

Reveal formulaTest your memory first

θangle

Exam tipThe adjacent side is next to θ but is not the hypotenuse.

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Trigonometry

Tangent ratio

Core & Extended

tan θ = oppositeadjacent

Reveal formulaTest your memory first

θangle

Exam tipUse inverse tan to find an angle.

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Trigonometry

Area using sine

Extended

A = ½ab sin C

Reveal formulaTest your memory first

Aarea a, btwo sides Cincluded angle

Exam tipThe angle must lie between the two chosen sides.

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Similarity

Area scale factor

Core & Extended

area factor = k²

Reveal formulaTest your memory first

klinear scale factor

Exam tipAreas change with the square of the linear scale factor.

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Similarity

Volume scale factor

Core & Extended

volume factor = k³

Reveal formulaTest your memory first

klinear scale factor

Exam tipVolumes change with the cube of the linear scale factor.

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Statistics

Mean from a frequency table

Core & Extended

mean = ΣfxΣf

Reveal formulaTest your memory first

ffrequency xvalue or class midpoint

Exam tipFor grouped data, use class midpoints, so the answer is an estimate.

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Statistics

Frequency density

Extended

frequency density = frequencyclass width

Reveal formulaTest your memory first

frequencynumber in class class widthupper boundary − lower boundary

Exam tipHistogram bar area represents frequency.

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Probability

Complement rule

Core & Extended

P(not A) = 1 − P(A)

Reveal formulaTest your memory first

P(A)probability of event A

Exam tipAll probabilities lie between 0 and 1.

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Probability

Independent events

Extended

P(A and B) = P(A) × P(B)

Reveal formulaTest your memory first

P(A), P(B)probabilities of independent events

Exam tipMultiply along branches of a probability tree.

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Probability

Mutually exclusive events

Extended

P(A or B) = P(A) + P(B)

Reveal formulaTest your memory first

P(A), P(B)probabilities of mutually exclusive events

Exam tipAdd only when A and B cannot happen together.

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Percentages

Loss percentage

Core & Extended

loss % = losscost price × 100%

Reveal formulaTest your memory first

losscost price − selling price

Exam tipLoss percentage is also based on cost price.

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Finance

Amount with simple interest

Core & Extended

A = P(1 + rt)

Reveal formulaTest your memory first

Afinal amount Pprincipal rannual rate as a decimal ttime in years

Exam tipUse r = 0.06 for 6%.

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Standard Form

Multiplying standard form

Core & Extended

(a × 10^m)(b × 10ⁿ) = ab × 10^m+n

Reveal formulaTest your memory first

a, bnumbers from 1 up to but not including 10 m, ninteger powers

Exam tipMultiply the numbers and add the powers, then normalise the answer.

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Standard Form

Dividing standard form

Core & Extended

a × 10^mb × 10ⁿ = ab × 10^m−n

Reveal formulaTest your memory first

a, bcoefficients m, ninteger powers

Exam tipDivide the coefficients and subtract the powers.

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Algebra

Completing the square identity

Extended

x² + bx = (x + b2)² − (b2)²

Reveal formulaTest your memory first

bcoefficient of x

Exam tipTake half the coefficient of x.

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Coordinate Geometry

Parallel line gradients

Core & Extended

m₁ = m₂

Reveal formulaTest your memory first

m1, m2gradients of parallel non-vertical lines

Exam tipParallel lines have the same gradient.

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Coordinate Geometry

Gradient from angle

Extended

m = tan θ

Reveal formulaTest your memory first

mgradient θangle measured anticlockwise from the positive x-axis

Exam tipCheck how the angle is measured before using tangent.

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Pythagoras

Three-dimensional Pythagoras

Core & Extended

d = √(l² + w² + h²)

Reveal formulaTest your memory first

dspace diagonal l,w,hperpendicular dimensions

Exam tipAll three dimensions must use the same unit.

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Angles and Polygons

Number of sides from exterior angle

Core & Extended

n = 360°exterior angle

Reveal formulaTest your memory first

nnumber of sides

Exam tipThis applies to a regular polygon.

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Mensuration

Area of a rectangle

Core & Extended

A = lw

Reveal formulaTest your memory first

Aarea llength wwidth

Exam tipUse perpendicular side lengths.

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Mensuration

Area of a rhombus or kite

Core & Extended

A = 12d₁d₂

Reveal formulaTest your memory first

d1,d2perpendicular diagonals

Exam tipThe formula uses the two diagonals, not two sides.

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Mensuration

Volume of a cuboid

Core & Extended

V = lwh

Reveal formulaTest your memory first

Vvolume l,w,hperpendicular dimensions

Exam tipUse the same unit for all dimensions.

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Mensuration

Total surface area of a cone

Extended

A = πr² + πrl

Reveal formulaTest your memory first

rradius lslant height

Exam tipUse slant height for the curved surface, not vertical height.

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Mensuration

Area of a circular segment

Extended

segment area = sector area − triangle area

Reveal formulaTest your memory first

segmentregion between a chord and an arc

Exam tipUse the triangle formed by the two radii and the chord.

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Statistics

Range

Core & Extended

range = maximum − minimum

Reveal formulaTest your memory first

maximumlargest value minimumsmallest value

Exam tipThe range measures spread but ignores all middle values.

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Probability

Conditional probability

Extended

P(A | B) = P(A ∩ B)P(B)

Reveal formulaTest your memory first

P(A|B)probability of A given B

Exam tipThe sample space is restricted to event B.

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Pure Mathematics

Finite geometric series

AS & A Level

Sₙ = a(1 − rⁿ)/(1 − r)

Reveal formulaTest your memory first

Sₙsum of first n terms afirst term rcommon ratio nnumber of terms

Exam tipUse consistent units and identify every quantity before substituting.

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Pure Mathematics

Binomial expansion

AS & A Level

(a + b)ⁿ = Σ ⁿCᵣ aⁿ⁻ʳbʳ

Reveal formulaTest your memory first

npositive integer power rterm index from 0 to n

Exam tipFor rational powers use the generalized expansion and its validity condition.

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Algebra

Sum and product of quadratic roots

AS & A Level

α + β = −b/a; αβ = c/a

Reveal formulaTest your memory first

α,βroots a,b,cquadratic coefficients

Exam tipUse consistent units and identify every quantity before substituting.

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Differentiation

Quotient rule

AS & A Level

d(u/v)/dx = [v(du/dx) − u(dv/dx)]/v²

Reveal formulaTest your memory first

unumerator function vdenominator function

Exam tipUse consistent units and identify every quantity before substituting.

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Differentiation

Exponential and logarithmic derivatives

AS & A Level

d(eˣ)/dx = eˣ; d(ln x)/dx = 1/x

Reveal formulaTest your memory first

eEuler number lnnatural logarithm

Exam tipUse consistent units and identify every quantity before substituting.

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Integration

Logarithmic integral

AS & A Level

∫1/x dx = ln|x| + C

Reveal formulaTest your memory first

Cconstant of integration

Exam tipUse consistent units and identify every quantity before substituting.

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Integration

Exponential and trigonometric integrals

A Level

∫eˣdx=eˣ+C; ∫sin x dx=−cos x+C; ∫cos x dx=sin x+C

Reveal formulaTest your memory first

Cconstant of integration

Exam tipUse consistent units and identify every quantity before substituting.

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Probability & Statistics

Binomial mean and variance

AS & A Level

E(X)=np; Var(X)=np(1−p)

Reveal formulaTest your memory first

ntrials psuccess probability

Exam tipUse consistent units and identify every quantity before substituting.

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Probability & Statistics

Poisson probability

A Level

P(X=r) = e⁻λ λʳ/r!

Reveal formulaTest your memory first

λmean number of events revent count

Exam tipUse consistent units and identify every quantity before substituting.

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Motion

Average speed

Core & Extended

v = dt

Reveal formulaTest your memory first

vaverage speed ddistance travelled ttime taken

Exam tipUse total distance divided by total time. Convert units before substituting.

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Motion

Acceleration

Core & Extended

a = v − ut

Reveal formulaTest your memory first

aacceleration uinitial velocity vfinal velocity ttime

Exam tipA negative value means deceleration when the chosen positive direction is unchanged.

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Forces

Resultant force

Core & Extended

F = ma

Reveal formulaTest your memory first

Fresultant force mmass aacceleration

Exam tipUse the resultant force, not one individual force, unless it is the only unbalanced force.

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Properties of Matter

Density

Core & Extended

ρ = mV

Reveal formulaTest your memory first

ρdensity mmass Vvolume

Exam tipKeep units consistent. 1 g/cm³ = 1000 kg/m³.

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Pressure

Pressure

Core & Extended

p = FA

Reveal formulaTest your memory first

ppressure Fnormal force Aarea

Exam tipA smaller contact area produces a larger pressure for the same force.

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Momentum

Momentum

Core & Extended

p = mv

Reveal formulaTest your memory first

pmomentum mmass vvelocity

Exam tipMomentum is a vector, so direction signs matter.

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Energy, Work and Power

Work done

Core & Extended

W = Fd

Reveal formulaTest your memory first

Wwork done / energy transferred Fforce in direction of motion ddistance moved

Exam tipUse the distance moved in the direction of the force.

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Energy, Work and Power

Kinetic energy

Extended

E_k = ½mv²

Reveal formulaTest your memory first

Eₖkinetic energy mmass vspeed

Exam tipSpeed is squared, so doubling speed makes kinetic energy four times larger.

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Energy, Work and Power

Gravitational potential energy

Extended

ΔE_p = mgΔh

Reveal formulaTest your memory first

ΔEₚchange in gravitational potential energy mmass ggravitational field strength Δhvertical height change

Exam tipUse vertical height, not distance travelled along a slope.

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Energy, Work and Power

Power from work

Core & Extended

P = Wt

Reveal formulaTest your memory first

Ppower Wwork done ttime

Exam tip1 watt means 1 joule transferred each second.

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Energy, Work and Power

Energy efficiency

Extended

efficiency = useful energy outputtotal energy input × 100%

Reveal formulaTest your memory first

efficiencyfraction or percentage of useful transfer

Exam tipEfficiency cannot exceed 100%. Ensure both energies use the same unit.

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Waves

Wave speed

Core & Extended

v = fλ

Reveal formulaTest your memory first

vwave speed ffrequency λwavelength

Exam tipFrequency must be in hertz and wavelength in metres for m/s.

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Electricity

Potential difference

Core & Extended

V = EQ

Reveal formulaTest your memory first

Vpotential difference Eenergy transferred Qcharge

Exam tip1 volt = 1 joule per coulomb.

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Electricity

Resistance

Core & Extended

R = VI

Reveal formulaTest your memory first

Rresistance Vpotential difference Icurrent

Exam tipUse the p.d. across and current through the same component.

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Electricity

Electrical power

Core & Extended

P = VI

Reveal formulaTest your memory first

Pelectrical power Vpotential difference Icurrent

Exam tipUseful for appliances when voltage and current are given.

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Momentum

Force from momentum change

Extended

F = ΔpΔt

Reveal formulaTest your memory first

Fresultant force Δpchange in momentum Δttime interval

Exam tipUse the change in momentum, not the final momentum alone.

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Forces

Gravitational field strength

Core & Extended

g = Wm

Reveal formulaTest your memory first

ggravitational field strength Wweight mmass

Exam tipMass is measured in kilograms and weight in newtons.

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Forces

Spring constant

Core & Extended

k = Fx

Reveal formulaTest your memory first

kspring constant Fforce xextension

Exam tipUse extension, not the total length of the spring.

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Thermal Physics

Boyle’s law

Extended

p₁V₁ = p₂V₂

Reveal formulaTest your memory first

p1initial pressure V1initial volume p2final pressure V2final volume

Exam tipThis applies to a fixed mass of gas at constant temperature.

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Space Physics

Redshift

Extended

z = λ − λ₀λ₀

Reveal formulaTest your memory first

zredshift λobserved wavelength λ0rest wavelength

Exam tipUse the same wavelength unit for both values.

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Measurements

Percentage uncertainty

AS & A Level

percentage uncertainty = absolute uncertainty / measured value × 100%

Reveal formulaTest your memory first

absolute uncertaintyestimated uncertainty

Exam tipUse consistent units and identify every quantity before substituting.

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Dynamics

Newton second law

AS & A Level

F = ma

Reveal formulaTest your memory first

Fresultant force mmass aacceleration

Exam tipUse consistent units and identify every quantity before substituting.

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Momentum

Momentum

AS & A Level

p = mv

Reveal formulaTest your memory first

pmomentum mmass vvelocity

Exam tipUse consistent units and identify every quantity before substituting.

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Momentum

Impulse

AS & A Level

impulse = FΔt = Δp

Reveal formulaTest your memory first

Fforce Δttime interval Δpchange in momentum

Exam tipUse consistent units and identify every quantity before substituting.

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Deformation

Stress

AS & A Level

stress = F/A

Reveal formulaTest your memory first

Ftensile force Across-sectional area

Exam tipUse consistent units and identify every quantity before substituting.

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Deformation

Young modulus

AS & A Level

E = stress/strain = FL/(AΔL)

Reveal formulaTest your memory first

EYoung modulus Fforce Loriginal length Aarea +1

Exam tipUse consistent units and identify every quantity before substituting.

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Waves

Inverse-square intensity

AS & A Level

I ∝ 1/r²

Reveal formulaTest your memory first

Iintensity rdistance from point source

Exam tipUse consistent units and identify every quantity before substituting.

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Superposition

Double-slit fringe spacing

AS & A Level

w = λD/a

Reveal formulaTest your memory first

wfringe spacing λwavelength Dscreen distance aslit separation

Exam tipUse consistent units and identify every quantity before substituting.

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Electricity

Resistivity

AS & A Level

R = ρL/A

Reveal formulaTest your memory first

Rresistance ρresistivity Llength Across-sectional area

Exam tipUse consistent units and identify every quantity before substituting.

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Circuits

Terminal potential difference

AS & A Level

V = ε − Ir

Reveal formulaTest your memory first

Vterminal p.d. εe.m.f. Icurrent rinternal resistance

Exam tipUse consistent units and identify every quantity before substituting.

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Circular Motion

Centripetal acceleration

A Level

a = v²/r = ω²r

Reveal formulaTest your memory first

acentripetal acceleration vlinear speed rradius ωangular speed

Exam tipUse consistent units and identify every quantity before substituting.

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Gravitational Fields

Gravitational field strength

A Level

g = GM/r²

Reveal formulaTest your memory first

Ggravitational constant Msource mass rdistance from centre

Exam tipUse consistent units and identify every quantity before substituting.

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Electric Fields

Electric field of a point charge

A Level

E = Q/(4πε₀r²)

Reveal formulaTest your memory first

Efield strength Qsource charge rdistance ε₀permittivity of free space

Exam tipUse consistent units and identify every quantity before substituting.

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Capacitance

Capacitance

A Level

C = Q/V

Reveal formulaTest your memory first

Ccapacitance Qcharge Vpotential difference

Exam tipUse consistent units and identify every quantity before substituting.

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Capacitance

Capacitor energy

A Level

W = ½QV = ½CV² = Q²/(2C)

Reveal formulaTest your memory first

Wstored energy Qcharge Vp.d. Ccapacitance

Exam tipUse consistent units and identify every quantity before substituting.

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Magnetic Fields

Force on current-carrying conductor

A Level

F = BIL sin θ

Reveal formulaTest your memory first

Fmagnetic force Bflux density Icurrent Llength in field

Exam tipUse consistent units and identify every quantity before substituting.

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Quantum Physics

Photon energy

A Level

E = hf = hc/λ

Reveal formulaTest your memory first

Ephoton energy hPlanck constant ffrequency λwavelength

Exam tipUse consistent units and identify every quantity before substituting.

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Nuclear Physics

Radioactive decay law

A Level

N = N₀e⁻λt

Reveal formulaTest your memory first

Nnumber remaining N₀initial number λdecay constant ttime

Exam tipUse consistent units and identify every quantity before substituting.

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Nuclear Physics

Half-life and decay constant

A Level

t½ = ln2/λ

Reveal formulaTest your memory first

t½half-life λdecay constant

Exam tipUse consistent units and identify every quantity before substituting.

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Motion

Average velocity

Core & Extended

v = ΔxΔt

Reveal formulaTest your memory first

vaverage velocity Δxdisplacement Δttime interval

Exam tipVelocity uses displacement, not total path length. Direction matters.

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Motion

Distance from a speed–time graph

Core & Extended

distance = area under the speed–time graph

Reveal formulaTest your memory first

distancedistance travelled

Exam tipSplit the area into rectangles and triangles when needed.

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Motion

Acceleration from a velocity–time graph

Extended

a = ΔvΔt

Reveal formulaTest your memory first

aacceleration Δvchange in velocity Δtchange in time

Exam tipAcceleration is the gradient. Use a large triangle on a straight section.

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Forces

Weight

Core & Extended

W = mg

Reveal formulaTest your memory first

Wweight mmass ggravitational field strength

Exam tipMass is measured in kg; weight is a force measured in N.

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Forces

Hooke’s law

Core & Extended

F = kx

Reveal formulaTest your memory first

Fforce kspring constant xextension

Exam tipValid only up to the limit of proportionality. Extension = stretched length − original length.

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Forces

Moment of a force

Core & Extended

moment = Fd

Reveal formulaTest your memory first

Fforce dperpendicular distance from pivot

Exam tipThe distance must be perpendicular to the line of action of the force.

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Forces

Principle of moments

Core & Extended

clockwise moments = anticlockwise moments

Reveal formulaTest your memory first

momentforce × perpendicular distance

Exam tipUse this only when the object is in rotational equilibrium.

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Pressure

Pressure in a liquid

Extended

p = ρgh

Reveal formulaTest your memory first

pliquid pressure ρliquid density ggravitational field strength hdepth

Exam tipThis gives pressure caused by the liquid column. Use vertical depth.

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Momentum

Impulse

Extended

FΔt = Δp

Reveal formulaTest your memory first

Faverage force Δtcontact time Δpchange in momentum

Exam tipIncreasing collision time reduces average force for the same momentum change.

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Momentum

Conservation of momentum

Extended

total p before = total p after

Reveal formulaTest your memory first

pmomentum

Exam tipChoose one direction as positive and keep signs consistent.

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Energy, Work and Power

Power from energy

Core & Extended

P = ΔEt

Reveal formulaTest your memory first

Ppower ΔEenergy transferred ttime

Exam tipUse this form when energy rather than work is given.

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Energy, Work and Power

Power efficiency

Extended

efficiency = useful power outputtotal power input × 100%

Reveal formulaTest your memory first

efficiencyfraction or percentage of useful power

Exam tipUse power values only; do not mix power with energy.

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Thermal Physics

Specific heat capacity

Extended

Q = mcΔT

Reveal formulaTest your memory first

Qthermal energy transferred mmass cspecific heat capacity ΔTtemperature change

Exam tipUse temperature change, not final temperature. Match mass units to c.

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Thermal Physics

Specific latent heat

Extended

Q = mL

Reveal formulaTest your memory first

Qthermal energy transferred mmass Lspecific latent heat

Exam tipDuring a change of state, temperature remains constant.

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Waves

Frequency and period

Core & Extended

f = 1T

Reveal formulaTest your memory first

ffrequency Tperiod

Exam tipPeriod is the time for one complete oscillation.

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Light

Refractive index

Extended

n = sin isin r

Reveal formulaTest your memory first

nrefractive index iangle of incidence rangle of refraction

Exam tipAngles are measured from the normal, not the surface.

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Light

Critical angle

Extended

n = 1sin c

Reveal formulaTest your memory first

nrefractive index of denser medium ccritical angle

Exam tipThis form applies when light travels from the material into air.

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Light

Magnification

Core & Extended

magnification = image heightobject height

Reveal formulaTest your memory first

magnificationimage size factor

Exam tipUse the same units for image height and object height.

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Electricity

Charge flow

Core & Extended

Q = It

Reveal formulaTest your memory first

Qelectric charge Icurrent ttime

Exam tipConvert minutes to seconds before substituting.

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Electricity

Resistors in series

Core & Extended

R_T = R₁ + R₂ + …

Reveal formulaTest your memory first

Rₜtotal resistance R₁, R₂individual resistances

Exam tipSeries resistance is always greater than any individual resistance.

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Electricity

Resistors in parallel

Extended

1R_T = 1R₁ + 1R₂ + …

Reveal formulaTest your memory first

Rₜtotal resistance R₁, R₂branch resistances

Exam tipParallel resistance is smaller than the smallest branch resistance.

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Electricity

Power in a resistor

Extended

P = I²R

Reveal formulaTest your memory first

Ppower Icurrent Rresistance

Exam tipUse when current and resistance are known.

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Electricity

Power from voltage and resistance

Extended

P = V²R

Reveal formulaTest your memory first

Ppower Vpotential difference Rresistance

Exam tipUse when voltage and resistance are known.

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Electricity

Electrical energy

Core & Extended

E = VIt

Reveal formulaTest your memory first

Eelectrical energy Vpotential difference Icurrent ttime

Exam tipThis is equivalent to E = Pt.

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Electromagnetic Effects

Transformer turns ratio

Extended

V_pV_s = N_pN_s

Reveal formulaTest your memory first

Vₚprimary voltage Vₛsecondary voltage Nₚprimary turns Nₛsecondary turns

Exam tipA step-up transformer has more turns on the secondary coil.

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Electromagnetic Effects

Ideal transformer power

Extended

V_pI_p = V_sI_s

Reveal formulaTest your memory first

Vₚ, Vₛprimary and secondary voltage Iₚ, Iₛprimary and secondary current

Exam tipFor an ideal transformer, input power equals output power.

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Electromagnetic Effects

Force on a current-carrying conductor

Extended

F = BIL

Reveal formulaTest your memory first

Fforce Bmagnetic flux density Icurrent Llength in magnetic field

Exam tipApplies when the conductor is perpendicular to the magnetic field.

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Nuclear Physics

Corrected count rate

Core & Extended

corrected count rate = measured count rate − background count rate

Reveal formulaTest your memory first

count ratedetected events per unit time

Exam tipAlways subtract background count measured over the same time interval.

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Nuclear Physics

Half-life decay

Core & Extended

N = N₀(½)ⁿ

Reveal formulaTest your memory first

Namount remaining N₀initial amount nnumber of half-lives

Exam tipn = elapsed time ÷ half-life. This model is useful for repeated halving.

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Space Physics

Hubble’s law

Extended

v = H₀d

Reveal formulaTest your memory first

vrecession speed H₀Hubble constant ddistance

Exam tipKeep distance in megaparsecs if H₀ is given in km/s/Mpc.

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Energy, Work and Power

Elastic potential energy

Extended

E_e = 12kx²

Reveal formulaTest your memory first

Eeelastic potential energy kspring constant xextension

Exam tipThe extension is squared, so convert it to metres before squaring.

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Simple Machines

Mechanical advantage

Core & Extended

MA = loadeffort

Reveal formulaTest your memory first

MAmechanical advantage loadoutput force effortinput force

Exam tipMechanical advantage is a force ratio and has no unit.

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Simple Machines

Velocity ratio

Core & Extended

VR = distance moved by effortdistance moved by load

Reveal formulaTest your memory first

VRvelocity ratio

Exam tipUse distances moved in the same unit.

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Simple Machines

Machine efficiency

Core & Extended

efficiency = MAVR × 100%

Reveal formulaTest your memory first

MAmechanical advantage VRvelocity ratio

Exam tipA real machine normally has an efficiency below 100%.

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Thermal Physics

Celsius to kelvin

Core & Extended

T = θ + 273

Reveal formulaTest your memory first

Tabsolute temperature θCelsius temperature

Exam tipKelvin temperatures do not use the degree symbol.

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Waves

Wavelength from wave speed

Core & Extended

λ = vf

Reveal formulaTest your memory first

λwavelength vwave speed ffrequency

Exam tipThis is the wave-speed equation rearranged for wavelength.

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Space Physics

Orbital speed

Extended

v = 2πrT

Reveal formulaTest your memory first

vorbital speed rorbital radius Torbital period

Exam tipThe distance travelled in one circular orbit is 2πr.

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Deformation

Strain

AS & A Level

strain = ΔL/L

Reveal formulaTest your memory first

ΔLextension Loriginal length

Exam tipUse consistent units and identify every quantity before substituting.

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Waves

Wave intensity

AS & A Level

I = P/A

Reveal formulaTest your memory first

Iintensity Ppower Aarea normal to propagation

Exam tipUse consistent units and identify every quantity before substituting.

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Gravitational Fields

Gravitational potential

A Level

φ = −GM/r

Reveal formulaTest your memory first

φpotential Msource mass rdistance from centre

Exam tipUse consistent units and identify every quantity before substituting.

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Quantum Physics

Photoelectric equation

A Level

hf = Φ + ½mvₘₐₓ²

Reveal formulaTest your memory first

Φwork function vₘₐₓmaximum electron speed

Exam tipUse consistent units and identify every quantity before substituting.

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