Formula Centre

Formula guides and key subject rules for every grade and subject, with worked examples and practice.

Addition Rule for Probability

Mathematics • Statistics and Probability • Grade 11

P(A or B) = P(A) + P(B) − P(A and B)
P(A)Probability of event A (—)
P(B)Probability of event B (—)

When to use it

Use it when two events can happen together and you must not double-count the overlap.

Worked example

P(A) = 0,5, P(B) = 0,4, P(A and B) = 0,2 → P(A or B) = 0,5 + 0,4 − 0,2 = 0,7.

Common mistakes

  • Leaving out the overlap term for non-mutually-exclusive events

Practice question

If P(A) = 0,45, P(B) = 0,3 and P(A and B) = 0,1, find P(A or B).

Concentration of a Solution

Physical Sciences • Chemistry: Mole and Stoichiometry • Grade 11

c = n / V
cConcentration (mol·dm⁻³)
nMoles of solute (mol)
VVolume of solution (dm³)

When to use it

Use it for solutions and titration calculations.

Worked example

0,5 mol in 250 cm³ = 0,25 dm³ → c = 0,5/0,25 = 2 mol·dm⁻³.

Common mistakes

  • Leaving the volume in cm³
  • Using mass instead of moles

Practice question

What is the concentration when 0,2 mol of NaOH is dissolved in 500 cm³ of solution?

Grade 11 Accounting essentials

Accounting • Essential reference • Grade 11

Assets = Owner’s equity + Liabilities
AssetsResources owned (R)
LiabilitiesAmounts owed (R)

When to use it

Use to check the accounting equation after transactions.

Worked example

If equity is R8 000 and liabilities R2 000, assets are R10 000.

Common mistakes

  • Recording a transaction on only one side.

Practice question

Calculate assets when equity is R12 000 and liabilities R3 500.

Grade 11 Afrikaans essentials

Afrikaans • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 Agricultural Sciences essentials

Agricultural Sciences • Essential reference • Grade 11

Gross margin = Income − Variable costs
IncomeMoney earned from production (R)
Variable costsCosts that change with output (R)

When to use it

Use when comparing the financial performance of farm enterprises.

Worked example

R50 000 income − R32 000 variable costs = R18 000 gross margin.

Common mistakes

  • Including fixed costs as variable costs.

Practice question

Calculate gross margin from R72 000 income and R49 500 variable costs.

Grade 11 Business Studies essentials

Business Studies • Essential reference • Grade 11

Profit = Revenue − Expenses
RevenueIncome from sales (R)
ExpensesCosts of operating (R)

When to use it

Use to assess whether a business earned a profit or loss.

Worked example

R10 000 revenue − R7 500 expenses = R2 500 profit.

Common mistakes

  • Treating revenue as profit.

Practice question

Find profit on R18 000 revenue and R11 200 expenses.

Grade 11 Computer Applications Technology essentials

Computer Applications Technology • Essential reference • Grade 11

Information cycle = Input + Processing + Output + Storage
InputData entered into a system (Not applicable)

When to use it

Use to explain how digital systems handle information.

Worked example

A spreadsheet receives figures, calculates totals, displays results and saves the file.

Common mistakes

  • Confusing raw data with processed information.

Practice question

Describe the information cycle for an online form.

Grade 11 Economics essentials

Economics • Essential reference • Grade 11

GDP per capita = GDP / population
GDPTotal value of final output (R)
populationNumber of people (people)

When to use it

Use for a simple comparison of average output between economies.

Worked example

Divide total GDP by the population for the period.

Common mistakes

  • Assuming GDP per capita measures income distribution.

Practice question

Explain what happens if GDP rises faster than population.

Grade 11 Engineering Graphics and Design essentials

Engineering Graphics and Design • Essential reference • Grade 11

Scale = Drawing length / Actual length
Drawing lengthLength shown on the drawing (mm)
Actual lengthReal-world length (mm)

When to use it

Use to create or interpret scaled technical drawings.

Worked example

50 mm / 500 mm = 1:10 scale.

Common mistakes

  • Using different units for the two lengths.

Practice question

Convert 2 m to a 1:20 drawing length.

Grade 11 English essentials

English • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 Geography essentials

Geography • Essential reference • Grade 11

Population density = population / area
populationNumber of people (people)
areaLand area (km²)

When to use it

Use when comparing how densely places are populated.

Worked example

20 000 people / 100 km² = 200 people per km².

Common mistakes

  • Forgetting the per-square-kilometre unit.

Practice question

Calculate density for 45 000 people in 150 km².

Grade 11 History essentials

History • Essential reference • Grade 11

Strong source analysis = Origin + Purpose + Evidence + Context
OriginWho created the source and when (Not applicable)

When to use it

Use when evaluating usefulness, reliability and bias in a source.

Worked example

Identify the creator, intended audience, evidence and historical setting.

Common mistakes

  • Calling a source unreliable only because it is biased.

Practice question

Apply the four-part rule to one historical source.

Grade 11 Information Technology essentials

Information Technology • Essential reference • Grade 11

Program flow = Input → Process → Output
InputData supplied to a program (Not applicable)

When to use it

Use when planning algorithms and tracing programs.

Worked example

Read two numbers, add them, then display the sum.

Common mistakes

  • Processing a value before it has been initialised.

Practice question

Write pseudocode that calculates an average.

Grade 11 IsiNdebele essentials

IsiNdebele • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 IsiXhosa essentials

IsiXhosa • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 IsiZulu essentials

IsiZulu • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 Life Orientation essentials

Life Orientation • Essential reference • Grade 11

SMART goal = Specific + Measurable + Achievable + Relevant + Time-bound
SMARTFive qualities of an effective goal (Not applicable)

When to use it

Use when planning study, career, health or personal goals.

Worked example

Improve my test mark from 60% to 70% by the end of term.

Common mistakes

  • Setting a goal with no measure or deadline.

Practice question

Rewrite one personal goal using SMART.

Grade 11 Life Sciences essentials

Life Sciences • Essential reference • Grade 11

Magnification = image size / actual size
image sizeMeasured size of the image (mm)
actual sizeReal size of the object (mm)

When to use it

Use when comparing microscope images with actual specimens.

Worked example

A 20 mm image of a 2 mm object has magnification 10×.

Common mistakes

  • Mixing measurement units.

Practice question

Find the magnification of a 30 mm image of a 3 mm object.

Grade 11 Mathematical Literacy essentials

Mathematical Literacy • Essential reference • Grade 11

Percentage = (part / whole) × 100
partThe selected amount (Same as whole)
wholeThe total amount (Same as part)

When to use it

Use for discounts, increases, budgets, data and comparisons.

Worked example

If 25 of 100 items qualify, percentage = (25 / 100) × 100 = 25%.

Common mistakes

  • Dividing the whole by the part.

Practice question

Calculate 15% of R800.

Grade 11 Sepedi essentials

Sepedi • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 Sesotho essentials

Sesotho • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 Setswana essentials

Setswana • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 SiSwati essentials

SiSwati • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 Tourism essentials

Tourism • Essential reference • Grade 11

Total tour cost = Fixed costs + Variable costs
Fixed costsCosts unchanged by group size (R)
Variable costsCosts per traveller or activity (R)

When to use it

Use when building a tour quotation or itinerary budget.

Worked example

R2 000 fixed + R500 variable = R2 500 total.

Common mistakes

  • Leaving out taxes, commissions or exchange-rate effects.

Practice question

Calculate the cost of a tour from a supplied budget.

Grade 11 Tshivenda essentials

Tshivenda • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Grade 11 Xitsonga essentials

Xitsonga • Essential reference • Grade 11

Clear sentence = Subject + Verb + Object
SubjectWho or what the sentence is about (Not applicable)
VerbThe action or state (Not applicable)

When to use it

Use as a foundation for building and checking complete sentences.

Worked example

The learner reads the book.

Common mistakes

  • Writing a sentence without a complete verb.

Practice question

Write one clear sentence and label its subject, verb and object.

Mole Calculation

Physical Sciences • Chemistry: Mole and Stoichiometry • Grade 11

n = m / M
nNumber of moles (mol)
mMass of sample (g)
MMolar mass (g·mol⁻¹)

When to use it

Use it to convert between mass and moles before applying a reaction ratio.

Worked example

36 g of water, M = 18 g·mol⁻¹ → n = 2 mol.

Common mistakes

  • Using kg instead of g
  • Reading molar mass off the wrong element

Practice question

Calculate the number of moles in 88 g of CO₂ (M = 44 g·mol⁻¹).

Ohm's Law

Physical Sciences • Electricity and Electric Circuits • Grade 11

V = IR
VPotential difference (V)
ICurrent (A)
RResistance (Ω)

When to use it

Use it for a conductor at constant temperature to relate potential difference, current and resistance.

Worked example

V = 12 V, I = 2 A → R = 12/2 = 6 Ω.

Common mistakes

  • Applying it across the wrong component
  • Adding parallel resistances directly

Practice question

A resistor of 15 Ω carries a current of 0,4 A. Calculate the potential difference.