Use these notes to understand a method before testing yourself. Read an example, try it without looking, then explain the steps in your own words.
Written by QuizChallenge SA · Updated 29 September 2026 · 116 questions available for this grade
Roots, identities and compound growth
The discriminant b² − 4ac describes the nature of a quadratic’s roots. A positive value gives two distinct real roots, zero gives a repeated real root, and a negative value gives no real roots. Trigonometric identities have domain restrictions when division is involved. Compound interest uses repeated growth factors rather than adding the same amount each year.
Worked example or application
For x² − 2x + 5 = 0, the discriminant is 4 − 20 = −16, so there are no real roots. R5 000 at 10% annually for two years grows to 5 000 × 1.10² = R6 050.
Common mistake: State restrictions such as cos θ ≠ 0 when using tan θ = sin θ/cos θ.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Tariffs and break-even decisions
Tariffs often combine a fixed charge with a charge per unit. Build the expression before substituting a quantity. Break-even compares total income with total cost. Unit contribution is selling price minus variable cost, and it helps cover fixed costs. Exchange-rate conversions should include fees and clearly state the rate used; examples do not establish current market rates.
Worked example or application
A hypothetical electricity charge of R50 + R2 per unit costs R290 for 120 units. A stall with R300 fixed costs and R15 contribution per item breaks even at 300/15 = 20 items.
Common mistake: A fixed fee is charged once in the stated billing period, not once per unit unless the tariff says so.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Forces and quantitative chemistry
Forces should be added as vectors. If net force is zero, velocity is constant; the object can be stationary or moving uniformly. Newton’s second law relates net force, mass and acceleration. In chemistry, use molar mass and amount of substance carefully, retaining units and balanced reaction ratios when required. A formula should be selected from the physical situation, not only familiar numbers.
Worked example or application
A net force of 10 N on a 2 kg object gives a = F/m = 5 m/s². Water has molar mass 18 g/mol using H = 1 and O = 16, so 36 g represents two moles.
Common mistake: Zero net force means zero acceleration, not necessarily zero velocity.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Plant nutrition, respiration and exchange
Photosynthesis uses light energy to form organic food, while cellular respiration transfers energy into usable forms such as ATP. Organ systems support digestion, gas exchange, circulation and excretion. Structure–function explanations connect features such as thin surfaces, large area or transport networks to the process they support, rather than simply listing body parts.
Worked example or application
Alveoli provide a large, thin exchange surface in the lungs. Digested nutrients are mainly absorbed in the small intestine, where villi increase area. These structures serve different processes despite both involving transfer across surfaces.
Common mistake: Do not confuse breathing, gas exchange and cellular respiration. They are connected but not identical processes.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Climate controls and development
Descending air in a high-pressure system often favours stable conditions. A temperature inversion is a layer where temperature increases with height instead of following the usual decrease. Development measures should distinguish overall production from living conditions. Consider how resources, infrastructure and access affect economic opportunities, and use spatial evidence to support explanations.
Worked example or application
A rise in nominal income does not establish improved purchasing power if prices rise faster. Similarly, the presence of a road is less useful than evidence about whether people can use it reliably.
Common mistake: Avoid explaining development using only one national average. Distribution and access matter.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Ideologies, nationalism and apartheid
Compare political and economic ideologies through their claims, institutions and consequences. The Russian Revolution and the Great Depression belong to different contexts, even though both affected wider political choices. In South African history, distinguish long-standing segregation from formal apartheid policies and connect resistance movements with specific aims and actions.
Worked example or application
The Defiance Campaign in 1952 involved deliberate opposition to unjust laws. The Freedom Charter was adopted at Kliptown in 1955. Knowing the dates helps chronology, but explain what these actions sought to achieve.
Common mistake: Do not merge organisations or campaigns simply because they opposed the same broad system.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Counterarguments and source limitations
A strong argument responds fairly to an important opposing view. Evaluate surveys by asking who was sampled and whether their views represent the population claimed. Euphemisms can soften unpleasant realities, while satire criticises through humour or ridicule. In literary analysis, distinguish tone—the expressed attitude—from mood, the atmosphere created for the reader.
Worked example or application
A survey of one class cannot automatically establish what all teenagers believe. The limitation concerns representation, not merely the number of pages in the report. State how that limits the conclusion.
Common mistake: Do not assume a source is reliable only because it agrees with your first opinion.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Partnerships, costs and business decisions
A partnership agreement sets arrangements such as profit sharing; do not assume equal shares. Accrual accounting matches expenses to the period incurred, including amounts unpaid at year-end. Businesses compare ownership forms, marketing decisions and investment risks. Economics distinguishes real growth from price increases and considers how supply, demand and infrastructure affect opportunities.
Worked example or application
A distributable partnership profit of R30 000 shared 2:1 gives R20 000 and R10 000. Depreciation at 20% of an R8 000 current book value is R1 600; the closing value is R6 400.
Common mistake: Separate an expense from an asset’s closing value, and distinguish a prediction from a guarantee.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Evidence-based planning and coping
Career planning compares goals with current results and verified requirements. Research alternatives rather than treating one pathway as the only possible future. When stress arises, identify practical causes and available support. Analysing study errors can reveal whether a change in knowledge, method or workload is needed. Community projects should be designed with the intended beneficiaries, not only assumptions about them.
Worked example or application
For an unfamiliar course, check the institution’s official entry requirements and contact it if details are unclear. A friend’s old message may help identify a possibility but is not final confirmation.
Common mistake: Review a plan when evidence changes. Adjustment can be a constructive response, not a failure.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Practise Grade 11
Choose from Accounting, Business Studies, Economics, English, Geography, History, Life Orientation, Life Sciences, Mathematical Literacy, Mathematics, Physical Sciences. Social Sciences is separated into Geography and History practice in Grades 6–9. Your school timetable may include other languages or electives.
Use your teacher’s current term plan and textbook to check what you need to cover. These notes select concepts for practice; they do not replace lessons, practical tasks, essays or examination preparation. Examples with financial rates are hypothetical unless clearly identified otherwise.