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 · 115 questions available for this grade
Calculus and probability with conditions
Differentiate term by term using appropriate rules. For f(x) = 3x² − 4x + 7, f′(x) = 6x − 4. A stationary point has derivative zero, but its nature requires further reasoning. In probability, identify whether events are independent before multiplying their individual probabilities for the intersection. State assumptions rather than applying a memorised formula blindly.
Worked example or application
For f(x) = x² − 6x + 5, f′(x) = 2x − 6, so the stationary point occurs at x = 3. The upward-opening parabola has a minimum there.
Common mistake: A zero derivative is not proof of a maximum. Check the function’s behaviour or use an appropriate test.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Financial models and critical data reading
Successive percentage changes use successive bases. Compare total repayment costs with upfront prices, while considering timing and affordability. Tax and tariff examples must use the supplied rules; do not substitute an assumed current rate. In graphs, read the axis scale before interpreting the visual size of a difference. Sampling methods affect how widely survey results can be applied.
Worked example or application
A 20% price rise followed by a 20% fall gives the factor 1.20 × 0.80 = 0.96: the final price is 4% lower. Twelve payments of R190 total R2 280, which is R280 more than R2 000 upfront.
Common mistake: Equal percentage increases and decreases do not cancel because their bases differ.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Energy, momentum and reactions
Momentum conservation applies to an isolated system under the stated model. Work and kinetic-energy reasoning must consider the relevant forces and motion. The Doppler effect relates observed frequency to relative movement. In chemistry, a catalyst provides an alternative pathway with lower activation energy; it does not change the equilibrium constant for a fixed temperature. Separate rate effects from equilibrium changes.
Worked example or application
For mass m and speed v, kinetic energy is ½mv². Doubling speed with unchanged mass makes kinetic energy four times as large. For an approaching sound source, the observed frequency is higher under the usual stationary-observer case.
Common mistake: Do not assume that faster reaction means a different equilibrium composition. Rate and position of equilibrium are different ideas.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
DNA, meiosis and inheritance
DNA replication copies genetic information before division. Messenger RNA carries a transcribed code used in protein synthesis. Meiosis produces haploid cells and contributes to genetic variation. Alleles are alternative forms of a gene; a heterozygous genotype has different alleles. In evolutionary explanations, variation, inheritance and different reproductive success must be connected over generations.
Worked example or application
Aa is heterozygous; AA and aa are homozygous. In DNA, adenine pairs with thymine. A Punnett square represents possible combinations, not a guarantee that a small family will have an exact predicted ratio.
Common mistake: Do not describe evolution as organisms changing because they decide to. Natural selection acts on heritable variation in populations.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Weather systems, settlement and spatial tools
Explain weather systems through air movement, pressure and energy rather than labels alone. Dense cold air undercuts warmer air at a cold front. Tropical cyclones obtain energy and moisture from suitable warm ocean conditions. Urban surfaces and human activity can contribute to heat-island effects. GIS represents spatial information with formats such as vector points, lines and polygons or raster cells.
Worked example or application
A stream-capture explanation must show how one river intercepts another’s drainage through processes such as headward erosion. A diagram should label the relationship, not merely draw two lines.
Common mistake: A condition that supports cyclone formation is not a guarantee that a cyclone will form.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Cold War, resistance and evidence-based essays
Analyse the Cold War through rivalry, ideology, alliances and particular confrontations. Civil rights, Black Power and Black Consciousness developed in different contexts and should not be treated as identical organisations. In South African history, connect resistance, negotiations and the transition to democracy through specific events and evidence. An essay needs a sustained argument rather than a list of dates.
Worked example or application
The Cuban Missile Crisis took place in 1962; Mandela was released in 1990; the first democratic election took place in 1994. Use dates to establish sequence, then explain relationships without claiming that one date alone proves causation.
Common mistake: Evaluate a source’s usefulness for the specific question. A source can be useful for one enquiry and limited for another.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Synthesis, nuanced claims and literary reasoning
Synthesis connects relevant ideas from sources while preserving important agreements and differences. Assess expertise, evidence, purpose and corroboration. Popularity does not prove a claim; personal attacks do not refute an argument. In literary analysis, explain how quotations and techniques support an interpretation. Qualify conclusions when evidence is limited instead of using unsupported absolutes.
Worked example or application
If incidents rise from one to two, they doubled, but the absolute increase is one. A critical reader needs both values to interpret the headline fairly. The percentage alone may exaggerate the impression.
Common mistake: Do not confuse an author’s dramatic wording with a substantiated conclusion.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Ratios, cash flow and interpretation
Company accounts distinguish shareholders’ equity from amounts owed to creditors. Dividends distribute profits rather than operate as ordinary costs of earning revenue. Ratios summarise relationships but need context: liquidity depends partly on when debts and receipts fall due and how recoverable assets are. A cash-flow statement separates operating, investing and financing movements.
Worked example or application
Current assets of R120 000 and current liabilities of R60 000 give a current ratio of 2:1. If current assets are R100 000 including R40 000 inventory and liabilities are R30 000, the acid-test ratio is (100 000 − 40 000)/30 000 = 2:1.
Common mistake: A favourable ratio is not a guarantee of financial health. Interpret it with trends, asset quality and other evidence.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Strategies, quality and accountability
A strategy should respond to an identified cause, not only an undesirable result. SWOT separates internal strengths and weaknesses from external opportunities and threats. Quality management uses ongoing evidence to improve processes. Human-resource decisions should use relevant requirements and fair criteria. Professional accountability includes correcting mistakes and preventing recurrence rather than concealing problems.
Worked example or application
If sales fall because customers experience poor service, review service processes and feedback before assuming that a price cut alone will solve the problem. Set measures to assess whether the change improves outcomes.
Common mistake: A named strategy is not a complete answer. Explain how it addresses the scenario and how results could be evaluated.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Cycles, externalities and exchange rates
Economic cycles describe expansions and contractions, but not every industry changes equally. Leading indicators can provide signals without predicting perfectly. A negative externality places costs on people outside a transaction. A weaker currency can increase the domestic cost of foreign-priced imports, other things equal. Policy responses should be assessed against evidence and their possible trade-offs.
Worked example or application
At a hypothetical change from R18 to R20 per US dollar, the rand depreciates against the dollar because more rand are required for one dollar. This statement does not describe the rand against every currency or establish the current exchange rate.
Common mistake: Distinguish nominal price increases from real production growth, and state the assumptions behind a predicted effect.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Post-school plans and realistic next steps
Compare entry requirements, costs, accreditation and support before choosing a study or work option. Track admission and funding deadlines separately. An honest CV gives accurate relevant information; an interview answer provides evidence through a concrete situation, action and result. Plans should be reviewed as new information appears. Wellbeing and support remain part of successful preparation.
Worked example or application
Create one checklist per opportunity: official source, requirements, documents, deadline and confirmation of submission. Submitting an application is not the same as receiving admission or funding.
Common mistake: Verify promises of guaranteed work or funding. Avoid sharing passwords or relying solely on unverified forwarded offers.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Practise Grade 12
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.