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 · 95 questions available for this grade
Factorisation and graph relationships
Factorisation rewrites an expression as a product. For x² + 5x + 6, find numbers with product 6 and sum 5: 2 and 3. The expression is (x + 2)(x + 3). Expand the result to check. For a straight line, gradient measures the change in y divided by the change in x between two points.
Worked example or application
From (0, 2) to (3, 8), the gradient is (8 − 2)/(3 − 0) = 6/3 = 2. This is a rate of change, not simply either coordinate.
Common mistake: Use corresponding points and keep the subtraction order consistent in the numerator and denominator.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Circuits, forces and chemical reactions
In a parallel circuit, branches connected across the same two points have the same potential difference. Current can split between paths, so branch current need not be identical. Weight is a force and depends on mass and gravitational field strength. In chemical reactions, atoms are rearranged; under suitable closed-system conditions, total mass is conserved.
Worked example or application
Using g = 10 N/kg, a 5 kg object has weight 5 × 10 = 50 N. Mass is given in kilograms; weight is given in newtons. The numerical value of g must be stated or supplied.
Common mistake: Do not use mass and weight as interchangeable scientific quantities. Read the units before selecting a formula.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Development, surface processes and resources
Development is broader than the total value of production. Compare health, education, income and access to services. Weathering breaks rock down in place; erosion involves removal and transport; deposition occurs when transported material is dropped. Land-use choices can affect runoff, soil loss and food production. Explain processes in sequence rather than using their names as synonyms.
Worked example or application
Vegetation helps protect soil. Removing it on a steep slope can increase runoff and erosion; terraces can slow runoff and reduce soil loss. The effect depends on local conditions and maintenance.
Common mistake: One development indicator rarely tells the whole story. Compare more than one measure and acknowledge its limits.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
War, authoritarianism and human rights
Study how political decisions, economic pressures and ideas interact. After World War I, peace settlements and later economic crises affected societies in different ways. Propaganda seeks to influence opinion and can omit or distort evidence. When examining Nazi rule or apartheid, connect policies with their effects on rights and people’s lives, and distinguish the government’s justification from historical evidence.
Worked example or application
A propaganda poster may be valuable evidence of the message authorities wanted to spread. It is not automatically reliable evidence that the message itself was true.
Common mistake: Do not repeat a source’s claim as your own conclusion without evaluating its purpose and checking other evidence.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Arguments, ambiguity and context
An argument needs a clear claim and relevant support. If a school needs more library space, evidence about full seats is more relevant than the colour of the walls. Ambiguity arises when language allows multiple readings. Tone, irony and register also depend on context; a soaked speaker calling a storm “lovely weather” may mean the opposite of the words.
Worked example or application
“I saw the man with the telescope” leaves it unclear whether the man had the telescope or the observer used it. Specify the relationship: “Using a telescope, I saw the man.”
Common mistake: A rhetorical or emotional effect is not necessarily factual evidence. Assess both meaning and reasoning.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Credit, pricing and planning
A credit sale creates a debtor for the selling business; buying on credit creates a creditor. Balances change when payments are recorded. Mark-up on cost and profit margin on sales use different denominators. A cash-flow forecast estimates when money arrives and leaves, which matters even when the business expects a profit.
Worked example or application
An item costing R80 and selling for R100 earns R20 gross profit. Mark-up on cost is 20/80 × 100 = 25%; margin on sales is 20/100 × 100 = 20%.
Common mistake: A credit sale is not an immediate cash receipt. A profitable business can still struggle to pay bills on time.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Controlled systems and design trade-offs
Systems have inputs, processes and outputs. A sensor can provide input information used to control a device. In hydraulics, force equals pressure multiplied by piston area, so a larger piston can exert a larger force at the same pressure. This changes the movement distance relationship; it does not create energy. Component choices and protection must suit the intended circuit or mechanism.
Worked example or application
If piston area increases fourfold at unchanged pressure, the force increases fourfold. For equal displaced liquid volume, the larger piston moves a shorter distance. Consider both force and movement when evaluating the design.
Common mistake: Test durability and repeated operation, not only whether the prototype works once.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Perspective, motifs and interpretation
Perspective organises depth in an image. In one-point perspective, suitable receding parallel lines appear to meet at a vanishing point on the horizon. A motif is a recognisable idea developed through repetition and variation. In drama, subtext is meaning beneath the spoken words; in music, texture describes how parts combine. Each concept concerns relationships, not only isolated features.
Worked example or application
In dance canon, performers begin the same phrase at different times. In unison, they perform it together. The different timing can create different expressive effects even when the movements match.
Common mistake: An interpretation needs evidence. Connect technique to meaning rather than judging an artwork only by size, price or fame.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Subject choices and future options
Choosing Grade 10 subjects involves interests, strengths and possible post-school requirements. Use reliable information and seek guidance rather than copying friends’ choices. A career interest is not an admission requirement: enjoying an area does not remove formal subject or mark requirements. Plans should include achievable study actions and be reviewed as you learn more about your abilities and opportunities.
Worked example or application
List each possible pathway, the required subjects, and the information source. If two options have different requirements, discuss how your subject combination affects each before making a choice.
Common mistake: Requirements can change. Check current official information instead of relying only on old forwarded messages.
Check your understanding: Cover the example and explain its reasoning. Change one detail and consider how the answer would change.
Practise Grade 9
Choose from Creative Arts, Economic and Management Sciences, English, Geography, History, Life Orientation, Mathematics, Natural Sciences, Technology. 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.