104 CHAPTERS · 416 PRACTICE SOLUTIONS
Lessons & revision
Understand the principle, keep a mental picture, then solve before checking. Tools are referenced at the step where they help you visualise, check or remember.
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Mathematics
Fractions: share the same whole
A fraction compares a quantity with a whole divided into equal parts.
Lesson and 4 exercisesMathematics
Powers and roots: count the factors
A positive integer power counts equal factors.
Lesson and 4 exercisesMathematics
Equations: keep the balance level
An equation states that two expressions have the same value.
Lesson and 4 exercisesMathematics
Statistics: centre and spread
The mean balances the sum of values; the median divides an ordered series in half.
Lesson and 4 exercisesMathematics
Right triangles: choose the ratio
The hypotenuse is opposite the right angle.
Lesson and 4 exercisesMathematics
Proportionality and percentages
Quantities are proportional when one constant factor maps every value of the first to the second.
Lesson and 4 exercisesMathematics
Expand, factor and recognise identities
Expansion turns products into sums by distribution.
Lesson and 4 exercisesMathematics
Pythagoras: lengths and right-angle checks
In a right triangle, the hypotenuse squared equals the sum of squares of the perpendicular sides.
Lesson and 4 exercisesMathematics
Similar triangles and parallel-line ratios
Similar triangles share angles and have proportional corresponding sides.
Lesson and 4 exercisesMathematics
Functions: an input and its image
A function gives each input in its domain one output.
Lesson and 4 exercisesMathematics
Vectors: displacement, not location
A point locates a position; a vector describes direction, orientation and length of a displacement.
Lesson and 4 exercisesMathematics
Inequalities: a region of solutions
An inequality compares expressions.
Lesson and 4 exercisesMathematics
Coordinate geometry: midpoint, distance and line
In an orthonormal frame, distance is the norm of coordinate differences, by Pythagoras.
Lesson and 4 exercisesMathematics
Quadratics: discriminant and roots
A polynomial ax² + bx + c with nonzero a draws a parabola.
Lesson and 4 exercisesMathematics
Derivatives: local slope
A rate of change compares two points.
Lesson and 4 exercisesMathematics
Sequences: add or multiply each step
A sequence gives values indexed by integers.
Lesson and 4 exercisesMathematics
Probability: read a tree
A probability lies between zero and one.
Lesson and 4 exercisesMathematics
Unit circle and radians
On the unit circle, angle θ gives coordinates (cos θ, sin θ).
Lesson and 4 exercisesMathematics
Exponential and logarithm: inverse operations
The exponential is positive and changes sums into products.
Lesson and 4 exercisesMathematics
Antiderivatives and integrals: accumulate change
An antiderivative F of f satisfies F′ = f.
Lesson and 4 exercisesMathematics
Binomial model: count successes
A binomial model requires a fixed number of independent trials, two outcomes and constant success probability p.
Lesson and 4 exercisesMathematics
Limits: describe behaviour near a point
A limit describes behaviour as x approaches a value or infinity, even if the function is undefined at that point.
Lesson and 4 exercisesMathematics
Conditional probability: change the reference group
P(B given A) measures B within A when P(A)>0, using P(A∩B)/P(A).
Lesson and 4 exercisesPhysics
Units: numbers have dimensions
A physical quantity combines a number and a unit.
Lesson and 4 exercisesPhysics
Electricity: voltage, current, resistance
Current is a rate of charge flow; voltage is a potential difference.
Lesson and 4 exercisesPhysics
Density and pressure
Density relates mass to volume through ρ=m/V, in kg/m³.
Lesson and 4 exercisesPhysics
Electrical power and energy
Power is energy transfer per unit time.
Lesson and 4 exercisesPhysics
Gravitation, weight and distant interaction
Masses attract gravitationally.
Lesson and 4 exercisesPhysics
Motion: position, velocity, acceleration
Position locates a system in a reference frame.
Lesson and 4 exercisesPhysics
Waves: propagate a disturbance
A wave carries a disturbance, without bulk transport of matter in the usual mechanical-wave model.
Lesson and 4 exercisesPhysics
Lenses: reconstruct an image
For a thin converging lens, a ray parallel to the axis exits through the image focus; a ray through the optical centre keeps its direction.
Lesson and 4 exercisesPhysics
Work of a force and energy balance
For constant force over straight displacement, W=Fd cos α, with angle between force and displacement.
Lesson and 4 exercisesPhysics
Forces and energy: choose the system
A force represents an interaction.
Lesson and 4 exercisesPhysics
Radioactive decay: halve each half-life
Individual decay is random.
Lesson and 4 exercisesPhysics
Ideal gas: pressure, volume and temperature
The ideal-gas model neglects particle volume and interactions outside idealised collisions.
Lesson and 4 exercisesBiology & life sciences
Cells and DNA: levels of organisation
A cell is a unit of life.
Lesson and 4 exercisesBiology & life sciences
Photosynthesis and respiration: matter and energy
Photosynthesis lets chlorophyll-containing organisms make organic matter from CO₂ and water using light energy, releasing oxygen in the school model.
Lesson and 4 exercisesBiology & life sciences
Ecosystems: networks and recycling
An ecosystem links organisms and their physical environment.
Lesson and 4 exercisesBiology & life sciences
Mitosis and meiosis: maintain or reduce
DNA replication creates two chromatids per chromosome.
Lesson and 4 exercisesBiology & life sciences
Scientific experiments: control and conclusion
Experiments test hypotheses by comparing conditions.
Lesson and 4 exercisesBiology & life sciences
Inheritance: gametes and probability
In a simple diploid model, an individual has two alleles at a locus and each gamete receives one.
Lesson and 4 exercisesBiology & life sciences
Gene expression: DNA, RNA, protein
Transcription makes RNA from a DNA template strand.
Lesson and 4 exercisesBiology & life sciences
Immunity: recognise, respond, remember
Innate immunity uses barriers, cells and receptors recognising microbial or damage-associated patterns.
Lesson and 4 exercisesBiology & life sciences
Plate tectonics: read the evidence
Lithospheric plates move relative to their neighbours.
Lesson and 4 exercisesBiology & life sciences
Evolution: populations and selection
Evolution changes allele frequencies in populations across generations.
Lesson and 4 exercisesBiology & life sciences
Earth and climate: stocks, flows, evidence
A reservoir holds an amount; a flow transfers matter or energy per unit time.
Lesson and 4 exercisesBiology & life sciences
Nerve signals: pathway and coding
A neuron transmits electrical signals along its membrane.
Lesson and 4 exercisesChemistry
Atoms, ions and molecules
Nuclei contain positive protons and neutral neutrons; electrons are negative.
Lesson and 4 exercisesChemistry
The mole: connect mass and particles
Amount of substance counts entities in defined-size groups called moles.
Lesson and 4 exercisesChemistry
Solutions: concentration and dilution
Molar concentration divides solute amount by final solution volume.
Lesson and 4 exercisesChemistry
Balance a reaction equation
Reaction equations conserve each element’s atoms and total charge.
Lesson and 4 exercisesChemistry
Reactions: ratios and limiting reagent
A reaction equation conserves atoms and charge.
Lesson and 4 exercisesChemistry
Redox: follow the electrons
Oxidation loses electrons; reduction gains them.
Lesson and 4 exercisesChemistry
Acids and bases: proton transfer
A Brønsted acid donates a proton; a base accepts one.
Lesson and 4 exercisesChemistry
Kinetics: rate and reaction time
A rate measures change per unit time.
Lesson and 4 exercisesChemistry
Chemical equilibrium: stable composition, active reactions
At equilibrium, forward and reverse reactions continue at equal rates, giving stable bulk composition.
Lesson and 4 exercisesChemistry
Titration: use equivalence
Titration determines an unknown amount using a suitable reaction with known-concentration solution.
Lesson and 4 exercisesLanguages
English tenses: meaning before triggers
A tense relates an event to a time reference.
Lesson and 4 exercisesLanguages
Listening comprehension in several passes
First identify topic, situation and purpose.
Lesson and 4 exercisesLanguages
Reading comprehension: overview to evidence
First identify document type, topic, voice and situation.
Lesson and 4 exercisesLanguages
Conditionals: hypothesis and consequence
Conditional sentences connect a condition and consequence.
Lesson and 4 exercisesLanguages
Writing: one clear idea per paragraph
Identify audience, format and purpose before drafting.
Lesson and 4 exercisesLanguages
Reported speech and reference points
Reported speech adapts another speaker’s words to pronouns and context.
Lesson and 4 exercisesHistory
History: dates, causes, consequences
Chronology locates events; explanation connects factors.
Lesson and 4 exercisesHistory
Analyse a historical document
Identify type, author, production date, audience and context.
Lesson and 4 exercisesHistory
Revolutions and democracy: ideals and practice
Sovereignty asks where political authority rests; citizenship concerns rights and participation.
Lesson and 4 exercisesHistory
Democracy and citizenship: institutions and participation
Citizenship links status, rights, duties and participation.
Lesson and 4 exercisesHistory
Industrialisation: change and contrasts
Industrialisation changes production, labour, energy, transport and society at different rates.
Lesson and 4 exercisesHistory
World wars and totalitarianism: connect without conflating
Total war widely mobilises societies and economies and affects soldiers and civilians.
Lesson and 4 exercisesHistory
After 1945: blocs, independence, actors
The Cold War combined ideological, strategic and economic rivalry without being constant direct warfare between the leading powers.
Lesson and 4 exercisesGeography
Maps and scale: what a map shows
A map selects information at a chosen scale; it is not the territory itself.
Lesson and 4 exercisesGeography
Read a map: legend, scale and choices
Maps select information about space.
Lesson and 4 exercisesGeography
Population and migration balances
Population changes through births, deaths, arrivals and departures.
Lesson and 4 exercisesGeography
Cities and metropolitan concentration
Urbanisation increases the role of cities in population and space.
Lesson and 4 exercisesGeography
Sustainable development: actors and trade-offs
Sustainable development considers present needs and future possibilities across social, economic and environmental dimensions.
Lesson and 4 exercisesGeography
Globalisation: flows, actors, inequalities
Globalisation intensifies relations between places without integrating them equally.
Lesson and 4 exercisesEconomics
Indicators: rates, indices, charts
An absolute change uses the original unit; a percentage change compares it with the initial value.
Lesson and 4 exercisesEconomics
Markets: supply, demand, model
A market model isolates mechanisms under explicit assumptions.
Lesson and 4 exercisesEconomics
Sociology: socialisation and evidence
Socialisation involves learning norms, values and ways of acting through interaction.
Lesson and 4 exercisesEconomics
Growth and development: distinguish indicators
Economic growth measures increased output, generally using real GDP.
Lesson and 4 exercisesEconomics
Inflation and purchasing power
Inflation is growth in a general price index over a period.
Lesson and 4 exercisesEconomics
Inequality and social mobility
Inequality concerns unequal access to valued resources such as income, wealth, education and health.
Lesson and 4 exercisesFrench & literature
Narrative: who speaks and sees?
The author is a real person; the narrator is the storytelling voice.
Lesson and 4 exercisesFrench & literature
Sentences, clauses and grammatical roles
A word class describes what a word is; a function describes its role in a sentence.
Lesson and 4 exercisesFrench & literature
Poetry: from device to interpretation
Analysis is not a collection of named devices.
Lesson and 4 exercisesFrench & literature
Drama: words, stage, audience
Drama combines dialogue and stage directions.
Lesson and 4 exercisesFrench & literature
Rhetorical devices: technique to meaning
Similes use an explicit comparison marker; metaphors compare without one.
Lesson and 4 exercisesFrench & literature
Literary commentary: show how a text works
Understand the whole passage, then form an interpretive question.
Lesson and 4 exercisesFrench & literature
French oral preparation: explain, do not recite
A linear explanation follows a passage’s movements and shows how meaning develops.
Lesson and 4 exercisesFrench & literature
Literary essay: reason with the assigned work
A literary essay answers a question about an assigned work and study pathway under your actual exam instructions.
Lesson and 4 exercisesPhilosophy
Philosophy: construct a problem
A philosophical question requires examining concepts and their relations.
Lesson and 4 exercisesPhilosophy
Truth and science: belief and justification
Distinguish belief, reasons for belief and what makes a statement true.
Lesson and 4 exercisesPhilosophy
Justice and freedom: distinguish criteria
Justice can mean rule compliance, equal treatment or justified distribution; these do not always coincide.
Lesson and 4 exercisesPhilosophy
Philosophical essays and text explanation
An essay develops a problem through arguments, distinctions and objections.
Lesson and 4 exercisesPhilosophy
Work and technology: power and dependence
Work can transform surroundings and build capacities, while its conditions may create dependence or remove meaning.
Lesson and 4 exercisesPhilosophy
Consciousness: knowing and judging oneself
Consciousness can mean awareness of experience, reflection on oneself or moral judgement.
Lesson and 4 exercisesPhilosophy
Art and interpretation: meaning and judgement
Interpretation connects observable features with a meaning hypothesis.
Lesson and 4 exercisesPhilosophy
Happiness and desire: satisfaction or fulfilment?
Happiness can mean satisfaction or a lasting assessment of life.
Lesson and 4 exercisesComputer science
Binary: position determines weight
Positional notation multiplies each digit by a power of the base.
Lesson and 4 exercisesComputer science
Algorithms: inputs, steps, output
An algorithm specifies operations for a family of problems.
Lesson and 4 exercisesComputer science
Logic: test every possibility
A boolean proposition is true or false.
Lesson and 4 exercisesComputer science
Loops and search: trace the algorithm
Loops repeat operations with state and continuation conditions.
Lesson and 4 exercisesComputer science
Data and networks: useful abstractions
Data structures organise values and operations: stacks are last-in first-out; queues are first-in first-out.
Lesson and 4 exercisesComputer science
Databases: tables, keys and queries
Relational tables contain rows and typed attributes.
Lesson and 4 exercisesUse your actual syllabus
These original primers explain essential concepts and methods. They do not alone cover every exam pathway, specialism or assigned work. Levels are guides. Check your syllabus and session with your teacher and official sources.