Official topics · annotated

HUMAT Test 2027: Full Topic List (Syllabus)

The HUMAT has 60 questions, 10 in each of Scientific Thinking, Academic Literacy, Biology, Chemistry, Mathematics and Physics. Every topic it covers is on Humanitas's own Syllabi 2027, posted on its Apply page on 1 October 2026 and quoted here in full: 139 lines, from 18 in Scientific Thinking and 5 in Academic Literacy to 31 in Mathematics.

All 139 topics of Humanitas University's official topic list, in its own words, each with what to know, the IvyTest lessons that teach it and the questions of our free sample test that test it. Tick a topic off when you have it; your ticks stay in this browser.

Based on "Syllabi 2027", dated 1 October 2026, the list Humanitas University's entrance-exam page still links (checked 30 October 2026). The official wording is quoted as printed; the notes and links are IvyTest's.

Before you start

How to use this list

Humanitas posted Syllabi 2027, the topics for the 2027 tests, before the 2027/28 call; its 2026/27 call put the programme in its Annex A, and Syllabi 2027 changes some science topics against it but not the subjects or the format. The PDF divides each subject into numbered sections with bullet points under them and does not number the bullets, so each section is a group here and each bullet one topic, numbered in the PDF's order and quoted as printed. Academic Literacy has no sections: its page sets out the texts ("CEFR level: C1 and above (text and items)", "adapted from real-world sources, about scientific topics", "approximately 700 words") and then five abilities tested, which are its topics. Humanitas says the test's objective "is not to evaluate previous knowledge, but to measure the skills and abilities relevant to undertaking highly scientific courses of study", so the science lines are what a question can draw on, not a list to recite. Work through a section at a time: read the note, learn it from the lesson, then check yourself on the practice paper's questions before you tick it.

The lessons are part of the Humanitas University Complete Admissions System and open for students who have it; a lesson marked "members" links to the Humanitas University guide, which says what it includes.

0 of 139 topics ticked

HUMAT Test

What's not on the test

Topics Annex A of the 2026/27 EU call named and Syllabi 2027 does not: photosynthesis and chromosome maps in Biology; in Chemistry Boyle's and Charles's laws by name (Physics still lists the ideal gas laws), empirical and molecular formulae, the classification and nomenclature of hydrocarbons and the main functional groups, so organic chemistry is only C–C bonds, structural formulae and isomerism; in Mathematics simple permutations and combinations, the areas, perimeters, surface areas and volumes of polygons and solids, and isometries, similarities and equivalences.

The ellipse and the hyperbola get a "brief mention", "without full treatment", in the syllabus's own words. There is no general culture section: the test is the six subjects above, and no calculator is allowed.

6 topics

Scientific Thinking: 1. Mathematical Thinking

  1. Mathematical Thinking

    What to know: Reading values, trends and rates off line and bar charts, often with two scales, and using a worked example to read a graph of a new kind.

    Lesson (members): Data, tables & graph interpretationSample question 18

  2. Mathematical Thinking

    What to know: How the output of a formula changes when one variable is doubled, halved or raised to a power, without calculating the whole thing.

    Lesson (members): Numerical & quantitative reasoningSample question 6

  3. Mathematical Thinking

    What to know: Substituting values into a given formula and calculating by hand, with units and without a calculator.

    Lesson (members): Numerical & quantitative reasoning

  4. Mathematical Thinking

    What to know: Puzzles where shapes or symbols stand for unknown numbers, solved as simultaneous equations.

    Lesson (members): Numerical & quantitative reasoningSample question 17

  5. Mathematical Thinking

    What to know: Ordering fractions, decimals, negative numbers and powers quickly and safely.

    Lesson (members): Numerical & quantitative reasoning

  6. Mathematical Thinking

    What to know: Estimating with powers of ten and converting units and prefixes (mg to kg, mL to m³, hours to seconds).

    Lesson (members): Numerical & quantitative reasoning

6 topics

Scientific Thinking: 2. Procedural Thinking

  1. Procedural Thinking

    What to know: Applying a set of steps or a flow chart exactly as written, in order, including its conditions and rounding rules.

    Lesson (members): Problem solving & constraint satisfactionSample question 5

  2. Procedural Thinking

    What to know: Tracing how a change in one part of a system of linked parts or rules spreads to the others, step by step.

    Lesson (members): Problem solving & constraint satisfactionSample question 20

  3. Procedural Thinking

    What to know: Choosing one item from each of several sets under constraints, and counting or listing the combinations that work.

    Lesson (members): Problem solving & constraint satisfaction

  4. Procedural Thinking

    What to know: Checking each hypothesis against every result: one counterexample disproves a general rule, and agreeing data only supports it.

    Lesson (members): Scientific method & experimental designSample question 19

  5. Procedural Thinking

    What to know: Picking out the figures a question needs from a table or text full of others.

    Lesson (members): Scientific method & experimental design

  6. Procedural Thinking

    What to know: Matching a short text to the diagram that shows its ideas and their links correctly: what causes what, what belongs to what.

6 topics

Scientific Thinking: 3. Visual Thinking

  1. Visual Thinking

    What to know: Folding nets into solids, turning a cube in your head, and seeing a shape from another side.

    Lesson (members): Abstract, pattern & spatial reasoningSample question 21Sample question 22

  2. Visual Thinking

    What to know: Finding the piece that completes a shape, allowing for rotation.

    Lesson (members): Abstract, pattern & spatial reasoning

  3. Visual Thinking

    What to know: Reflections in a vertical, horizontal or diagonal line, and what a pattern looks like from the other side of a pane.

    Lesson (members): Abstract, pattern & spatial reasoningSample question 23Sample question 24

  4. Visual Thinking

    What to know: Spotting the rule in a sequence or grid of figures, or the figure that matches a description.

    Lesson (members): Abstract, pattern & spatial reasoning

  5. Visual Thinking

    What to know: Reading a figure closely: which object is above, left of or next to which, and what has changed between two pictures.

    Lesson (members): Abstract, pattern & spatial reasoning

  6. Visual Thinking

    What to know: Choosing the statement that describes a picture or a set of shapes exactly, with nothing missing or wrong.

    Lesson (members): Data, tables & graph interpretation

5 topics

Academic Literacy: Abilities tested

  1. Critical Thinking

    What to know: Finding the conclusion an argument supports, its assumptions and flaws, and what weakens or strengthens it, correlation against causation included.

    Lesson (members): Verbal reasoning & argument evaluationLesson (members): Correlation, causation & evidenceSample question 1Sample question 2Sample question 11Sample question 12

  2. Local Expeditious Reading

    What to know: Scanning a 700-word passage for a name, figure or claim without reading every line.

    Sample question 13

  3. Global Expeditious Reading

    What to know: Skimming for the passage's gist, purpose and best title.

    Sample question 14

  4. Global Careful Reading

    What to know: The main idea, how each paragraph builds on the last, and what the passage as a whole does and does not say.

    Sample question 3Sample question 15

  5. Word- and Sentence-Level Processes

    What to know: What a word, connective or preposition means in its sentence, and what signal words like "however" tell you about the writer's view.

    Sample question 4Sample question 16

3 topics

Biology: 1. The chemistry of living organisms

  1. Chemistry of Living Things

    What to know: Hydrogen bonds, ionic and hydrophobic interactions and van der Waals forces, and what they hold together: protein shape, the DNA helix, membranes.

    Lesson (members): Water, weak interactions & the chemistry of life

  2. Chemistry of Living Things

    What to know: The monomers and polymers of each class, protein structure from primary to quaternary, how enzymes work, and what each class does in the cell.

    Lesson (members): CarbohydratesLesson (members): Lipids & biological membranesLesson (members): Proteins & enzymesLesson (members): Nucleic acids & nucleotidesSample question 25

  3. Chemistry of Living Things

    What to know: Each property on the list, why hydrogen bonding causes it, and what it means for living things (cooling by sweating, transport in xylem, stable temperatures).

    Lesson (members): Water, weak interactions & the chemistry of life

6 topics

Biology: 2. The cell as the basis of life

  1. Cell as the Basis of Life

    What to know: The cell theory, why cells stay small (surface area to volume), and what prokaryotic, eukaryotic, animal and plant cells do and do not share.

    Lesson (members): Cell theory, prokaryotes & eukaryotesSample question 26

  2. Cell as the Basis of Life

    What to know: A virus as genome plus capsid (sometimes an envelope), with no metabolism of its own, and its replication inside a host cell.

  3. Cell as the Basis of Life

    What to know: The fluid-mosaic membrane, diffusion, osmosis (cells in hypo- and hypertonic solutions), facilitated diffusion, active transport, endo- and exocytosis.

    Lesson (members): Cell membranes & membrane transportSample question 27

  4. Cell as the Basis of Life

    What to know: Each organelle and its job, and how they work together, from the ribosome and ER to the Golgi and the secretory pathway.

    Lesson (members): Cell structure & organelles

  5. Cell as the Basis of Life

    What to know: Interphase and its checkpoints, the stages of mitosis and of meiosis, and how their products differ.

    Lesson (members): Cell cycle & mitosis

  6. Cell as the Basis of Life

    What to know: The circular bacterial chromosome against linear eukaryotic chromosomes packed with histones, and the human karyotype: 22 pairs of autosomes and the sex chromosomes.

    Lesson (members): Cell cycle & mitosis

6 topics

Biology: 3. Bioenergetics

  1. Bioenergetics

    What to know: ATP's structure, how its hydrolysis releases energy, and how it couples energy-releasing to energy-using reactions.

    Lesson (members): ATP, redox & energy coupling

  2. Bioenergetics

    What to know: Oxidation as loss of electrons or hydrogen, and NAD⁺ and FAD as the carriers that pass them on.

    Lesson (members): ATP, redox & energy coupling

  3. Bioenergetics

    What to know: Where each stage happens, what goes in and comes out, and how much ATP each yields, ending with oxygen as the final electron acceptor.

    Lesson (members): Glycolysis & cellular respirationSample question 28

  4. Bioenergetics

    What to know: Respiration with and without oxygen, and how much less ATP the anaerobic route gives.

    Lesson (members): Glycolysis & cellular respirationLesson (members): Fermentation & anaerobic metabolism

  5. Bioenergetics

    What to know: Pyruvate to ethanol and CO₂ in yeast, or to lactate in muscle, and why both exist: to regenerate NAD⁺ so glycolysis can go on.

    Lesson (members): Fermentation & anaerobic metabolismSample question 29

  6. Bioenergetics

    What to know: How fats (via β-oxidation and acetyl-CoA) and amino acids (after deamination) feed into respiration alongside glucose.

    Lesson (members): Glycolysis & cellular respiration

9 topics

Biology: 4. Reproduction and inheritance

  1. Reproduction and Inheritance

    What to know: Haploid and diploid phases of a life cycle, asexual against sexual reproduction, gamete formation and fertilisation.

    Lesson (members): Meiosis & gametogenesisLesson (members): Reproductive system & human development

  2. Reproduction and Inheritance

    What to know: Segregation and independent assortment, monohybrid, dihybrid and test crosses, and their ratios.

    Lesson (members): Mendelian geneticsSample question 7

  3. Reproduction and Inheritance

    What to know: Incomplete dominance against codominance, multiple alleles, and working out ABO and Rhesus blood groups from parents' genotypes.

    Lesson (members): Non-Mendelian & human geneticsSample question 30

  4. Reproduction and Inheritance

    What to know: Semi-conservative replication, transcription into mRNA, the triplet code, and translation on the ribosome.

    Lesson (members): DNA structure & replicationLesson (members): Transcription, RNA & translation

  5. Reproduction and Inheritance

    What to know: How genes are switched on and off: the lac operon in bacteria, and transcription factors and chromatin in eukaryotes.

    Lesson (members): Gene regulation, mutations & biotechnology

  6. Reproduction and Inheritance

    What to know: Single-gene traits against traits shaped by many genes and the environment, such as height.

    Lesson (members): Non-Mendelian & human genetics

  7. Reproduction and Inheritance

    What to know: The four patterns, carriers, and reading a pedigree to tell them apart.

    Lesson (members): Non-Mendelian & human genetics

  8. Evolution and Selection

    What to know: Point, chromosomal and genomic mutations as the source of variation, then natural selection against selective breeding.

    Lesson (members): Evolution & natural selectionSample question 31

  9. Evolution and Selection

    What to know: Lamarck, Darwin and the modern synthesis, and evolution as changing allele frequencies through selection, drift, mutation and gene flow.

    Lesson (members): Evolution & natural selection

3 topics

Biology: 5. Anatomy and physiology of animals and humans

  1. Anatomy, Physiology and Homeostasis

    What to know: The four tissue types, what each looks like and where it is found.

    Lesson (members): Tissues & histology

  2. Anatomy, Physiology and Homeostasis

    What to know: Each of the eleven systems: its organs, what it does and the key mechanism (the cardiac cycle, gas exchange, digestion, the action potential, contraction, hormones, the nephron).

    Lesson (members): Cardiovascular system & bloodLesson (members): Respiratory system & gas exchangeLesson (members): Digestive system & nutritionLesson (members): Nervous system & sensory physiologyLesson (members): Skeletal system, bones & jointsLesson (members): Muscular systemLesson (members): Endocrine system & hormonesLesson (members): Urinary system, kidney & osmoregulationLesson (members): Reproductive system & human developmentSample question 32

  3. Anatomy, Physiology and Homeostasis

    What to know: Negative feedback in each example: the receptor, the control centre and the effector, and the hormones involved (insulin and glucagon, ADH, PTH and calcitonin).

    Lesson (members): Integrated physiology & homeostatic controlLesson (members): Endocrine system & hormonesSample question 33

5 topics

Chemistry: 1. Structure of matter and the periodic table

  1. Structure of Matter and the Periodic Table

    What to know: Protons, neutrons and electrons, isotopes, and atoms against molecules, elements against compounds.

    Lesson (members): Atomic structure & electronic configurationSample question 34

  2. Structure of Matter and the Periodic Table

    What to know: The four quantum numbers and filling orbitals by the Aufbau order, Pauli's principle and Hund's rule.

    Lesson (members): Atomic structure & electronic configurationSample question 35

  3. Structure of Matter and the Periodic Table

    What to know: Where metals, non-metals and metalloids sit, and the trends in radius, ionisation energy and electron affinity across a period and down a group.

    Lesson (members): Periodic table & periodic trends

  4. Structure of Matter and the Periodic Table

    What to know: Solid, liquid and gas, and homogeneous against heterogeneous mixtures.

    Lesson (members): States of matter & gas laws

  5. Structure of Matter and the Periodic Table

    What to know: pV = nRT, equal volumes holding equal numbers of molecules (Avogadro), and partial pressures adding up (Dalton).

    Lesson (members): States of matter & gas laws

7 topics

Chemistry: 2. Chemical bonding and properties of matter

  1. Chemical Bonding and Properties of Matter

    What to know: How each bond forms and the properties it gives a substance.

    Lesson (members): Chemical bonding & molecular structure

  2. Chemical Bonding and Properties of Matter

    What to know: Electronegativity and its trend, polar against non-polar bonds, and why a molecule with polar bonds can be non-polar overall.

    Lesson (members): Chemical bonding & molecular structureSample question 36

  3. Chemical Bonding and Properties of Matter

    What to know: Counting bonding and lone pairs to predict shape and bond angle (linear, trigonal planar, tetrahedral, pyramidal, bent).

    Lesson (members): Chemical bonding & molecular structureSample question 38

  4. Chemical Bonding and Properties of Matter

    What to know: sp, sp² and sp³ hybrids and the 180°, 120° and 109.5° geometries they give, as in ethyne, ethene and methane.

    Lesson (members): Chemical bonding & molecular structure

  5. Chemical Bonding and Properties of Matter

    What to know: Each force, which molecules show it, and how it affects boiling point and solubility.

    Lesson (members): Intermolecular forces

  6. Chemical Bonding and Properties of Matter

    What to know: The four kinds of solid, what holds each together, and their melting points, hardness and conductivity.

    Lesson (members): Chemical bonding & molecular structureLesson (members): Intermolecular forces

  7. Stoichiometry and Chemical Reactions

    What to know: Relative atomic and molecular mass, the mole and 6.02 × 10²³, and converting between mass, moles and particles.

    Lesson (members): Stoichiometry & chemical equations

6 topics

Chemistry: 3. Chemical reactions and equilibrium

  1. Stoichiometry and Chemical Reactions

    What to know: Recognising each type from its equation.

    Lesson (members): Stoichiometry & chemical equations

  2. Stoichiometry and Chemical Reactions

    What to know: Balancing atoms (and charge) in an equation by inspection.

    Lesson (members): Stoichiometry & chemical equations

  3. Stoichiometry and Chemical Reactions

    What to know: Mole ratios from an equation, masses of product, and the limiting reactant and what is left over.

    Lesson (members): Stoichiometry & chemical equationsSample question 8

  4. Stoichiometry and Chemical Reactions

    What to know: Molarity, dilution, and titration-style calculations such as the volume of base that neutralises an acid.

    Lesson (members): Solutions, solubility & concentrationSample question 37

  5. Equilibria, Acids-Bases and Redox

    What to know: Dynamic equilibrium, the equilibrium constant, and which way an equilibrium shifts when concentration, pressure or temperature changes.

    Lesson (members): Chemical equilibrium

  6. Equilibria, Acids-Bases and Redox

    What to know: Water moving across a semi-permeable membrane towards higher osmolarity, and osmolarity counting every dissolved particle (1 mol NaCl gives 2 osmol).

6 topics

Chemistry: 4. Acids and bases

  1. Equilibria, Acids-Bases and Redox

    What to know: The two definitions and conjugate acid-base pairs.

    Lesson (members): Acids, bases, pH & buffers

  2. Equilibria, Acids-Bases and Redox

    What to know: pH = -log[H⁺], pOH and Kw, and how pH changes when a strong acid is diluted.

    Lesson (members): Acids, bases, pH & buffersSample question 39

  3. Equilibria, Acids-Bases and Redox

    What to know: Acid plus base giving salt and water, and the stoichiometry of a neutralisation.

    Lesson (members): Acids, bases, pH & buffers

  4. Equilibria, Acids-Bases and Redox

    What to know: Strong against weak by degree of dissociation, and Ka and Kb.

    Lesson (members): Acids, bases, pH & buffers

  5. Equilibria, Acids-Bases and Redox

    What to know: Why some salt solutions are acidic or basic, from the strength of the acid and base they come from.

    Lesson (members): Acids, bases, pH & buffers

  6. Equilibria, Acids-Bases and Redox

    What to know: How a weak acid and its conjugate base resist pH change, and pH = pKa + log([A⁻]/[HA]).

    Lesson (members): Acids, bases, pH & buffers

4 topics

Chemistry: 5. Oxidation–reduction reactions and introductory organic chemistry

  1. Equilibria, Acids-Bases and Redox

    What to know: The rules for assigning oxidation numbers in molecules and ions.

    Lesson (members): Redox & electrochemistry

  2. Equilibria, Acids-Bases and Redox

    What to know: Which species is oxidised and which reduced, and that the oxidising agent is the one reduced.

    Lesson (members): Redox & electrochemistrySample question 40

  3. Equilibria, Acids-Bases and Redox

    What to know: Balancing electrons lost and gained, by oxidation numbers or half-equations.

    Lesson (members): Redox & electrochemistry

  4. Fundamentals of Organic Chemistry

    What to know: Single, double and triple carbon-carbon bonds, drawing structural formulae, and structural and cis-trans isomers.

    Lesson (members): Organic chemistry foundations & nomenclatureLesson (members): Isomerism & stereochemistrySample question 41Sample question 42

10 topics

Mathematics: 1. Arithmetic and algebra

  1. Algebra and Number Sets

    What to know: ℕ, ℤ, ℚ and ℝ, which contains which, and irrational numbers.

    Lesson (members): Sets, number systems & intervals

  2. Algebra and Number Sets

    What to know: Order of operations and the properties of operations, absolute value and its inequalities, proportions, and successive percentage changes.

    Lesson (members): Arithmetic, fractions, ratios & percentagesSample question 44Sample question 46

  3. Algebra and Number Sets

    What to know: The laws of indices, roots as fractional powers, and the laws of logarithms in base 10 and base e.

    Lesson (members): Powers, roots, exponentials & logarithms

  4. Algebra and Number Sets

    What to know: Expanding and factorising, the special products, (a + b)ⁿ by Pascal's triangle, and simplifying algebraic fractions.

    Lesson (members): Algebraic expressions & equations

  5. Algebra and Number Sets

    What to know: Solving linear and quadratic equations and inequalities, rational inequalities by sign tables, and two equations in two unknowns.

    Lesson (members): Algebraic expressions & equations

  6. Functions

    What to know: What a function is, its domain and codomain, where it is positive or negative, increasing or decreasing, and where its maximum or minimum is.

    Lesson (members): Functions & graphsLesson (members): Polynomials & quadraticsSample question 45

  7. Functions

    What to know: The shape and key features of each family's graph.

    Lesson (members): Functions & graphsLesson (members): Polynomials & quadratics

  8. Functions

    What to know: f(g(x)), finding an inverse, and when a function has one.

    Lesson (members): Functions & graphs

  9. Functions

    What to know: Solving equations like 3ˣ⁺¹ = 81, log x = 2 and sin x = ½, and the matching inequalities.

    Lesson (members): Functions & graphsSample question 43

  10. Functions

    What to know: Sketching a graph, translations and reflections, and even and odd functions.

    Lesson (members): Functions & graphs

6 topics

Mathematics: 2. Analytical geometry and trigonometry

  1. Geometry and Trigonometry

    What to know: The distance and midpoint formulae, gradient, and the equation of a line through given points.

    Lesson (members): Coordinate geometry

  2. Geometry and Trigonometry

    What to know: Equal gradients for parallel lines, gradients multiplying to -1 for perpendicular ones, and the point-to-line distance formula.

    Lesson (members): Coordinate geometrySample question 47

  3. Geometry and Trigonometry

    What to know: The circle's centre-radius equation, the parabola's vertex and axis, and recognising the equations of an ellipse and a hyperbola.

    Lesson (members): Coordinate geometry

  4. Geometry and Trigonometry

    What to know: Converting between degrees and radians (π rad = 180°).

    Lesson (members): Trigonometry

  5. Geometry and Trigonometry

    What to know: The three functions, their graphs, and their exact values at 0°, 30°, 45°, 60° and 90°.

    Lesson (members): TrigonometrySample question 48

  6. Geometry and Trigonometry

    What to know: sin² + cos² = 1, the sum, difference and double-angle formulae, and solving triangles with the sine and cosine rules.

    Lesson (members): Trigonometry

5 topics

Mathematics: 3. Logic and mathematical reasoning

  1. Logic and Mathematical Reasoning

    What to know: AND, OR, NOT and IF...THEN, truth tables, and equivalent forms such as the contrapositive.

    Lesson (members): Formal & propositional logicSample question 50

  2. Logic and Mathematical Reasoning

    What to know: "For all" and "there exists", and negating them: the negation of "all passed" is "at least one did not".

    Lesson (members): Formal & propositional logicSample question 49

  3. Logic and Mathematical Reasoning

    What to know: Working out whether a compound statement is true from the truth of its parts.

    Lesson (members): Formal & propositional logic

  4. Logic and Mathematical Reasoning

    What to know: Valid patterns such as modus ponens and modus tollens, and the fallacies that look like them.

    Lesson (members): Formal & propositional logic

  5. Logic and Mathematical Reasoning

    What to know: Assuming the opposite and reaching a contradiction, as in the proof that √2 is irrational.

    Lesson (members): Formal & propositional logic

5 topics

Mathematics: 4. Probability

  1. Probability, Statistics and Combinatorics

    What to know: Sample space and events, probability as favourable over possible outcomes, and relative frequency.

    Lesson (members): Probability

  2. Probability, Statistics and Combinatorics

    What to know: Multiplying for independent events, adding for mutually exclusive ones, and not confusing the two.

    Lesson (members): Probability

  3. Probability, Statistics and Combinatorics

    What to know: P(A|B) = P(A and B)/P(B), and drawing without replacement.

    Lesson (members): ProbabilitySample question 9

  4. Probability, Statistics and Combinatorics

    What to know: Adding the probability of an event over every way it can happen, with a tree diagram.

    Lesson (members): Probability

  5. Probability, Statistics and Combinatorics

    What to know: Reversing a conditional probability, as in the chance of disease given a positive test.

    Lesson (members): Probability

5 topics

Mathematics: 5. Statistics

  1. Probability, Statistics and Combinatorics

    What to know: Telling the four kinds of variable apart, with an example of each.

    Lesson (members): Statistics & data interpretation

  2. Probability, Statistics and Combinatorics

    What to know: Frequency tables, bar charts, histograms and pie charts, and cumulative frequency.

    Lesson (members): Statistics & data interpretation

  3. Probability, Statistics and Combinatorics

    What to know: Calculating each, and finding a missing value from a given mean.

    Lesson (members): Statistics & data interpretationSample question 51

  4. Probability, Statistics and Combinatorics

    What to know: Measures of spread, and calculating variance and standard deviation for a small data set.

    Lesson (members): Statistics & data interpretation

  5. Probability, Statistics and Combinatorics

    What to know: What a percentile means, and quartiles as the 25th, 50th and 75th.

    Lesson (members): Statistics & data interpretation

6 topics

Physics: 1. Measures and Kinematics

  1. Measures and Kinematics

    What to know: Base and derived quantities, checking an equation by its dimensions, and scalars against vectors.

    Lesson (members): Measurement, units, scalars & vectors

  2. Measures and Kinematics

    What to know: The SI base units, derived units in base units (the newton as kg·m/s²), CGS units, and prefixes from pico to giga.

    Lesson (members): Measurement, units, scalars & vectorsSample question 52

  3. Measures and Kinematics

    What to know: The definitions, and reading them from position-time and velocity-time graphs.

    Lesson (members): Kinematics

  4. Measures and Kinematics

    What to know: Constant velocity in a line, and uniform circular motion: period, frequency, angular velocity and centripetal acceleration.

    Lesson (members): Kinematics

  5. Measures and Kinematics

    What to know: The equations of constant acceleration and free fall.

    Lesson (members): KinematicsSample question 53

  6. Measures and Kinematics

    What to know: Simple harmonic motion: amplitude, period and frequency, as for a mass on a spring or a pendulum.

6 topics

Physics: 2. Dynamics

  1. Dynamics

    What to know: Resolving and adding forces, and the moment of a force about a point.

    Lesson (members): Forces & Newtonian dynamicsLesson (members): Statics, equilibrium & gravitationSample question 54

  2. Dynamics

    What to know: Mass against weight (W = mg), and F = Gm₁m₂/r² with how g changes with height.

    Lesson (members): Statics, equilibrium & gravitation

  3. Dynamics

    What to know: Newton's three laws and free-body diagrams.

    Lesson (members): Forces & Newtonian dynamics

  4. Dynamics

    What to know: Work as force times displacement, kinetic and potential energy, conservation of energy, and the work done against friction or by a braking force.

    Lesson (members): Work, energy & powerSample question 10

  5. Dynamics

    What to know: Impulse as change of momentum, and conservation of momentum in collisions and explosions.

    Lesson (members): Momentum, impulse & collisions

  6. Dynamics

    What to know: L = Iω, and why a spinning skater speeds up when pulling in the arms.

6 topics

Physics: 3. Fluid mechanics and Optics

  1. Fluid Mechanics and Optics

    What to know: Density, pressure as force over area, gauge against absolute pressure, and converting pascals, atmospheres, bar and mmHg.

    Lesson (members): Fluid statics & dynamics

  2. Fluid Mechanics and Optics

    What to know: Pressure passing through a fluid (the hydraulic press), and the buoyant force equal to the weight of fluid displaced.

    Lesson (members): Fluid statics & dynamics

  3. Fluid Mechanics and Optics

    What to know: Pressure at depth, p = p₀ + ρgh, continuity and Bernoulli's equation for a moving fluid.

    Lesson (members): Fluid statics & dynamicsSample question 55

  4. Fluid Mechanics and Optics

    What to know: Light takes the path of least time, and how that gives the laws of reflection and refraction.

    Lesson (members): Geometrical & physical optics

  5. Fluid Mechanics and Optics

    What to know: The law of reflection, n₁ sin θ₁ = n₂ sin θ₂, what changes when light enters glass (speed and wavelength, not frequency), and total internal reflection.

    Lesson (members): Geometrical & physical opticsSample question 56

  6. Fluid Mechanics and Optics

    What to know: Dispersion in a prism, images in mirrors and lenses, and interference and diffraction as evidence that light is a wave.

    Lesson (members): Geometrical & physical optics

6 topics

Physics: 4. Thermodynamics

  1. Thermodynamics

    What to know: Temperature scales, Q = mcΔT, heat capacity, and mixing problems.

    Lesson (members): Heat & thermodynamicsSample question 57

  2. Thermodynamics

    What to know: Conduction, convection and radiation, and Q = mL at melting and boiling.

    Lesson (members): Heat & thermodynamics

  3. Thermodynamics

    What to know: Boyle's, Charles's and Gay-Lussac's laws and pV = nRT, always in kelvin.

    Lesson (members): Gases & molecular physicsSample question 58

  4. Thermodynamics

    What to know: ΔU = Q - W with its sign convention, and the second law's statements about heat flow and engines.

    Lesson (members): Heat & thermodynamics

  5. Thermodynamics

    What to know: Entropy as a measure of disorder that never decreases in an isolated system.

    Lesson (members): Heat & thermodynamics

  6. Thermodynamics

    What to know: A cycle on a p-V diagram, work as the enclosed area, efficiency = W/Q_in and the Carnot limit.

    Lesson (members): Heat & thermodynamics

6 topics

Physics: 5. Electrostatics and Electrodynamics

  1. Electrostatics and Electrodynamics

    What to know: The inverse-square force between charges, field and potential of a point charge, and Gauss's law for symmetric charge distributions.

    Lesson (members): Electrostatics & electric fieldsSample question 60

  2. Electrostatics and Electrodynamics

    What to know: Combining capacitors and resistors in series and parallel, Ohm's two laws (V = IR and R = ρL/A), and Kirchhoff's current and voltage rules.

    Lesson (members): Electrostatics & electric fieldsLesson (members): Current, circuits & electrical powerSample question 59

  3. Electrostatics and Electrodynamics

    What to know: Emf and internal resistance, electrical work and power (P = VI = I²R), and heating by the Joule effect.

    Lesson (members): Current, circuits & electrical power

  4. Electrostatics and Electrodynamics

    What to know: Fields of magnets and currents, the force on a moving charge and on a wire, and the field of a straight wire from Ampère's law.

    Lesson (members): Magnetism & electromagnetism

  5. Electrostatics and Electrodynamics

    What to know: Faraday's and Lenz's laws, generators and transformers, and alternating current.

    Lesson (members): Magnetism & electromagnetism

  6. Electrostatics and Electrodynamics

    What to know: The electromagnetic spectrum, c = fλ, and photon energy E = hf.

    Lesson (members): Magnetism & electromagnetism

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