Class 11 questions with answers

15 questions, 1 with pictures · Diversity, taxonomy, and systematics · Meanings of ranks and organism examples · Identification and binomial nomenclature · Logic and direction of the taxonomic hierarchy

15 questions · Changing classification systems and five-kingdom criteria · Protist groups and their adaptations · Monera: diversity, nutrition, and reproduction · Fungal structure, reproduction, and classes · Plantae, Animalia, and alternation of generations · Viruses, viroids, prions, and lichens

15 questions · Changing systems of plant classification · Bryophyte structure and gametophyte-dominant life cycle · Pteridophytes, vascular tissues, and heterospory · Seed plants: gymnosperms and angiosperms · Comparative life-cycle reasoning across plant groups · Algal diversity, reproduction, and classes

15 questions · Chordate features, subphyla, and vertebrate divisions · Fundamental bases of animal classification · Porifera, Cnidaria, and Ctenophora · Flatworms, roundworms, and segmented worms · Arthropod and mollusc body plans · Echinoderm and hemichordate diagnostics · Tetrapod classes: Amphibia, Reptilia, Aves, and Mammalia · Cyclostomes, cartilaginous fishes, and bony fishes

15 questions, 15 with pictures · Regions of the root tip · Root systems and their functions · Leaf structure and venation · Simple, pinnate and palmate leaves · Flower organisation, sexuality and symmetry · Patterns of phyllotaxy · Racemose and cymose inflorescences · Calyx, corolla and aestivation · Ovary position and insertion of floral parts · Types of placentation · Fruit development and pericarp structure · Structure of a dicotyledonous seed · Structure of a monocotyledonous seed · Diagnostic description of Solanaceae · Semi-technical description, floral formula and diagram

15 questions, 9 with pictures · Tissue systems and epidermal specialisations · Vascular bundle arrangement and cambium · Dicot and monocot root anatomy · Dicot and monocot stem anatomy · Dorsiventral and isobilateral leaf anatomy

15 questions, 7 with pictures · Animal organisation from tissues to organ systems · Frog adaptations and external morphology · Frog reproduction, development and ecological role · Frog digestive system and nutrition · Frog respiration and circulation · Frog neural, endocrine and sensory coordination · Frog excretion and cloacal pathways

15 questions, 13 with pictures · Cell as the unit of life, cell theory and cellular diversity · Prokaryotic cell organisation, envelope and surface structures · Eukaryotic cell plan, plasma membrane and cell wall · Endomembrane system: ER, Golgi, lysosomes and vacuoles · Mitochondria, plastids and chloroplast architecture · Ribosomes, cytoskeleton, cilia, flagella and centrioles · Nucleus, chromatin and chromosome form

15 questions, 10 with pictures · Chemical analysis of living tissue and its composition · Protein composition, functions and structural hierarchy · Small biomolecules: amino acids, sugars and lipids · Metabolite categories and biomolecular size fractions · Polysaccharide architecture and biological roles · Nucleotide components and nucleic acids · Enzyme catalysis, reaction energy and action cycle · Enzyme activity, reaction classes and cofactors

15 questions, 8 with pictures · Cell-cycle phases, timing and the G0 state · DNA content and chromosome-number accounting · Mitotic chromosome and spindle dynamics · Prophase I pairing and recombination · Cytokinesis and the significance of mitosis · Meiosis I and II segregation and outcomes · Mitosis–meiosis comparison and biological significance

15 questions, 9 with pictures · Chloroplast compartmentation and light–carbon reaction dependency · Thylakoid chemiosmosis and ATP synthase · Experimental evidence and the overall photosynthetic process · Photosynthetic pigments, spectra and photosystem organisation · Electron flow, water splitting and photophosphorylation · Calvin-cycle fixation, stages and energy budget · C4 spatial pathway and suppression of photorespiration · Limiting factors and photosynthetic response curves

15 questions, 4 with pictures · Glycolysis sequence, carbon flow and energy accounting · Respiration foundations, plant gas exchange and step-wise energy capture · Pyruvate fates, fermentation and aerobic contrast · Pyruvate oxidation and TCA-cycle regeneration · Mitochondrial ETS, oxygen and oxidative phosphorylation · Respiratory balance-sheet assumptions and ATP accounting · Amphibolic respiration and alternative substrate entry · Respiratory quotient calculation and substrate inference

15 questions, 8 with pictures · Growth definition, measurement and indeterminate meristems · Growth phases, root zones and environmental conditions · Arithmetic, geometric and sigmoid growth patterns · Absolute and relative growth rates and growth equations · Differentiation, dedifferentiation and redifferentiation · Development, plasticity and intrinsic–extrinsic control · PGR identity, functional groups and discovery evidence · PGR physiological effects, applications and interactions

15 questions, 8 with pictures · Respiratory-organ diversity and the steps of respiration · Human airway, conducting and exchange parts, and pleura · Inspiration and expiration: thoracic volume and pressure mechanics · Respiratory volumes, pulmonary capacities and spirometry · Partial-pressure gradients, gas diffusion and the alveolar membrane · Oxygen transport, haemoglobin loading and dissociation curve · Carbon-dioxide transport and reversible bicarbonate formation · Neural regulation of respiration and respiratory disorders

15 questions, 9 with pictures · Blood, plasma and the functions of formed elements · ABO and Rh grouping, transfusion compatibility and Rh incompatibility · Blood coagulation, tissue fluid and lymph · Double circulation, vessel structure and special vascular pathways · Open and closed circulation and vertebrate heart patterns · Human heart structure, valves and nodal conduction · Cardiac cycle, output, heart sounds and ECG · Cardiac regulation and major circulatory disorders

15 questions, 6 with pictures · Human urinary system, kidney organisation and nephron structure · Micturition, urine characteristics and accessory excretory organs · Urine formation by filtration, reabsorption and secretion · Segment-specific functions of the renal tubule · Counter-current mechanism and concentration of urine · Hormonal and feedback regulation of kidney function · Excretory disorders, haemodialysis and kidney transplantation · Nitrogenous wastes, excretory modes and animal excretory structures

15 questions, 4 with pictures · Movement, locomotion and types of muscular tissue · Skeletal-muscle organisation and sarcomere bands · Sliding-filament contraction, relaxation and muscle-fibre energetics · Actin, myosin and regulatory contractile proteins · Axial skeleton: skull, vertebral column, sternum and ribs · Appendicular skeleton, limb bones and girdles · Joint types, mobility and anatomical examples · Muscular and skeletal disorders

15 questions · Neural coordination and organisation across animals · Human CNS, PNS and directional pathways · Neuron structure, types and myelination · Resting membrane polarisation and ion gradients · Action-potential generation and axon conduction · Electrical and chemical synaptic transmission · Forebrain structure and integrative functions · Midbrain, hindbrain and brainstem functions

15 questions, 4 with pictures · Endocrine coordination, hormone definition, and gland locations · Hypothalamus–pituitary control and pituitary hormone functions · Pineal, thyroid, parathyroid, and thymus regulation · Pancreatic glucose homeostasis and diabetes mellitus · Hormones from heart, kidney, and gastrointestinal tissues · Adrenal compartments, stress responses, and corticoid actions · Gonadal hormone sources and reproductive actions · Hormone receptor specificity and signal mechanisms

15 questions · Chemistry, matter, states, and classification · Measurement, SI units, uncertainty, and dimensional analysis · Laws of chemical combination and Dalton's atomic theory · Atomic, average atomic, molecular, and formula mass · Mass percent, mole fraction, molarity, molality, and dilution · Mole, Avogadro constant, entities, and molar mass · Mass composition, empirical formula, and molecular formula · Balanced equations and stoichiometric calculation · Limiting reagent, excess reagent, and product yield

15 questions, 1 with pictures · Atomic spectra, hydrogen series, and the Rydberg relation · Subatomic particles, atomic identity, isotopes, and ions · Thomson and Rutherford models: evidence and limitations · Electromagnetic radiation, quantization, and photoelectric effect · Bohr model of hydrogen-like species · Matter waves and Heisenberg uncertainty · Orbital probability, shapes, and nodes · Quantum-mechanical orbitals and quantum numbers · Orbital energies, shielding, and effective nuclear charge · Electronic configurations, filling rules, and subshell stability

15 questions · Mendeleev's predictions and the modern periodic law · Need for classification and historical periodic schemes · Electronic configuration, periodic position, and blocks · Periods, groups, and systematic element nomenclature · Block characteristics, metallicity, and second-period anomalies · Atomic radius, ionic radius, and isoelectronic ordering · Ionization enthalpy, successive removal, and exceptions · Electron gain enthalpy and electronegativity · Valence, oxidation state, and periodic compound formulas · Periodic reactivity and acidic-basic character of oxides

15 questions · Hydrogen bonding: cause, types, and consequences · Kössel–Lewis bonding, Lewis structures, formal charge, and octet limits · Ionic bond formation and lattice enthalpy · Bond parameters, bond order trends, and resonance · Bond polarity, molecular dipole moment, and polarisation · Hybridisation, molecular geometry, and multiple bonding · VSEPR electron-domain geometry and molecular shape · Valence-bond overlap, potential energy, and σ/π bonds · MO electron configurations, bond order, stability, and magnetism · Molecular-orbital formation, symmetry, and energy ordering

15 questions · Systems, surroundings, properties, states, and processes · Heat, pressure-volume work, sign conventions, and the first law · Enthalpy, internal energy, and process conditions · Heat capacity, specific heat, and calorimetry · Thermochemical equations and standard enthalpy changes · Hess's law, bond enthalpy, atomisation, and lattice cycles · Second and third laws, surroundings entropy, and stability · Spontaneity, entropy, and total-entropy criteria · Gibbs energy, temperature, and spontaneity · Standard Gibbs energy and equilibrium constants

15 questions · Dynamic physical and chemical equilibrium · Equilibrium composition and stoichiometric change tables · Gibbs energy and the equilibrium constant · Heterogeneous equilibria and the relation between Kp and Kc · Law of mass action and equilibrium-constant expressions · Reaction quotient, direction, and extent of reaction · Le Chatelier responses to concentration, pressure, and temperature · Arrhenius, Brønsted-Lowry, and Lewis acid-base models · Water ionization, pH, and strong electrolytes · Weak-acid/base ionization, Ka, Kb, and common-ion effects · Salt hydrolysis and buffer solutions · Solubility product, common ions, and selective precipitation

15 questions · Ion–electron balancing in acidic and basic media · Average, fractional, and atom-specific oxidation states · Classical, electron-transfer, and oxidation-number views of redox · Oxidants, reductants, and oxidation-state limits · Oxidation-number rules, exceptions, and Stock notation · Balancing redox equations by oxidation-number change · Combination, decomposition, displacement, and disproportionation · Redox titrations, indicators, endpoints, and stoichiometry · Redox couples, the Daniell cell, and charge transport · Standard reduction potentials, redox strength, and feasibility

15 questions · Carbon hybridisation, molecular shape, and sigma/pi bonding · Structural representations, functional groups, and homologous series · IUPAC nomenclature of chains, functional groups, and benzene derivatives · Structural isomerism, stereoisomerism, and resonance distinction · Bond fission, reactive intermediates, electrophiles/nucleophiles, and arrows · Inductive, resonance, electromeric, and hyperconjugative effects · Substitution, addition, elimination, and rearrangement reactions · Purification, extraction, distillation, and chromatography · Qualitative detection by sodium fusion and specific tests · Quantitative estimation of C, H, N, halogens, S, P, and O

15 questions · Hydrocarbon classification, IUPAC naming, and structural isomerism · Substituent effects, orientation, reactivity, and hydrocarbon toxicity · Alkyne structure, preparation, acidity, and additions · Preparation of alkanes and limits of coupling methods · Alkane properties, combustion, pyrolysis, and radical halogenation · Alkene bonding and geometrical isomerism · Conformations of ethane and torsional strain · Alkene preparation, electrophilic addition, peroxide effect, and ozonolysis · Benzene structure, resonance, and aromaticity · Preparation and electrophilic substitution of benzene

15 questions, 4 with pictures · Writing a set in roster form and in set-builder form · A set is a well-defined collection, and membership is written with the element symbol · Finite and infinite sets, and the number of elements n(S) · The empty set · Equal sets · Establishing that two set expressions are equal · Subsets, proper subsets and supersets · Intervals as subsets of the real numbers · The universal set and its picture as a Venn diagram · The difference of two sets · The complement of a set and De Morgan's laws · The intersection of two sets, and disjoint sets

15 questions, 2 with pictures · An ordered pair records two objects in a fixed order, and two pairs are equal only when both components match · Given the pairs of A × B, A is the set of first entries and B the set of second entries · The cartesian product A × B collects every ordered pair whose first entry comes from A and second from B · If A has p elements and B has q, then A × B has exactly pq elements · Repeating the product gives ordered triples, and over R it gives the plane and space · A cartesian product distributes over union and over intersection, reaching both terms · A × B and B × A have the same size but are different sets · A function is evaluated by substituting the input, and a linear rule can be recovered from its pairs · A relation from A to B is a subset of A × B, cut out by a stated rule · The domain holds the first entries, the range the second entries, and the codomain is the whole target set · A relation is a function when every element of the first set has one and only one image · Every subset of A × B is a relation, so there are 2^(pq) of them · The domain is every input the rule admits, and the range is every value it actually takes · Two real functions may be added, subtracted, scaled, multiplied and divided pointwise · Identity, constant, polynomial, rational, modulus, signum and greatest-integer functions each have a fixed rule and shape

15 questions, 2 with pictures · 2sin²(x/2) = 1 − cos x and 2cos²(x/2) = 1 + cos x give the half-angle magnitudes, and the quadrant of x/2 decides their signs · An angle records an amount of rotation together with its direction, so it may exceed a full turn and may be negative · In a circle of radius r an arc of length l subtends l = rθ, with θ measured in radians · One radian is the angle an arc of length one subtends in a unit circle, so a radian measure is an arc divided by a radius · Since π radian = 180°, a degree measure is multiplied by π/180 and a radian measure by 180/π · At the quadrantal angles the point sits on an axis, and going round a whole turn returns every value unchanged · For the point P(a, b) at angle x on the unit circle, cos x is the first coordinate and sin x the second · Shifting by π/2 exchanges sine and cosine, while shifting by π or 2π keeps the function and only decides a sign · cosec, sec, tan and cot are built as quotients of sine and cosine, so each is undefined exactly where its denominator vanishes · One ratio fixes the magnitude of the rest through the identities, and the quadrant fixes their signs · Because the values repeat after 2π, any angle can be shifted by whole revolutions into a range where the table applies · The signs of the coordinates in each quadrant fix the sign of every function there, and reflecting in the x-axis gives the odd-even rules · The table for 0, π/6, π/4, π/3 and π/2 gives every value the chapter's evaluations are built from · cos(x ± y) and sin(x ± y) mix both functions of both angles, and tan(x ± y) has the product in its denominator · sin and cos take every real input and land in [−1, 1]; the four quotients drop the inputs their denominators kill, and sec and cosec never land inside (−1, 1)

15 questions, 2 with pictures · A complex number is a number of the form a + ib with a and b real; a is Re z and b — not ib — is Im z · One equation between complex numbers is two real equations: a + ib = c + id exactly when a = c AND b = d · The product is (ac − bd) + i(ad + bc): the minus sign in the real part is i² = −1 arriving · The real numbers leave x² = −1 unsolved, so a symbol i is defined with i² = −1 and the system is enlarged to contain it · z·z̄ = |z|² = a² + b²: multiplying by the conjugate is how a complex expression is turned into a real one · |a + ib| = √(a² + b²) is a single NON-NEGATIVE REAL number, not a complex one · Addition is defined part by part, and subtraction is adding the additive inverse, so the minus sign reaches BOTH parts · A quotient is made real-denominatored by multiplying above and below by the conjugate of the divisor · The powers of i cycle with period four — i⁴ᵏ = 1, i⁴ᵏ⁺¹ = i, i⁴ᵏ⁺² = −1, i⁴ᵏ⁺³ = −i — and negative powers cycle too · Because complex numbers obey the same laws, (z₁ ± z₂)² and ³ and z₁² − z₂² expand exactly as for reals — the only extra step is i² = −1 · Every non-zero complex number has an inverse a/(a²+b²) + i(−b)/(a²+b²), which is the conjugate divided by the modulus squared · Plotting x + iy at the point (x, y) turns the complex numbers into a plane, in which the modulus is a distance from the origin and the axes acquire names · Both pass straight through a product and a quotient — |z₁z₂| = |z₁||z₂| and conj(z₁z₂) = z̄₁z̄₂ — which is why they simplify what expansion would not · √−a means √a·i for positive a, and the rule √a·√b = √(ab) FAILS when both a and b are negative · The conjugate z̄ = a − ib reverses the sign of the IMAGINARY part only, and in the Argand plane it is the mirror image in the real axis

15 questions, 2 with pictures · A solution is drawn by marking the boundary with an open circle for a strict inequality or a dark circle for a slack one and shading the side the solutions lie on · An inequality using less than or greater than is strict, and one using at most or at least is slack, which is what decides whether the boundary value is a solution · Many real statements fix a limit rather than a value, and a limit needs one of the symbols less than, greater than, at most or at least instead of an equals sign · A linear inequality is solved by clearing any denominators, collecting the variable on one side with Rule 1 and dividing by its coefficient with Rule 2 · A worded condition is turned into an inequality by naming the unknown, writing the quantity the words describe and choosing the symbol the words demand · An inequality between numbers alone is numerical, one containing a variable is literal, and one that bounds a quantity on both sides at once is double · An inequality is linear when the variables appear only to the first power, and the chapter names ax plus b compared with 0 as linear in one variable and ax plus by compared with c as linear in two · A solution is a value of the variable that makes the inequality a true statement, and the solution set is the collection of all of them · Two real numbers or two algebraic expressions related by less than, greater than, at most or at least form an inequality · The same inequality has different solution sets over the natural numbers, the integers and the real numbers, and over a restricted set it may have none at all · When both sides of an inequality are multiplied or divided by a negative number the inequality symbol is reversed · A solution over the real numbers is written as an interval, with a round bracket where the endpoint is excluded and a square bracket where it is included · A double inequality is solved by performing the same operation on all three parts at once, reversing both symbols if that operation is a multiplication or division by a negative number · Adding or subtracting the same number on both sides, and multiplying or dividing both sides by the same positive number, leave the inequality symbol unchanged · A system of two inequalities is solved by solving each one separately and keeping the values common to both

15 questions, 1 with pictures · Choosing r objects is the same as rejecting the other n minus r, so n C r equals n C of n minus r; two equal C symbols therefore have lower indices that are either equal or add up to n, and n C r plus n C r minus one is n plus one C r · When one position is restricted -- the last digit must make the number even, the first digit may not be zero -- that position is filled first and the free positions are counted afterwards from what is left · A problem of arranging objects is counted by drawing one vacant place for each position and filling them in succession, each place taking one fewer object than the one before it when repetition is not allowed · When the outcomes fall into separate cases that cannot both happen, each case is counted on its own and the counts are added, which is how 'at least' and 'at most' questions are answered · Every combination of r objects yields r factorial permutations, so n P r equals n C r times r factorial, and n C r is n factorial divided by r factorial times n minus r factorial · If each of r places may take any of the n objects, with repetition allowed, the number of arrangements is n multiplied by itself r times, written n to the power r · The number of permutations of n different objects taken r at a time is the falling product n(n-1)(n-2)...(n-r+1), which equals n! divided by (n-r)! and is written n P r · The symbol n factorial denotes the product of the first n natural numbers, satisfies n! = n times (n-1)!, and is defined to be 1 when n is 0 · When one choice is followed by another, the number of ways the two happen in that order is the first count multiplied by the second, and the same holds for any number of successive choices · When so many objects must come from each of several groups, the separate selections are multiplied; if the chosen objects must then be arranged, that count multiplies again · When some objects are indistinguishable, the count of all arrangements is divided by the factorial of the number of objects of each repeated kind · A permutation is an arrangement of objects in a definite order, so two selections of the same objects in different orders are different permutations · An equation relating two P symbols is solved by writing each as a falling product, cancelling the factors common to both sides, and rejecting any root that cannot be a number of objects · Objects that must stay together are tied into a single block, arranged with the rest and then arranged inside the block; objects that must stay apart are placed into the gaps left by the others, or counted as the total minus the together count · A combination is a selection of objects in which the order is not important, so the same objects chosen in a different order are the same combination

15 questions, 1 with pictures · Adding or subtracting the expansions of a sum and a difference · Computing a numerical power by splitting the base · Expanding a trinomial by grouping it into a binomial · Expanding when the quantities themselves carry coefficients · How the two powers move through the expansion · Pascal's triangle and the addition rule that builds it · The entries of the triangle are the numbers nCr · Approximating a power with the first few terms · How many terms an expansion has · The statement of the binomial theorem and its proof by induction · Why expanding a binomial needs a theorem · The expansion of (1+x) to the n, and the two sums it gives · Why the signs alternate in the expansion of a difference · Expanding when one quantity is a fraction or a reciprocal · Comparing a large power with a number using only the first terms

15 questions · A sequence as a function whose domain is the natural numbers · Finding which term of a G.P. a given value is · Finite and infinite sequences · How two given terms fix the whole G.P. · Reading terms off a formula for the nth term · The series associated with a sequence · What makes a list a sequence, and how its terms are named · A sequence given by a recurrence relation · The general term of a G.P. · Choosing three unknown terms of a G.P. symmetrically · Sigma notation for a series · How many terms of a G.P. reach a given sum · What makes a progression geometric · The sum of the first n terms of a G.P. · The geometric mean of two numbers, and inserting several

15 questions, 11 with pictures · The coordinate formulae the chapter recalls before it begins · Parallel lines and the equality of their slopes · Perpendicular lines and the product of their slopes · The inclination of a line and the definition of its slope · The angle between two lines from their slopes · Equations of horizontal and vertical lines · Computing the slope from the coordinates of any two points on the line · The point of intersection of two lines, and when three lines are concurrent · The point-slope form of the equation of a line · The two-point form of the equation of a line · The intercept form of the equation of a line · The slope-intercept form, with a y-intercept or an x-intercept · Feet of perpendiculars, mirror images, and distance measured along a given line · The distance between two parallel lines · The perpendicular distance of a point from a line

15 questions, 5 with pictures · How the cutting plane decides which conic appears · Fixing a circle from the conditions it must meet · Recovering a circle's centre and radius by completing the square · Writing a circle from its centre and radius · The eccentricity and latus rectum of a hyperbola · The focus and directrix that define a parabola · The latus rectum of a parabola · The latus rectum of an ellipse · The two foci that define an ellipse · Building an ellipse's equation from given measurements · How an ellipse's semi-axes, focal distance and eccentricity are tied together · Reading an ellipse off its standard equation · The four standard parabolas and what their equations say · The two foci that define a hyperbola · Conics that model a real object

15 questions, 2 with pictures · The three axes, the three coordinate planes and the origin · Deciding whether three points are collinear or form a right angled triangle · The form a point takes when it lies on an axis or in a coordinate plane · The octant a point lies in, read from the signs of its three coordinates · A point's triplet as its three perpendicular distances from the coordinate planes · The distance between two points in space · The foot of the perpendicular from a point onto a coordinate plane or axis · Naming a quadrilateral from its sides and diagonals, and finding a missing vertex · The equation of a set of points described by a condition on distances · The centroid of a triangle as the average of its three vertices

15 questions, 3 with pictures · Matching the angle so that the standard limit applies · The average rate of change, the instantaneous rate, and the slope of the tangent · The left hand limit, the right hand limit, and when the limit exists · The power rule and the derivative of a polynomial · The product rule for derivatives · The quotient rule for derivatives · The standard limit of the difference of nth powers · The limit at a point and the value of the function there may differ · The algebra of limits: sum, difference, product, quotient and constant multiple · The derivative function from the first principle · The limit of a polynomial function is its value at the point · The limit of a rational function when the denominator does not vanish · The order of limits, the sandwich theorem, and the bounds on sine over x · The zero over zero form and cancelling the factor that causes it · The two standard trigonometric limits

15 questions · The range of a series · What adding to, or multiplying, every observation does to the spread · Why a measure of central tendency is not enough · Mean deviation about the mean for ungrouped data · The median of a list, and mean deviation about it · Deviations about a central value, and why their signs are dropped · The limitations of mean deviation · The step-deviation shortcut for the mean, variance and standard deviation · From squared deviations to the variance · The standard deviation and its units · The sum-of-squares formula for the variance · Mean deviation for a continuous frequency distribution · Mean deviation for a discrete frequency distribution · Variance and standard deviation of a frequency distribution · Recovering or correcting observations from a given mean and variance

15 questions, 2 with pictures · An event is a subset of the sample space · Simple events and compound events · The impossible event and the sure event · The probability of an event as the sum of its outcome probabilities · The algebra of events: not A, A or B, A and B, A but not B · Exhaustive events, and mutually exclusive and exhaustive events · Mutually exclusive events · Deciding whether an assignment of probabilities is valid · The axioms of probability · Equally likely outcomes and the ratio of favourable outcomes · Probability when the outcomes have to be counted · The addition rule for the event A or B · The probability of the event not A · The probability that neither event occurs, and that atleast one occurs

15 questions, 2 with pictures · Measurement standards and SI units · Indirect measurement, magnification and instrument precision · Rounding and preserving guard digits · Significant figures and scientific notation · Significant-figure arithmetic and relative uncertainty · Dimensional formulae from physical definitions · Dimensionless angles and angular change · Dimensional homogeneity and limits of checking · Converting powered and compound units · Deriving power laws and estimating physical scales

15 questions, 4 with pictures · Point-object approximation and the description of motion · Displacement, path length and average motion · Instantaneous velocity and its calculation · Reading position-time graphs · Signed acceleration and speed changes · Areas of motion graphs · Constraints on physically possible motion plots · Constant-acceleration equations and initial position · Vertical motion under constant gravity · Stopping, reaction time and free-fall scaling · Relative velocity in one dimension

15 questions, 5 with pictures · Free-vector equality and scalar multiplication · Head-to-tail addition, subtraction and vector bounds · Path length, displacement and average velocity · Scalars, vectors and meaningful operations · Resolution, signed components and unit vectors · Flight time, maximum height and unequal levels · Independent simultaneous component motion · Instantaneous velocity and acceleration in components · Analytical sums and relative velocity · Projectile independence, trajectory and highest point · Range, complementary angles and constrained launches · Uniform circular motion, angular rate and acceleration

15 questions, 7 with pictures · Inertia, equilibrium and the instantaneous force · Resolving concurrent forces · Vector second law and finite force intervals · Position-time slopes and impulsive changes · Vector impulse and collision duration · Connected bodies, tension and contact forces · Momentum conservation and recoil · Mutual forces and system boundaries · Normal force, apparent weight and spring restoration · Inclined-plane limiting friction · Level and banked circular roads

15 questions, 3 with pictures · Mechanical energy and dissipative transfers · Potential energy, conservative forces and reference choice · Scalar product and work by a specified force · Kinetic energy and speed comparisons · Net work and kinetic-energy change · Work from force-position graphs and integrals · Allowed positions and turning points · Spring energy and energy exchange · Energy and the taut-string condition in a vertical circle · Power, efficiency and energy units · Collision systems, momentum and kinetic-energy conversion · Head-on and planar collision predictions · Mass leaving a moving system

15 questions, 3 with pictures · Rigid-body translation, rotation and rolling · Centre of gravity and centre of mass · Centre of mass of particles and composite bodies · External forces and centre-of-mass motion · Angular velocity and linear velocity vectors · Vector products, area and volume · Angular momentum of particles and systems · Force balance, torque balance and support reactions · Torque, moment arms and couples · Moment of inertia, standard shapes and radius of gyration · Fixed-axis rotational kinematics · Rotational dynamics, energy, work and power · Axial angular momentum and conservation

15 questions, 3 with pictures · Elliptical orbits, equal areas and angular momentum · Kepler period scaling and estimating central masses · Measuring G with a torsion balance · Universal attraction, inverse-square scaling and action–reaction · Shell theorem, hemispheres and absence of shielding · Vector superposition and neutral points · Surface gravity and changes with altitude and depth · Conservative work, exact potential differences and pair counting · Potential, field and zero reference · Escape threshold and residual speed · Binding energy and transfers between circular orbits · Circular orbital speed and satellite mass · Weightlessness, shielding and tidal effects

15 questions, 2 with pictures · Stress and reference-length strain · Poisson ratio and transverse contraction · Elastic extension with series and shared loads · Young modulus, material stiffness and wire geometry · Reading Young modulus and strength from stress-strain data · Shear modulus and deformation of coils · Bulk compression, density and compressibility · Elastic energy under gradual loading · Elastic recovery and proportionality · Load limits, beam shape and material failure

15 questions, 2 with pictures · Hydrostatic balance and communicating liquids · Pascal transmission and hydraulic displacement · Pressure, force and area · Absolute pressure, gauge pressure and barometers · Bernoulli energy balance and its limits · Steady flow and mass continuity · Efflux and dynamic lift · Viscous pipe flow and radius sensitivity · Stokes drag, buoyancy and terminal motion · Viscous shear and temperature response · Curvature pressure in drops and bubbles · Surface energy, surface tension and soap films · Contact angle, wetting and capillarity

15 questions, 2 with pictures · Conductive heat current and thermal resistance · Thermometric scales and gas thermometers · Blackbody spectra and thermal-radiation laws · Free expansion and constrained thermal stress · Linear, area and volume expansion · Thermal density change and anomalous water · Heat capacities, power and calorimetry · Phase-change energy and heating curves · Pressure, phase coexistence and triple points · Temperature, heat and energy transfer · Convection, radiation and thermal insulation · Newton cooling and excess temperature

15 questions, 2 with pictures · Thermal equilibrium and the zeroth law · First law, signs and path independence · Internal energy and modes of energy transfer · Isochoric and isobaric energy balances · Reversibility requires restoration of system and surroundings · Heat capacity, calorimetry and heating rates · Ideal-gas heat capacities and Cp−Cv · Isothermal ideal-gas energy and work · State variables, equations of state and scaling · Quasi-static paths and insulated free expansion · Reversible adiabatic relations and temperature change · Cyclic state changes and signed PV work · Second-law restrictions, engines and refrigerators · Carnot cycle, temperature limit and working substance

15 questions, 3 with pictures · Molecular matter and dynamic equilibrium · Molecular volume, number density and spacing · Avogadro law and partial pressures · Ideal-gas equation, amount and pressure conventions · Ideal-gas limits and real-gas graphs · Wall collisions, isotropy and pressure · Temperature, translational energy and rms speed · Active degrees of freedom and equipartition · Gas and solid heat capacities · Mean free path and collision times

15 questions, 1 with pictures · Combining harmonic functions and commensurate periods · Energy partition, amplitude scaling and energy period · Period, frequency and angular frequency · Periodic, oscillatory and simple harmonic motion · Initial conditions and phase conventions · Uniform circular motion and its linear projections · Direction of velocity, acceleration and restoring force · Maximum speed and speed at a given displacement · Pendulum equilibrium under horizontal acceleration · Amplitude, equilibrium offset and sinusoidal displacement · Restoring linear force and the defining SHM condition · Spring period, calibration and gravity independence · Two restoring springs and a free two-mass spring · Small-angle pendulum and period scaling · Buoyant cork and liquid-column restoring forces

15 questions, 2 with pictures · Mechanical disturbances and wave types · Algebraic superposition and phase interference · Progressive wave equations, phase and units · Beat envelope and frequency determination · Wave speed and tension on strings · Wave speed, source frequency and flight times · Elasticity, sound speed and Laplace correction · Air-column modes and displacement-pressure nodes · Reflection and boundary conditions · Standing-wave structure, amplitude and phase · String normal modes and musical quality