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Define a matrix and its order, test when two matrices are equal, recognise row, column, square, diagonal, scalar, identity and zero matrices, add, subtract and scale matrices using their properties, and solve matrix equations for unknown entries.
Read articleSee why sine, cosine and tangent need restricted domains before they can be inverted, learn the principal value branch of all six inverse trigonometric functions, evaluate principal values, and sketch each graph as a reflection in the line y = x.
Read articleTest relations for the reflexive, symmetric and transitive properties, recognise equivalence relations and their classes, prove a function one-one or onto, and count the one-one, onto and bijective functions between finite sets.
Read articleFind the hormones made by the heart, kidney and gut, compare how protein and steroid hormones act on cells, relate growth hormone and thyroid imbalances to dwarfism, acromegaly, cretinism and goitre, and understand diabetes mellitus and Addison's disease.
Read articleDefine hormones and tell endocrine from exocrine glands, meet the hypothalamus and the hormones of the anterior and posterior pituitary, study the pineal, thyroid and parathyroid glands, and see how adrenal, pancreatic and gonadal hormones act.
Read articleCompare neural and hormonal coordination and map the central, peripheral and visceral nervous system, describe the parts and types of a neuron, follow resting and action potentials along an axon, and compare synapses before touring the forebrain, midbrain and hindbrain.
Read articleCount the 80 bones of the axial skeleton and sort ribs into true, false and floating, list the 126 bones of the limbs and girdles, classify joints and find ball-and-socket, hinge, pivot, gliding and saddle joints, and learn common muscle and bone disorders.
Read articleTell movement from locomotion and compare amoeboid, ciliary and muscular movement, contrast skeletal, visceral and cardiac muscle, map the sarcomere with its A band, I band, H zone and Z line, and follow the sliding filament theory step by step.
Read articleLearn what each part of the nephron reabsorbs and secretes, see how the counter-current mechanism concentrates urine, follow ADH, the renin-angiotensin-aldosterone system and ANF, and understand micturition, other excretory organs, kidney disorders and dialysis.
Read articleSort animals by the nitrogen waste they excrete, label the cortex, medulla, pyramids and columns of Bertini of the kidney, trace the parts and types of a nephron, and follow filtration, reabsorption and secretion with a GFR calculation.
Read articleExplore the chambers, valves and nodal tissue of the human heart and why the SA node sets the pace, follow the cardiac cycle and calculate cardiac output, read the P wave, QRS complex and T wave of an ECG, and learn about double circulation and heart disorders.
Read articleLearn what plasma and the formed elements contain, compare RBCs, the five kinds of WBCs and platelets, work out safe transfusions using ABO and Rh groups, follow the clotting cascade, and see how lymph and tissue fluid work.
Read articleSee how partial pressure differences move oxygen and carbon dioxide across the alveoli and tissues, read the oxygen dissociation curve and the Bohr effect, follow the three ways carbon dioxide travels, and learn how breathing is regulated and what goes wrong in lung disorders.
Read articleCompare respiratory organs from sponges to mammals, trace air from the nostrils to the alveoli, understand how the diaphragm and intercostal muscles change lung pressure, and calculate tidal volume, vital capacity and other lung volumes.
Read articleSort plant growth regulators into promoters and inhibitors and learn the observations that revealed each one, then see how auxins, gibberellins, cytokinins, ethylene and abscisic acid control growth, ripening, ageing and dormancy.
Read articleSee why growth is an irreversible increase and which meristems keep plants growing, read the lag, log and stationary phases of a sigmoid curve, compare arithmetic and geometric growth, calculate absolute and relative growth rates, and learn differentiation and plasticity.
Read articleTrace pyruvic acid through the link reaction and the Krebs cycle, follow electrons through complexes I to IV to oxygen, build the ATP balance sheet for one glucose with its assumptions, and calculate the respiratory quotient of different foods.
Read articleLearn how plants exchange gases without lungs, how cellular respiration differs from burning, why ATP is the cell's energy currency, how glycolysis turns glucose into pyruvic acid, and how alcoholic and lactic acid fermentation compare.
Read articleFollow the Calvin cycle through carboxylation, reduction and regeneration, count the ATP and NADPH for one glucose, see how Kranz anatomy concentrates carbon dioxide in C4 plants, understand photorespiration, and apply the law of limiting factors.
Read articleFollow the classic experiments behind the equation of photosynthesis, locate the grana and stroma, read absorption and action spectra, trace the Z-scheme through photosystems II and I, and see how a proton gradient drives ATP synthase.
Read articleWork through leptotene, zygotene, pachytene, diplotene and diakinesis, follow homologous chromosomes through metaphase I, anaphase I and telophase I, compare meiosis II with mitosis, and see how meiosis keeps chromosome numbers constant and creates variation.
Read articleFollow a cell through G1, S, G2 and M phases and the resting G0 stage, track chromosomes through prophase, metaphase, anaphase and telophase, compare cytokinesis in animal and plant cells, and see why mitosis matters for growth and repair.
Read articleCompare monosaccharides, oligosaccharides and polysaccharides such as starch, glycogen, cellulose and chitin, understand fatty acids, glycerides and phospholipids, compare DNA and RNA nucleotides, and learn how enzymes work and what affects their activity.
Read articleSee how chemical analysis separates the acid-soluble pool from the acid-insoluble fraction, tell primary from secondary metabolites, draw and classify amino acids, and understand the four levels of protein structure and what proteins do.
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