Study notes · Free to read
Chapter-by-chapter notes written straight from the curriculum. Read free, then practise the same chapter with an AI-generated quiz.
Latest posts
Filter by board, class, and subject to find notes for exactly what you're studying.
Learn the features of pteridophytes and their four classes, trace the fern life cycle and tell homospory from heterospory, follow the gymnosperm life cycle, and see why ferns and conifers matter to people.
Read articleCompare green, brown and red algae and their economic importance, describe the features of bryophytes and tell liverworts from mosses, trace the life cycle of Funaria through alternation of generations, and explain why bryophytes matter.
Read articleDescribe the features, reproduction and four classes of fungi, explain their economic importance along with lichens and mycorrhiza, outline the structure and status of viruses with the contributions of Ivanowsky, Beijerinck and Stanley, and define viroids and prions.
Read articleDistinguish the three domains of life and the five kingdoms, describe the bacterial cell and classify bacteria by shape, nutrition, respiration and Gram stain, explain bacterial reproduction and uses, and survey the main groups of protists.
Read articleUnderstand why living things are classified, the branches of taxonomy, the species concept and taxonomic hierarchy for man, housefly, mango and wheat, the rules of binomial nomenclature, and artificial, natural and phylogenetic systems.
Read articleDefine a random variable and construct its probability distribution, check that a distribution is valid by testing non-negativity and a total of one, and compute the mean or expected value of a random variable.
Read articleApply the theorem of total probability across a partition of the sample space, use Bayes' theorem to find reverse or posterior probabilities, and solve diagnostic-test and defective-item word problems step by step.
Read articleCompute the conditional probability of one event given another, apply the multiplication theorem, test whether events are independent, and solve mixed problems that combine conditional probability with the addition and multiplication theorems.
Read articleSolve two-variable linear programming problems graphically, identify bounded, unbounded and empty feasible regions, tell feasible from infeasible solutions, decide whether an optimum exists, and find the optimal solution.
Read articleLearn the language of linear programming — decision variables, constraints, objective function and optimisation — weigh its advantages and limitations, and translate real-world word problems into linear programming formulations.
Read articleWrite equations of planes in one-point, normal and intercept form, find the normal and the distance of a point from a plane, calculate angles between planes and between a line and a plane, and find where a line meets a plane.
Read articleFind direction cosines and ratios of a line, write vector and Cartesian equations of lines, decide whether two lines are coplanar, intersecting or skew, and calculate the shortest distance between skew lines and from a point to a line.
Read articleDefine the vector product and its geometric meaning with the right-hand rule, use it to find the areas of triangles and parallelograms, and test whether two vectors are collinear.
Read articleDefine the scalar product and its geometric meaning, use its properties to find angles and test perpendicularity, and compute the scalar and vector projections of one vector on another.
Read articleRepresent vectors as directed line segments with magnitude and direction, classify equal, unit, zero and collinear vectors, find direction cosines, work with i, j, k components, and use the section formula for position vectors.
Read articleSolve homogeneous first-order differential equations with the substitution y = vx, solve linear equations dy/dx + Py = Q with an integrating factor, and handle the analogous form dx/dy + Px = Q.
Read articleFind the order and degree of a differential equation, form differential equations by eliminating arbitrary constants, tell general from particular solutions, and solve first-order equations by separating the variables.
Read articleFind areas bounded by lines, circles, parabolas and ellipses and the axes, handle polynomial, modulus, exponential and logarithmic curves, find the area between two curves, and set up applied area problems.
Read articleEvaluate definite integrals with the fundamental theorem of calculus, reverse and split limits, use the reflection property about the midpoint, and apply the even-odd and zero-to-2a properties.
Read articleIntegrate reciprocals of linear combinations of sine and cosine and of their squares, integrate one sine-cosine combination divided by another, and use power substitutions for integrals such as 1 over x times x to the n plus 1.
Read articleLearn the standard integrals involving x squared plus or minus a squared and their square roots, integrate reciprocals of quadratics and their roots by completing the square, handle linear numerators, and reduce integrals to these forms.
Read articleIntegrate products with integration by parts, split proper rational functions into partial fractions with linear, repeated and irreducible quadratic factors, and integrate improper rational functions after division.
Read articleIntegrate by substitution, evaluate integrals where a function appears with its own derivative in power and quotient forms, and derive the integrals of the tangent, cotangent, secant and cosecant functions.
Read articleUnderstand integration as the inverse of differentiation, find anti-derivatives of polynomials and standard trigonometric functions, integrate powers of sine and cosine up to the fourth power, and integrate the reciprocal and exponential functions.
Read article