GCE A-Level Further Mathematics study guide
GCE A-Level Further Mathematics · Work through your exam, one topic at a time.
This independent study page provides practice for GCE A-Level Further Mathematics. Its editorial learning areas include Complex; Vectors; Differential Equations; Sequences Series; Calculus; Dynamics; Probability Statistics. The GCE A-Level Further Mathematics study guide has 7 sections and about 2,840 words.
01Complex numbers
Complex numbers tests arithmetic in the form a + bi, conjugates, modulus and argument, the Argand diagram, modulus–argument form, and the roots of polynomial equations with real coefficients. De Moivre's theorem and geometric interpretations appear in the more demanding questions.
364 words, about 2 min02Linear Algebra and Vector Geometry
Linear algebra and vector geometry practice is about structure: whether a system has solutions, what a matrix does to space, and how lines, planes and vectors sit relative to one another in three dimensions. Reduce the augmented matrix to row echelon form; count pivots in the coefficient block (rank A) and in the augmented block (rank [A b]).
465 words, about 2 min03Differential Equations
Differential-equation practice develops whether you can classify an equation, choose the right solution method, and apply initial or boundary conditions without losing constants along the way. Separable: separate and integrate, then apply the initial condition before rearranging if possible.
389 words, about 2 min04Sequences and series
Sequences and series examines arithmetic and geometric progressions, sigma notation, sums to infinity and the binomial expansion. You should be able to derive and apply the standard formulae, decide when an infinite sum converges, and extract a specified coefficient from a binomial expansion without expanding everything.
390 words, about 2 min05Calculus
Calculus practice develops the ability to move fluently between a function, its rate of change, and its accumulated total. Expect differentiation of composite, implicit and parametric forms, evaluation of definite and improper integrals, and questions that require you to justify a limit before differentiating.
348 words, about 2 min06Dynamics: Newton's Laws and Forces
Dynamics explains motion through force. This section tests Newton's three laws, F = ma applied to single particles and to connected bodies, weight and normal reaction, limiting friction, motion on inclined planes, lift problems and the transmission of tension through light inextensible strings.
487 words, about 2 min07Statistics and Probability
This statistics and probability chapter explores how data are collected, summarized, and interpreted, and how probability models uncertainty. Expect measures of centre and spread, graphical displays, normal distributions and z-scores, counting-based probability, conditional probability, and critical evaluation of study design and correlation versus causation.
397 words, about 2 min