The following collection of worksheets cover the realms of Pure Mathematics, Statistics, and Discrete Mathematics at both AS and A-level (including Further Mathematics) and can be downloaded and photocopied as appropriate.
Some of the worksheets are VERY extensive in their coverage of the underlying topic(s).
A.
Application of calculus: stationary points, related rates of change, volumes.
Arrangements: basic counting, permutations, combinations (extensive!)
Arrangements: exam questions.
B.
Binomial expansions: positive integer index only.
C.
Central limit theorem (includes binomial and poisson distributions).
Circular measures: arcs & sectors practice.
Circular measures: exam practice.
Circular measures: radians, arcs, sectors etc. (quite extensive).
Complex numbers: basic practice. Includes conjugates, modulus argument form etc.
Complex numbers: De Moivre's theorem; nth roots, trig. id's., series etc.
Complex numbers: loci.
Confidence intervals: population means (using the Central limit).
Continuous random variables: (including means and variances).
Co-ordinate geometry (all the usual! - Quite extensive.) Updated.
Co-ordinate geometry: circles (finding equations etc.)
Co-ordinate geometry: tangents & normals to circles (does not require differentiation!)
Correlation: product moment and Spearmans rank correlation.
D.
Data representation: cumulative frequencies, histograms etc.
Differential equations: a worked example.
Differential equations: two difficult worked examples (Further Mathematics!)
Differential equations: forming and solving (includes related rates of change).
Differential equations: integrating factors.
Differential equations: separating the variables.
Second order differential equations: a worked example (with full solution).
Second order differential equations: linear, constant coefficients.
Differentiation (quite an extensive first exercise).
Differentiation: chain / product / quotient rules. Parametric & implicit differentiation.
Differentiation: an updated version of the above sheet.
Differentiation: implicit and inverse differentiation.
Differentiation: Further Mathematics; inverse funtions, hyperbolic functions etc.
Discrete random variables: expectation and variance.
Discrete random variables: binomial distributions.
Discrete random variables: geometric distributions.
Discrete random variables: binomial and geometric distributions.
Discrete random variables: poisson distributions (includes various approximations).
E.
Errors in measurements: absolute and relative errors.
F.
Functions: domains, ranges, one-one, inverses etc. Updated.
G.
Graph theory: basic theory. Includes Eulerian and Planar graphs.
Group theory: algebra in groups.
Group theory: basic group theory.
Group theory: a list of the basic isomorphism classes.
Group theory: subgroups and cyclic groups.
H.
Hyperbolic functions.
Hypothesis testing: binomial and poisson distributions; large / small samples; type I / II errors etc. (very extensive).
Hypothesis testing: normal distribution questions (using Central limit).
Hypothesis testing: type I / II errors (normal distribution and large sample binomials).
I.
Indices and surds.
Applications of integration: arc lengths and surface areas of rev. Cartesian and parametric equations.
Applications of integration (more extensive version of above sheet - includes approximating areas).
Integration: areas between graphs.
Integration (quite an extensive first exercise).
Integration by substitution.
Integration: (involves inverse trig. functions etc.)
Integration: an 'advanced' worksheet using mostly substitution.
Iteration (involves some radian measure).
Iteration: staircase / cobweb diagrams. Error terms. Newton-Raphson method.
L.
Linear programming: graphical solutions.
Linear programming: the Simplex algorithm.
Logarithms: logarithms and exponential growth / decay.
M.
Matrices: 2 by 2 matrices.
Matrices: 3 by 3 matrices.
Matrices: 2 by 2 and 3 by 3 matrices. Determinants, adjoints, inverses and transformations.
Modulus functions.
Modulus functions & basic graphs.
N.
Networks: minimum connector problems (Prim's and Kruskal's algorithms).
Networks: route inspection problems (the Chinese postman algorithm).
Networks: shortest route problems (Djikstra's algorithm).
Normal distribution: basic questions.
Normal distribution homework: exam questions.
Numerical solution of differential equations: Eulers method (including his modified method).
P.
Polynomial functions: factor theorem etc.
Probability (includes tree diagrams and conditional probability).
Q.
Quadratic functions (very extensive!)
R.
Rational functions and asymptotes.
Reduction formulae.
S.
Sample proportions: confidence intervals and hypothesis testing of binomial proportions (includes type I / II errors).
Sequences and series: A.P.'s, G.P.'s, sigma notation, covergence etc. (very extensive!)
Sequences, series and induction.
Series expansions: binomial expansions with fractional indices. Maclaurin series.
Stationary values (a few questions.)
T.
Trigonometry: no radians. Graphs, equations, Pythagoras etc. (very extensive!)
Trigonometrical functions: identities, equations, compound angle formulae etc. Includes some radians. (Very extensive!)
V.
Vectors: (Quite extensive. Includes lines in 3-d and scalar product etc.)
Vectors and plane geometry. (Thoroughly comprehensive coverage!)
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