# FURTHER MATHEMATICS PDF

The Cambridge International AS & A Level. Further Mathematics syllabus. 1 Matrices and transformations. 2 Series and induction. 3 Roots of polynomials. Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0). First teaching from September First certification from A Level. Further. Familiarise yourself with the syllabus content and assessment structure of this qualification. International A-level Further Mathematics specification. (PDF, MB).

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PETER JONES. MICHAEL EVANS. KAY LIPSON. Further. Mathematics. Fourth edition. ESSENTIAL. ESSENTIALESSENTIALFurther Mathematics. Fourth Edition . Thank you for your interest in studying Further Mathematics at A-Level. A-level Further Mathematics is made up of Further Pure Mathematics, in which we both. MFP2 Textbook– A-level Further Mathematics – 2. Further Pure 2: Contents . Chapter 1: Complex numbers. 4. Introduction. 5. The general complex.

Australian curriculum Science incl. Curriculum Links Mathematics: Mathematics Domain DEECD This site contains links teaching support materials such as websites, publications, assessment examples, professional learning support and links to current research in the area of Mathematics education. Wolfram MathWorld Interactive mathematics encyclopedia and resources for students and teachers.

Mathematical Association of Victoria Professional support for mathematics education. Australian Curriculum: Mathematics Contains key documents and information on the Mathematics learning area in the Australian curriculum.

Purple Math Helping students gain understanding and self-confidence in algebra and other mathematical concepts. Algebra Help A collection of lessons, calculators, and worksheets created to assist students and teachers of algebra.

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Khan Academy An award-winning library of over 2, videos covering everything from arithmetic to trigonometry and over practice exercises. The focus-directrix properties of the parabola, ellipse and hyperbola, including the eccentricity.

Students are expected to be able to use algebraic differentiation to find dy dx for these curves. The vector product a b of two vectors. The scalar triple product a. Students should be able to use the scalar triple product to find the volume of a tetrahedron and a parallelepiped.

Direction ratios and direction cosines of a line. Numerical solution of first order and second order differential equations. Simpson s rule. The manipulation and solution of algebraic inequalities and inequations, including those involving the modulus sign. The Axioms of a group..

## CSM VCE Further Mathematics Units 3 & 4 Revised Edition

Examples of groups. Cayley tables. Cyclic groups.. Guidance The terms binary operation, closure, associativity, identity and inverse. Isomorphisms will be restricted to groups that have a maximum order of 8.

Further calculus 3 Further matrix algebra. Further Integration Reduction formulae.. The calculation of arc length and the area of a surface of revolution.

Eigenvalues and eigenvectors of and 3 3 matrices.

Understand the term characteristic equation for a matrix. Repeated eigenvalues and complex eigenvalues. Normalised vectors may be required. Reduction of matrices to diagonal form. Further loci and regions in the Argand diagram. Elementary transformations from the z-plane to the w-plane. An understanding of the division theorem and its application to the Euclidean Algorithm and congruences.

## Curriculum Links

Guidance Students should be able to find a matrix P such that P AP is diagonal Symmetric matrices and orthogonal diagonalisation.

Students should understand and be able to use the fact that, every or 3 3 matrix satisfies its own characteristic equation.

Students should be able to apply the algorithm to find the highest common factor of two numbers. Bezout's identity. Students should be able to use back substitution to identity the Bezout's identity for two numbers. Understanding what is meant by two integers a and b to be congruent modulo an integer n. Properties of congruences.

The notation a b mod n is expected. Knowledge of the following properties: a a mod n if a b mod n then b a mod n if a b mod n and b c mod n then a c mod n Addition and subtraction laws for congruences. Multiplication and power laws. For example, students should be able to find the least positive residue of 4 0 modulo 7 Proof is not required. For divisibility by, 3, 4, 5, 6, 9, 0 and. Conditions under which solutions exist should be known. Use of Bezout's identity to find multiplicative inverses.

The multiplicative principle of counting. Set notation is expected; the number of subsets of a set should be known. Addition and subtraction principles. Students should, for example, be able to determine the number of positive integers less than containing the digit 3 at least once. Understanding both n P r and n Cr and when to use them. For example, to determine how many ways there are to select a team of players from a squad of a regardless of playing positions and b if positions matter 6 Further sequences and series 6.

First and second order recurrence relations. The solution of recurrence relations to obtain closed forms. Use of recurrence relations to model applications, e.

Calculation of the mean and variance of discrete probability distributions. Extension of expected value function to include E g X. Questions may require candidates to use these calculations to assess the suitability of models. Students will be expected to use this distribution to model a real-world situation and to comment critically on the appropriateness.

Students will be expected to use their calculators to calculate probabilities including cumulative probabilities. Students will be expected to use the additive property of the Poisson distribution. The additive property of Poisson distributions. The mean and variance of the binomial distribution and the Poisson distribution..

When n is large and p is small the distribution B n, p can be approximated by Po np. Derivations are not required. Geometric and negative binomial distributions.

## FORMULA MF10 Further Mathematics.pdf - List MF10 UNIVERSITY...

Extend ideas of hypothesis tests to test for the mean of a Poisson distribution 4. Extend hypothesis testing to test for the parameter p of a geometric distribution. Applications of the Central Limit Theorem to other distributions. Goodness of fit tests and Contingency Tables The null and alternative hypotheses. Degrees of freedom. Guidance Applications to include the discrete uniform, binomial, Poisson and geometric distributions.

Lengthy calculations will not be required.

Students will be expected to determine the degrees of freedom when one or more parameters are estimated from the data. Definitions, derivations and applications. Use of the probability generating function for the negative binomial, geometric, binomial and Poisson distributions. Use to find the mean and variance.

Type I and Type II errors. Size and Power of Test. The power function. Proofs of standard results may be required.

Appendix 9, Entry codes for optional routes shows how each optional route incorporates the optional papers. Least squares linear regression. The concept of residuals and minimising the sum of squares of residuals.. Guidance Students should have an understanding of the process involved in linear regression.

They should be able to calculate the regression coefficients for the equation y on x using standard formulae. An intuitive use of residuals to check the reasonableness of linear fit and to find possible outliers. Use in refinement of mathematical models. The concept of a continuous random variable. The probability density function and the cumulative distribution function for a continuous random variable.

Derivations are not required Students will be expected to link with their knowledge of histograms and frequency polygons. The formulae used in defining f x and the calculus required will be consistent with the level expected in A level Mathematics and A level Further Mathematics. Relationship between probability density and cumulative distribution functions.. Extension of expected value function to include E g X Mode, median and percentiles of continuous random variables.

Idea of skewness. Use of formulae to calculate the product moment correlation coefficient. Knowledge of the conditions for the use of the product moment correlation coefficient. A knowledge of the effects of coding will be expected. Spearman s rank correlation coefficient, its use, interpretation.

The formulae used to define g x will be consistent with the level required in A level Mathematics and A level Further Mathematics Questions may require candidates to use these calculations to assess the suitability of models. Candidates will be expected to describe the skewness as positive, negative or zero and give a suitable justification.

Including the derivation of the mean, variance and cumulative distribution function. Students will be expected to be able to use the formula to calculate the value of a coe fficient given summary statistics.

An understanding of how to deal with ties will be expected. Students will be expected to calculate the resulting correlation coefficient on their calculator or using the formula. Distribution of linear combinations of independent Normal random variables. Concepts of standard error, estimator, bias. Quality of estimators 5. Concept of a confidence interval and its interpretation. Use of tables for critical values of Spearman s and product moment correlation coefficients.

Students will be expected to know that the critical values for the product moment correlation coefficient require that the data comes from a population having a bivariate normal distribution.

## Further Mathematics

Formal verification of this condition is not required. Candidates will be expected to compare estimators and look for features such as unbiasedness and small variance. Link with hypothesis tests. Candidates will be expected to know how to apply the Normal distribution and use the standard error and obtain confidence intervals for the mean, rather than be concerned with any theoretical derivations. Hypothesis test and confidence interval for the variance of a Normal distribution.

Hypothesis test that two independent random samples are from Normal populations with equal variances. Hypothesis test and confidence interval for the mean of a Normal distribution with unknown variance.

Paired t-test. Use of the pooled estimate of variance. Use of t-distribution. Momentum and impulse. The impulsemomentum principle. The principle of conservation of momentum applied to two spheres colliding directly.. Momentum as a vector. The impulse-momentum principle in vector form.. Kinetic and potential energy, work and power. The workenergy principle. The principle of conservation of mechanical energy.

Elastic strings and springs. Hooke s law. Energy stored in an elastic string or spring.

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Direct impact of elastic spheres. Newton s law of restitution. Loss of kinetic energy due to impact. Guidance The spheres may be modelled as particles.Extension of expected value function to include E g X. Australian curriculum Mathematics incl. Use of t-distribution. This consultation ran from pm on 2 December to pm on 11 January Consultation description This consultation is about the rules and guidance we need to put in place for new AS and A levels in mathematics and further mathematics.

Conditions under which solutions exist should be known.

Solve any quadratic equation with real coefficients.