 # GROUP 5 - ANALYSIS AND APPROACHES

This course is offered at Standard Level and Higher Level and is designed for competent mathematics students who wish to pursue studies in mathematics at university or subjects that have a large mathematical content; it is for students who enjoy developing mathematical arguments, problem solving and exploring real and abstract applications, with and without technology. It is best suited to students interested in mathematics, engineering, physical sciences and some economics.

#### Standard Level

The standard level course consists of number and algebra: scientific notation, arithmetic and geometric sequences and series and their applications including financial applications, laws of logarithms and exponentials, solving exponential equations, simple proof, approximations and errors, and the binomial theorem; functions: equations of straight lines, concepts and properties of functions and their graphs, including composite, inverse, the identity, rational, exponential, logarithmic and quadratic functions, solving equations both analytically and graphically, and transformation of graphs; geometry and trigonometry: volume and surface area of 3 dimensional solids, right-angled and non-right-angled trigonometry including bearings and angles of elevation and depression, radian measure, the unit circle and Pythagorean identity, double angle identities for sine and cosine, composite trigonometric functions, solving trigonometric equations; statistics and probability; collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation, regression, calculating probabilities, probability diagrams, the normal distribution with standardisation of variables, and the binomial distribution; calculus: informal ideas of limits and convergence, differentiation including analysing graphical behaviour of functions, finding equations of normals and tangents, optimisation, kinematics involving displacement, velocity, acceleration and total distance travelled, the chain and product and quotient rules, definite and indefinite integration.

ASSESSMENT
Internal Assessment
An individual exploration. (20%)
This is a piece of written work that involves investigating an area of mathematics that holds particular interest to the student.

External Examinations
Paper 1: (1.5 hours, calculator free, 40%)
Paper 2: (1.5 hours, calculator active, 40%)

#### Higher Level

The Higher Level course is more challenging and requires good algebraic skills. It consists of number and algebra: permutations and combinations, partial fractions, complex numbers, proof by induction, contradiction and counter-example, and solutions of systems of linear equations; functions: factor and remainder theorems, sums and products of roots of polynomials, rational functions, odd and even functions, self-inverse functions, solving function inequalities and the modulus function; geometry and trigonometry: reciprocal trigonometric ratios, inverse trigonometric functions, compound angle identities, double angle identity for tangent, symmetry properties of trigonometric graphs, vector theory, applications with lines and planes, and vector algebra; statistics and probability: Bayes theorem, probability distributions, probability density functions, expectation algebra; calculus: introduction to continuity and differentiability, convergence and divergence, differentiation from first principles, limits and L’Hopital’s rule, implicit differentiation, derivatives of invers and reciprocal trigonometric functions, integration by substitution and parts, volumes of revolution, solution of first order differential equations using Euler’s method, by separating variables and using the integrating factor, Maclaurin series, in addition to all of the content in the standard level course and is intended to meet the needs of students who enjoy developing their mathematics to become fluent in the construction of mathematical arguments and develop strong skills in mathematical thinking.

ASSESSMENT
Internal Assessment
An individual exploration. (20%)
This is a piece of written work that involves investigating an area of mathematics that holds particular interest to the student.

External Examinations
Paper 1: (2 hours, calculator free, 30%)
Paper 2: (2 hours, calculator active, 30%)
Paper 3: (1 hour, calculator active, 20%)

## MATHEMATICS PATHWAY AT GGS

Mathematics
Year 11 and 12 - VCE

Mathematics
Year 10

Mathematics
Timbertop - Year 9

Mathematics
Years 5 to 8