# GROUP 5 - APPLICATIONS AND INTERPRETATIONS

This course is offered at Standard Level and Higher Level and is designed for competent mathematics students who enjoy describing the real world and solving practical problems using mathematics, those who are interested in harnessing the power of technology alongside exploring mathematical models and statistics and enjoy the more practical side of mathematics. It is best suited to students interested in social sciences, natural sciences, medicine, statistics, business, engineering, some economics, psychology and design.

#### Standard Level

The standard level course consists of number and algebra: scientific notation, arithmetic and geometric sequences and series and their applications in finance including loan repayments, simple treatment of logarithms and exponentials, simple proof, approximations and errors; functions: creating, fitting and using models with linear, exponential, natural logarithm, cubic and simple trigonometric functions; geometry and trigonometry: volume and surface area of 3 dimensional solids, right-angled and non-right-angled trigonometry including bearings, surface area and volume of composite 3 dimensional solids, establishing optimum positions and paths using Voronoi diagrams; statistics and probability; collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation using Pearson’s product-moment and Spearman’s rank correlation coefficients, regression, calculating probabilities, probability diagrams, the normal distribution Chi-squared test or independence and goodness of fit; calculus: differentiation including analysing graphical behaviour of functions and optimisation, using simple integration and the trapezium/trapezoidal rule to calculate areas of irregular shapes.

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 active, 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: laws of logarithms, complex numbers and their practical applications, matrices and their applications for solving systems of equations, for geometric transformations and their applications to probability; functions: use of log-log graphs, graph transformations, creating, fitting and using models with further trigonometric, logarithmic rational, logistic and piecewise functions; geometry and trigonometry: vector concepts and their applications in kinematics applications of adjacency matrices, and tree and cycle algorithms; statistics and probability: binomial and Poisson distributions, designing data collection methods, tests for reliability and validity, hypothesis testing and confidence intervals; calculus: kinematics and practical problems involving rates of change, volumes of revolution, setting up and solving models involving differential equations using numerical and analytic methods, slope fields, coupled and second-order differential equations in context, in addition to all of the content in the standard level course and is intended to meet the needs of students whose interest in mathematics is more practical than theoretical but seek more challenging content.

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

## MATHEMATICS PATHWAY AT GGS

Group 5 - Analysis and Approaches
Year 11 and 12 - IB

Mathematics
Year 10

Mathematics
Timbertop - Year 9

Mathematics
Years 5 to 8