### Analysis and Approaches

**Prerequisites**

- Students wishing to study the HL course will need to have completed Year 10 Maths: Higher Level or Mathematical Methods Unit 1&2.
- Students wishing to study the SL course will need to have completed Year 10 Algebra Maths (SL) or Year 10 Maths: Higher Level.

**Course Structure: **SL and HL

**Course Description**

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 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%)

### Applications and Interpretation

**Prerequisites**

- Students wishing to study the HL course will need to have completed Year 10 Maths: Higher Level or Mathematical Methods Unit 1&2.
- Students wishing to study the SL course will need to have completed Year 10 Algebra Maths (SL) or Year 10 Maths: Higher Level.

**Course Structure: **SL and HL

#### Course Description

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, 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%)