**Year 9 Advanced Mathematics**

In this collection of lessons and live exercises, students will explore content relevant to the current high school Mathematics curriculum. They will develop existing skills and acquire new knowledge of various mathematical concepts. Video lessons and live exercises allow our students to learn about mathematical concepts through highly-detailed video tutorials, from which they can apply their learning and practise their skills with corresponding live exercises.

Each video tutorial simplifies and expands on Mathematical concepts, and caters for students at any ability level. At the conclusion of each unit, there is also a set of ‘challenge’ exercises that will test the knowledge of students at all levels.
Content for Year 9 includes:

- In Arithmetic and Algebra, students learn about using numbers and figures, as well as a variety of algebraic concepts. These concepts include linear algebra, quadratic factorisations and algebraic fractions.
- In Indices, students learn about factorising integers; as well as the various index laws for addition, subtraction, powers, zeroes and negative indices.
- In Measurement, students look at conversion and simplifying length and mass; converting capacities and time; perimeter, circumference and Pythagoras’ Theorem; in addition to the learning about finding the areas of various polygons.
- In Consumer Arithmetic, students cover ‘real-world’ financial concepts such as salary, wages, deductions, budgets, tax and discounts.
- In Rates and Variation, live exercises are available which cover ratio and proportion, as well as a number of challenge exercises.
- In Equations, students cover types of basic types of linear and quadratic equations, including equations with fractions, inequalities, and substitution of formulas.
- In Surds, students cover the basic rules of simplifying and arithmetic involving surds, the product of surds and rationalising denominators of surds.
- In Coordinate Geometry, students will explore gradients and equations involving lines, sketching of lines, parallel and perpendicular lines, as well as sketching and writing regions and inequalities of lines.
- In Simultaneous Equations, students engage with the various methods of simultaneous equations, as well as the applications of those equations.

**Year 10 Advanced Mathematics**

In Year 10, students further develop their knowledge of mathematical concepts they cover as part of the Year 9 curriculum. As students come to grips with increasingly advanced mathematical concepts, our video tutorials and live exercises continue to focus on giving simple, detailed instruction that makes it easy for students to further enhance their skills.
As students prepare for the transition into senior level Maths studies in Year 11 and 12, it is essential that they are able to fully comprehend Mathematical concepts and their applications. For this reason, each lesson includes extended live exercises and practise questions so they are ready for the tough road ahead.

Content for Year 10 includes:

- In Further Consumer Arithmetic, students learn about simple and compound interest and its daily applications; including how interest is calculated for loans and credit cards. This is an important life skill for students who are learning to manage their finances.
- In Quadratic Equations, students expand upon equation concepts they covered in Year 9. This includes the skills of solving quadratic equations, perfect squares, the quadratic formula and its applications. This unit also includes further quadratic equations, such as those which include factors and substitutions.
- In Surface Area and Volume, students learn to calculate the dimensions and space of three-dimensional shapes such as prisms and spheres.
- In Further Graphs, students expand on their knowledge of graphs, straight lines, regions and parabolas to include hyperbolas, exponential curves and circles.
- In Further Simultaneous Equations, students expand their knowledge of solving linear and quadratic equations to include multiple types of equations
- In Further Statistics, students learn about the calculation of means and standard deviations, using different variables and dispersion, as well as understanding the range and distribution of such variables.
- In Probability, students learn about the laws and nature of chance. This includes understanding of Venn Diagrams, and calculating probability through one or more dependent or independent events.
- In Similarity, students learn to calculate the area and volume of shapes by finding similar forms and shapes. This enables students to calculate the area of unusual polygons and solids using proofs and problem solving.
- In further Trigonometry, students learn the rules of sine and cosine and the applications of these rules, in addition to utilising these rules in calculating the lengths of angles and the areas of triangles.
- In Functions, students learn of the relationships between various functions, and how they can be applied and tested through various problem-solving methods.
- In Further Indices, students continue to expand their knowledge of various index laws to include negative indices, fractional indices, which they are then able to apply to exponential equations.
- There are also additional exercises available under both Polynomials and Logarithms to test students who want to be challenged in each of these areas.

**Year 11 Mathematics**

As students enter senior stages of Mathematics, it is assumed they have capable knowledge of earlier Mathematical concepts. Throughout the Year 11 course, they expand upon these topics and engage further with unknown variables, functions, geometry, trigonometry and sequences. It is yet another step up from the level of mathematical thinking students cover in Year 9 and 10, and prepares students for yet another step up in Year 12. Students who fall behind in Year 11 often find it very difficult to make up ground in Year 12.

Content for Year 11 Mathematics includes:

- In Basic Arithmetic and Algebra, students reinforce their knowledge of earlier concepts from Years 9 and 10. By covering this unit, students can ensure there are no gaps in their mathematical thinking that could impede future learning.
- In Real Functions, students are introduced to a wider range of mathematical functions which cover the domain and range of equations, graphing of circles, absolute value and square roots, as well as exponential graphs and hyperbolas. This unit is also inclusive of limits and regions of equations, inequations and curves.
- In Trigonometry, students apply their understanding of trigonometric concepts to include ratios and equations, graphs and identities. Students apply this knowledge toward solving problems involving a variety of angles, shapes and properties.
- In Linear Functions and Lines, students further develop formulae and equations for problems involving distance, circles, lines and gradients, in addition to parallel and perpendicular lines.
- In Derivative of a Function, students learn differentiations of various functions and how to apply their knowledge of functions into new and varied contexts. This unit also inclusive of chain, product and quotient rules and higher derivatives; as well the equations of tangents and normals.
- In Quadratic Functions, students learn to graph quadratic equations, as well as be able to find vertexes, symmetries, inequalities, coefficients and ranges. This unit also includes discriminates, the properties of quadratics, and the reducible of quadratics.
- In Locus and Parabola, students learn to understand a locus and its applications, for both circle geometry and parabolas. Students also further develop their understanding of tangents and normals in this unit.
- In Sequences and Series, students engage with both arithmetical and geometrical series and sequences.

**Year 11 Mathematics Extension 1**

Mathematics Extension 1 in Year 11 requires students to make an effective transition from Years 9 and 10, as they will encounter a greater number of complex mathematical concepts. Students focusing on this level of mathematics require proficiency in all aspects of maths, and must be able to keep pace with the quick-fire nature of its content and curriculum. Our videos and exercises are the best way to ensure students to keep up with the demands of the course, as this is essential for students seeking E4 bands for their HSC.

Students in this subject complete all of the Year 11 Mathematics subjects (see above), in addition to:

- In Further Algebra, students focus on further developing their understanding and application of inequalities, including those using absolute values.
- In Further Trigonometry, students learn additional trigonometric properties, such as the sums, differences and double-identities of sine, cosine and tangent. In addition, students will learn about t-formula and transformations, as well as general solutions and three dimensions of trigonometric values.
- In Further Linear Functions and Lines, students will study angles between lines and find the gradients between these lines. They will also learn about internal and external divisions.
- Additionally, there are challenge exercises available in Parabola and Perimeter, as well as Polynomials.

**Year 12 Mathematics Gneral**

**Year 12 Mathematics**

In Year 12 Mathematics, students will encounter further modes of Mathematical thinking, as the content accelerates quickly beyond the conclusion of Year 11. Students will begin applying complex number patterns and formulae to specific applications and to the physical world, in addition to being required to understand complex functions and methods of reasoning. Now, more than ever, students require a sound knowledge of their prior learning, as the accelerated introduction of new and difficult concepts often leaves many students behind. Our videos and live exercise are now even more important for keeping pace with the curriculum, especially those seeking a HSC Band Six.

Content for Year 12 Mathematics includes:

- In Probability, students complete their exploration of chance. Applied to real-world concepts such as dice and cards, students will also cover the rules of probability, Venn and tree diagrams, as well as extended probability formulae.
- In Series and Applications, students complete their analysis of financial applications of mathematics. This includes formulae for interest rates, loans and repayments, as well as understanding superannuation and the way it is accrued.
- In Geometrical Applications of Calculus, students learn to apply the basic laws of calculus to curves and graphs. This includes understanding of stationary points, concavities, maxima and minima and primitive functions, in addition to being able to sketch these values.
- In Integration, students learn to apply indefinite and definite integrals, and learn to apply integration to area and volume. Students also cover numerical methods such Trapezoidal Rule and Simpson’s Rule.
- In Exponential and Logarithmic Functions, students learn the basics of logarithms in addition to their applications and functions. Students learn to then apply differentiation and integration into various logarithmic structures. Students also learn about exponential functions, including the process of graphing and applying differentiation and integration.
- In Trigonometric Functions, students learn to further apply trigonometric equations into various other forms. This includes radian measurements as well as the various types of equations. Students also learn to apply further trigonometric equations to circles and small angles, as well as graphing. Additionally, students will learn about differentiation rules of sine, cosine, quotient and tangent.
- In Applications of Calculus to the Physical World, students learn to apply calculus into physical applications such as to measure velocity, acceleration, range and rates of change, as well as how to graph these movements. Students will also cover exponential growth and decay and use it to solve various types of problems.

**Year 12 Mathematics Extension 1**

In Year 12 Mathematics Extension 1, students have to be prepared for a lot of hard work! Every subject covered as part of the Year 12 Mathematics course is extended and further developed, and often overwhelms those who lack confidence and proficiency. In order to achieve an E4, students need no less than a mastery of what they have covered in previous years. Therefore, it is important to look at our videos and live exercises to supplement and pre-empt the topics covered in class, in addition to those covered as part of the regular Year 12 Maths course.

Students in this subject complete all of the Year 12 Mathematics subjects (see above), in addition to:

- In Mathematical Induction, students focus on induction and methods of proof. Students will also cover multiple indices and divisibility, as well as inequalities within various sets of values.
- In Further Integration, students further develop their repertoire of integration methods, including substitution, removal of pronumerals, definite integrals, trigonometric functions, as well as exponential and logarithmic functions.
- In Further Trigonometric Functions, students further their knowledge of calculus formulae and concepts, and apply these skills into substitutions, double angles, tangents and secants.
- In Related Rates of Change, students further apply their knowledge of calculus in the physical world to include combined rates of change and those involving angles.
- In Inverse Functions, students focus on inverse formulae of exponential and logarithmic functions; sine, cosine and tangent values, equations, substitutions, symmetries and graphs. Students will also focus on calculus of inverse functions, including how they can be differentiated and integrated among different functions.
- In Numerical Estimation, students learn methods of estimating a number on a plane by halving the interval method of approximation, in addition to Newton’s Method.
- In Binomial Theorem, students explore the expansion of binomials using Pascal’s Triangle and Sigma Notation, as well as binomial probability. Students also learn about finding a coefficient and finding the greatest coefficient.
- In Permutations and Combinations, students explore factorials in terms of counting techniques and arrangements, in addition to understanding the various facets of permutations and combinations
- In Projectile Motion, students study the fundamentals and applications of motion in terms of velocity, horizontal and vertical motions, trajectory, flight time and range.
- In Simple Harmonic Motion, students learn about the features and equations of harmonic motion, in addition to how it can be applied in the real-world.
- In Circle Geometry, students explore circle geometry in-depth and gain a comprehensive repertoire of skills for measuring arcs, angles and tangents.

**Year 12 Mathematics Extension 2**

In Year 12 Mathematics Extension 2, students go well beyond the fundamentals of complex mathematical thinking and explore concepts in even greater depth. Students studying this subject need to have a complete and absolute understanding of the curriculum, not only for the purposes of high HSC bands but also for the purposes of tertiary study. Our videos equip students with clear and comprehensive demonstrations of these concepts, with live exercises that will surely test even the brightest mathematical thinkers.

Content for Year 12 Mathematics Extension 2 includes:

- In Sketching the Graph, students learn to graph a multitude of complex functions including polynomials, logarithms, trigonometric, exponential and inverse functions.
- In Complex Numbers, students will begin with the fundamentals of conjugate pairs and square roots. Students then expand on this knowledge to focus on modulus and argument, locus, and geometrical representations of complex numbers.
- In Conics, students explore equations, tangents and normal of ellipses, as well hyperbolas and rectangular hyperbolas.
- In Integration, students further develop their understanding of logarithmic and trigonometric functions. Students also focus on integration strategies as well as recurrence formulae.
- In Volumes, students will encounter complex equations involving measures of volume. Students will learn problem-solving strategies such as the slicing method and cylindrical shells method, in addition to parallel cross sections.
- In Mechanics, students will learn about the dynamics of motion and forces, including those to with gravity, resistance, circular motion and conical pendulum, as well as banked tracks and friction.
- In Polynomials, students will encounter topics such as remainder and factor theorems, multiplicity and multiple roots, as well as roots and coefficients.
- In Miscellaneous Topics, students will find live exercises that will test their knowledge of varied skills and require them to apply what they learn throughout the Extension 2 Mathematics course.