# Overview - Mathematics Extension 2 Year 12

## Available Class Times

##### 1:30pmSunday

HSC Mathematics Extension 2 extends the boundaries of mathematics notably beyond the expected standard at the high school level, and begins to scrape the surface of first year university. The course is intended to challenge students who have excelled in Year 11 Mathematics Extension 1 to think more deeply and creatively in proving powerful mathematical results and working through more intense computation. Although the course is only treated as assumed knowledge for degrees involving a mathematics major, it is still recommended for many students interested in STEM-based degrees as the coverage of university level content provides a small, but effective head start to their coursework. It is commonly regarded as one of the hardest high-school mathematics courses in the country.

## Studying Mathematics Extension 2 Year 12, at TuteSmart

We train our MX2 tutors at TuteSmart extensively so that they can confidently and effectively guide the students through the demanding nature of the course. The tutors have full mastery of all mathematics subjects, including the new and old content in Extension 2. Having had their own struggles in the course, they understand its time-consuming and challenging nature, but they have all felt it was one of the most rewarding experiences ever. The tutors know what the students require - they possess the advanced tricks and insight the examiners seek out in high performing students. They teach from their own experience of the subject’s stress and difficulty. The objective is to build the students’ confidence even further from where it has advanced thus far, achieve the highest possible results they can, and develop an even stronger appreciation for the power of mathematics today!

ATAR 99.5

## HSC Mathematics Extension 2 Year 12 Curriculum

 Introduction, N1.1 Use the complex number system N1.1: Represent and use complex numbers in Cartesian form, N1.2: Represent and use complex numbers in the complex plane and in polar (mod-arg) N1.2: Represent and use complex numbers in the complex plane and in polar (mod-arg) form, N1.3: Other representations of complex numbers N1.2: Prove and use the basic identities involving modulus and argument N2.1: Solving equations with complex numbers (De Moivre’s theorem and real quadratic equations) N2.1: Solving equations with complex numbers (Complex quadratic equations and real polynomials) N2.2: Addition, subtraction of complex numbers as vectors in the complex plane; the geometric relationship of the conjugate, multiplication by i and by a real constant N2.2: Examine and use the geometric interpretation of multiplying complex numbers, including rotation and dilation P1: The nature of proof (Proof on inequalities) N2.2: Identify subsets of the complex plane determined by relations P1: The nature of proof (Language of proof) Test 1: Complex Numbers, Proofs P1: The nature of proof (Examples and counter-examples, inequalities) P1: The nature of proof (Inequalities) Introduction?/P2: Further proof by mathematical induction (different initial values, different increments, sigma notation ) P2: Further proof by mathematical induction (divisibility, inequalities, calculus) P2: Further proof by mathematical induction (probability, first-order recurrences, geometry) Spare lesson: Advice + Worksheet V1.1: Introduction to three-dimensional vectors, V1.2: Define and use the magnitude and scalar product in three dimensions Half Yearly Exam Review of Half Yearly Exam V1.2: Prove geometric results in the plane and in three dimensions V1.3: Use Cartesian coordinates in 2D and 3D space; spheres; uses vector equations V1.3 Understand and use the vector equation of a line and line segments; connection to y=mx+c (2D case) V1.3: Determine when lines in vector form are parallel or perpendicular; determine when a given point lies on a given line C1: Further integration (integration by substitution, quadratic denominators) C1: Further integration (partial fractions, integration by parts) C1: Further integration (recurrences) Harder integration, Revision - Student poll? M1.1: Simple harmonic motion M1.1: Simple harmonic motion/ More mechanics ATAR Notes Trials ATAR Notes Trials Review M1.2: Use formulae for acceleration and Newton's laws Continued Trials Review + Small worksheet M1.2: Examine constant and non constant acceleration; outside of projectiles and simple harmonic M1.3: Solve problems involving resisted motion of a particle moving along a horizontal line M1.3: Solve problems involving the motion of a particle moving vertically (upwards or downwards) in a resisting medium and under the influence of gravity M1.4: Solve problems involving projectiles in a variety of contexts M1.4: Solve problems involving projectile motion in a resisting medium and under the influence of gravity Exam Tips + Worksheet Revision Revision Revision Revision Final Lesson

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