overview

**High performance in Mathematics Advanced is the best way for your child to have the opportunity to study numerous courses at top universities, such as engineering, economics and commerce. Make sure your child has access to as many courses as possible by ensuring they learn the fundamentals that underpin HSC Mathematics Advanced in Potentia's Year 11 Mathematics Advanced Tutoring.**

Year 11 Mathematics Advanced focuses on enhancing your child's ability to work mathematically, through improving their understanding and application of theoretical concepts and mathematical models. The development of your child's abilities to utilise efficient strategies and to apply complex techniques to solve problems is at the core of Potentia's Year 11 Mathematics Advanced tutoring. Your child will learn about and feel confident in functions, calculus and statistical analysis, preparing them for Year 11 and Year 12 success in Mathematics Advanced.

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breakdown

Review and Reinforcement

A review of prior week to reinforce learning and retention.and a quiz to assess their understanding of the previous week’s lesson.

Explain and Explore

Students are guided through detailed analysis of the subject material by the tutor. The aim is to break up material so that it can be manageably understood and retained by students.

BREAK

BREAK.

Practice and Performance 1

A practical session where students are guided on how to answer math questions

and offered feedback on their answers and working out.

and offered feedback on their answers and working out.

BREAK

BREAK.

Practice and Performance 2

A practical session where students are guided on how to answer math questions

and offered feedback on their answers and working out.

and offered feedback on their answers and working out.

Synthesise

Students test their mastery of the concepts presented through a short quiz. Real

time feedback is given to identify areas for further practice.

time feedback is given to identify areas for further practice.

program

Potentia term 1 Oct - Dec

- Index rules
- Factorising methods
- Algebraic fractions
- Perfect squares (sums and difference)
- Sum and difference of two cubes

- Solving linear equations
- Quadratic equations by factorising, complete the square, the formula
- Equations reducing to quadratics

- Notation – definition, function-relation
- Define domain and range
- Dependent/independent variables
- Odd/even
- Define composite functions f(g(x)), g(f(x)). Given f(x) and g(x).

- Recognise direct variation
- Significance of m and c in f(x) = mx + c
- Use y – y1 = m(x – x1) to find the equation of a line
- Use two points to find the equation of a line
- Parallel and perpendicular lines
- Model and solve problems involving linear functions

- Recognise features of a quadratic function including turning points, axis of symmetry and intercepts
- Find the x-intercepts by solving the equation using an appropriate method
- Understand the rule of the discriminant in relation to the graph
- Solve practical problems involving a pair of simultaneous equations, linear and/or quadratic

- Graph y = x3, f(x) = (x – b)3 and f(x) = (x – a)(x – b)(x – c)
- The polynomial function: identify coefficients and degree
- Graph a polynomial given a factorised form
- Hyperbolic functions: f(x) = k/x

- Definition, graph
- Shape and features of the graph of y =|ax + b|
- Solve |ax + b| = k both graphically and algebraically

- Use g = f(x) to graph y = -f(x) and y = f(-x)
- Circle: (x – a)2 + (y – b)2 = r2 and graphs
- Semi circles

Potentia term 2 Jan - April

Weeks 2 - 7 Trigonometric functions

Week 2

- Right-angled triangle rules
- Sine and cosine rules for non right-angled triangles
- Area of triangle

- Angles of elevation and depression
- Bearings

- Solving problems in 2D and 3D situation

- Introduce radian measures – conversions
- Angles of any magnitude
- Graphing of trigonometric functions (include domains)

- Derive formula L = rΘ, A = 1/2r
^{2}Θ - Problems involving length of an arc and area of a sector
- Define reciprocal functions (sec Θ, cosecΘ and cotΘ)
- Graphs of reciprocal functions
- Identities and proofs

- Solving trigonometric functions, including quadratics

Week 9

- Continuous and discontinuous functions
- Limits
- Gradient of a secant – tangent
- Lim
__f(x + h) – f(x)__→ d/dxX^{n}; as h → 0

- The derivative function and its graph
- Gradient to the tangent
- Equation of the tangent and the normal
- Using the gradient function (derivative) to find stationary points and identify their nature

Potentia term 3 April - July

Week 1

- The Chain Rule
- The Product Rule
- The Quotient Rule

- Rates of change
- Velocity = dx/dt, acceleration = d
^{2}x/dt^{2 } - Practical situations

- Introduction to logarithms
- Relation of y = a
^{x}and y = log_{a}x - Graphs of the exponential function and logarithms

- Logarithm rules
- Equations
- Scales

- Exponential functions and natural logs
- d/dxe
^{x}= e^{x}, d/dx(log_{e}x), d/dxax , d/dx(log_{a}x) - Apply differential rules to logs and exponential functions

- Modelling real life situations
- Growth and decay

Week 9

- Language of probability
- Venn Diagrams

- Events A, A’, A Ω B and A U B and their components; mutually exclusive events
- P(A’) = 1 – P(A)
- P(A/B) = P(A Ω B)/P(B)
- P(A Ω B) = P(A) P(B)

Potentia term 4 July - Sept

- Discreet probability distribution
- Define and categorise random variables
- Difference between discreet and continuous variables
- Use discreet variables to solve problems
- Sample mean (X bar) to estimate population mean (υ)

Week 3 - Further problems in Advanced Mathematics 1

Week 4 - Further problems in Advanced Mathematics 2

Week 5 - Further problems in Advanced Mathematics 3

Week 6 - Further problems in Advanced Mathematics 4

Week 7 - Prelim Practice

Week 8 - Prelim Practice

Week 9 - Course final exam

Week 10 - Summary and review