overview

**Mathematics Advanced is a critical pre-requisite for a variety of university courses, including science, engineering and economics. Potentia’s Year 12 Mathematics Advanced Tutoring will give your child the theoretical knowledge and application of the key concepts of HSC Mathematics for them to achieve great marks in their HSC and for Mathematics Advanced to contribute substantially to their ATAR.**

The main concept that your child will learn comprehensively and apply in Year 12 Mathematics is the use and application of calculus to provide solutions for complex problems and equations. Potentia’s Year 12 Mathematics Advanced Tutoring will ensure your child has a solid grasp of how to integrate calculus with algebraic, deductive and modelling skills to solve mathematical problems that they will encounter during their HSC year. Your child’s logical reasoning and mathematical communication skills will be developed at Potentia, to ensure they have the capability to achieve HSC success in Mathematics.

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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

Graphing techniques

- Transformation of y = f(x) → y = k(f(ax + b)) + c where f(x) is a polynomial, reciprocal function, absolute value function, exponential function or logarithmic function and a, b, c and k are constants.

- y = f(x) → y = f(x) + c
- → y = f(x + b)
- → y = kf(x)
- → y = f(ax)

- Using graphical methods to solve equations, find intercepts, asymptotes
- Trigonometric functions and graphs

- Graphs of trigonometric functions and then translations

- Solve trigonometric equations
- Use trigonometric equations in practical problems including periodic phenomena

Calculus

- Derivatives of trigonometric functions

- Derivative of exponential functions

- Derivatives of log functions

- Apply the Product Rule, Chain Rule
- Composite functions on trigs, logs and exponential functions

- Review and topic test1

Potentia term 2 Jan - April

- Applications of derivatives
- Sign of f’(x) when f(x) is increasing or decreasing
- Use f’(x) to find turning points
- Use f”(x) to identify concavity and find inflexion points
- Graph the function

- Using rates of change to solve optimisation problems
- Evaluate the solutions

- Define anti-derivative and use notation Sf(x).dx
- Sxn.dx
- Sf’(x).f(x).dx the reverse of the Chain Rule
- S(ax + b)n.dx

- S(trig functions)

- Integration of exponential functions and logarithmic functions

- Review and topic test

- Area as a definite integral
- Determine area under the curve
- Use approximation methods (Trapezoidal Rule)
- Area between the curve and the y-axis

- aSbf(x)dx = F(b). F(a)
- Use symmetry properties
- Area between two curves
- Use integrals to solve practical problems

- Further problems

- Review and topic test

Potentia term 3 April - July

- Define terms Tn = Tn-1 + d<
- Tn = a + (n – 1).d
- Find the sum or a partial sum: Sn = n/2 x (a + l)
- S
_{n}= n/2(2a + (n – 1) d)

Geometric sequences

- Define, T
_{n}= a.rn-1 - Find the sum of n terms, Sn = a[rn – 1]/r – 1
- Derive a formula for a limiting sum when |r| < 1, S = a/1-r

- Identify and annuity
- Use a table of future values

Financial applications to sequences and series

- Use a GP (geometric progression) to model and analyse problems involving exponential growth and decay
- Calculate effective interest rate
- Solve problems involving loans and investments
- Solve problems involving financial decisions

Statistical Analysis

- Classify data relating to a single random variable
- Organise, interpret and display data into tabular and graphical representation

Calculate measures of central tendencies

- Identify outliers:
- Q1 – 1.5 x IQR (inter quartile range)
- Q3 + 1.5 x IQR
- Describe, compare and interpret distributions

Bivariate data analysis

- Construct scatter plots
- Describe relationships
- Calculate correlation coefficients, “r” to quantify the strength of the linear relationship
- Model the relation in a line of best fit

Continuous random variables

- Use relative frequencies to estimate probabilities
- -∞S+∞ f(x).dx = 1
- Define the probability as the area under the curve of the probability density P(X ≤ x) = aSx f(x).dx
- Obtain and analyse cumulative distribution with respect to a given probability density function

Potentia term 4 July - Sept

- The normal distribution
- Identify numerical and graphical properties of normally distributed data
- Practical applications
- Z-scores, z = x - φ/σ
- Use scores to compare results

- Use collected data to illustrate empirical rules for normally distributed variables
- Sketch f(x) = e-x2
- And the probability density function, f(x) = 1/σ√2π e-(x-φ)2/2φ2

- Review and topic test

- General review

- End of year exam and complete Trial HSC

- HSC Practice

- HSC Practice

- HSC Practice

- HSC Practice