Lesson
breakdown

 10 min
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.

 40 min
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.

  10 min
BREAK
 
BREAK.

 50 min
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.

  10 min
BREAK
 
BREAK.

 50 min
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.

 10min
Sythesise
 
Students test their mastery of the concepts presented through a short quiz. Real
time feedback is given to identify areas for further practice.

Term course
program

Potentia term 1 Oct - Dec

Potentia Term 1

Week 1  

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.

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

Week 2 
  • Using graphical methods to solve equations, find intercepts, asymptotes
  • Trigonometric functions and graphs

Week 3
  • Graphs of trigonometric functions and then translations

Week 4
  • Solve trigonometric equations
  • Use trigonometric equations in practical problems including periodic phenomena

Week 5    Review and topic test

Week 6  

Calculus
  • Derivatives of trigonometric functions

Week 7    
  • Derivative of exponential functions

Week 8
  • Derivatives of log functions

Week 9    
  • Apply the Product Rule, Chain Rule 
  • Composite functions on trigs, logs and exponential functions

Week 10  
  •  Review and topic test1   

Potentia term 2 Jan - April

Potentia Term 2

Week 1
  • 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

Week 2 
  • Using rates of change to solve optimisation problems
  • Evaluate the solutions

Week 3

Integral calculus
  • 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

Week 4 
  • S(trig functions)

Week 5    
  • Integration of exponential functions and logarithmic functions

Week 6
  • Review and topic test

Week 7    
  • Area as a definite integral
  • Determine area under the curve
  • Use approximation methods (Trapezoidal Rule)
  • Area between the curve and the y-axis

Week 8
  • aSbf(x)dx = F(b). F(a)
  • Use symmetry properties
  • Area between two curves
  • Use integrals to solve practical problems

Week 9    
  • Further problems

Week 10
  • Review and topic test

Potentia term 3 April - July

Potentia Term 3

Week 1

Financial  Mathematics

Arithmetic series
  • Define terms Tn = Tn-1 + d<
  • Tn = a + (n – 1).d
  • Find the sum or a partial sum: Sn = n/2 x (a + l)
  • Sn = n/2(2a + (n – 1) d)

Week 2    

Geometric sequences
  • Define, Tn = 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
Week 3  

Solve compound interest problems
  • Identify and annuity
  • Use a table of future values
Week 4    
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
Week 5  Review and topic test

Week 6

Statistical Analysis
  • Classify data relating to a single random variable
  • Organise, interpret and display data into tabular and graphical representation
Week 7    

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
Week 8  

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
Week 9  

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
Week 10    Review and topic test1    

 

Potentia term 4 July - Sept

Potentia Term 4

Week 1
  • 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

Week 2
  • 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

Week 3
  • Review and topic test

Week 4
  • General review

Week 5
  •  End of year exam and complete Trial HSC

Week 6 
  • HSC Practice

Week 7
  • HSC Practice

Week 8   
  • HSC Practice

Week 9
  • HSC Practice

Results

Improve your mark and rank at school by getting a head start on your subject. Potentia courses are three months (one term) in advance of the school year. Vertical streaming ensures that all students can be extended to their level of ability.

Confidence

As you achieve success build confidence in your ability. This will help you not just at high school but in your journey of lifelong learning.

Foundation

Continue to build a solid foundation for your future success both at school and in life. Learning at Potentia helps you to be expert inr your subject which prepares you for post-school learning.

Learning philosophy

Learning materials


Constantly updated to reflect curriculum changes as well as best practice in learning, our materials are uniquely developed by highly trained teachers with many years’ experience.

Expert tutors

From recent HSC high achiever mentors to qualified professional teachers with subject expertise, all our tutors are trained in our unique system.

Continuous tutor training

We’re at the forefront of teaching and learning leadership, continually adapting our programs and approach to ensure the very best educational experience for your child.

Learning software

Enhancing our face-to-face teaching, our leading platform provides additional material to aid learning, as well as online assessment and reporting so we can monitor your child’s progress.

Power sessions

Power Sessions reinforce the concepts explored in our Excel class groups, pairing your child with other high-performers in a small work group to review materials and practice study skills.

Wellbeing

We look after the whole child, not just their results. As the only tutoring college working with psychologists, we provide opportunities to learn additional life skills to foster both learning and wellbeing.

Learning Hubs

Designed to optimise your child’s learning experience and provide a safe, welcoming space, our tech-enabled classrooms provide digital screens and interactive digital whiteboards. We also offer quiet study areas, kitchen facilities and free Wi-Fi.

Feedback Loop

Potentia’s proven process of continual improvement draws on current best practice in achieving great performance – proactively supporting your child to unlock their potential.