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- Algebraic techniques
  • Index rules
  • Factorising methods
  • Algebraic fractions
  • Perfect squares (sums and difference)
  • Sum and difference of two cubes
Week 2 - Equations
  • Solving linear equations
  • Quadratic equations by factorising, complete the square, the formula
  • Equations reducing to quadratics
Week 3 - Review Test – algebra and equations

Week 4 - Functions
  • 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).
Week 5 - Linear Functions
  • 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
Week 6 - Quadratic 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
Week 7 - The cubic function f(x) = x3
  • 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
Week 8 - Review Test on functions: linear, quadratic and cubic

Week 9 - Absolute value function, f(x) = |x|
  • Definition, graph
  • Shape and features of the graph of y =|ax + b|
  • Solve |ax + b| = k both graphically and algebraically
Week 10 - All reflections and shifts of graphs
  • 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

Potentia Term 2

Week 1 - Review Test absolute value functions and reflections

Weeks 2 - 7 Trigonometric functions

Week 2
  • Right-angled triangle rules
  • Sine and cosine rules for non right-angled triangles
  • Area of triangle
Week 3 
  • Angles of elevation and depression
  • Bearings
Week 4
  • Solving problems in 2D and 3D situation

Week 5
  • Introduce radian measures – conversions
  • Angles of any magnitude
  • Graphing of trigonometric functions (include domains)
Week 6 
  • Derive formula L = rΘ, A = 1/2r2Θ
  • 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
Week 7
  • Solving trigonometric functions, including quadratics
Week 8 - Review and topic test

Weeks 9-10 Calculus

Week 9
  • Continuous and discontinuous functions
  • Limits
  • Gradient of a secant – tangent
  • Lim   f(x + h) – f(x) → d/dxX n; as h → 0
                              h

Week 10
  • 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

Potentia Term 3

Week 1-2 Calculus

Week 1
  • The Chain Rule
  • The Product Rule
  • The Quotient Rule
Week 2
  • Rates of change
  • Velocity = dx/dt, acceleration = d2x/dt2
  • Practical situations
Week 3 - Review/Topic Test

Week 4-7 -Exponential and logarithmic functions

Week 4 
  • Introduction to logarithms
  • Relation of y = ax and y = logax
  • Graphs of the exponential function and logarithms
Week 5
  • Logarithm rules
  • Equations
  • Scales
Week 6
  • Exponential functions and natural logs
  • d/dxex = ex,  d/dx(logex),  d/dxax ,  d/dx(logax)
  • Apply differential rules to logs and exponential functions
Week 7
  • Modelling real life situations
  • Growth and decay
Week 8 - Review and topic test

Week 9-  10 - Statistical Analysis

Week 9
  • Language of probability
  • Venn Diagrams
Week 10
  • 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

Potentia Term 4

Week 1- Probability
  • 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 2 - Review and topic test

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

 

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.