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Our Objective

The year 12 Extension Mathematics program at Cosmos aims at helping students understand all the concepts in Extension Maths in detail and score maximum marks in their assessments and final exam. We achieve this by providing them with the ultimate combination of our interactive lectures, study material, quizzes, worksheets and continuous formative assessments. Students learn the entire year 12 Extension Mathematics syllabus as per the latest NSW curriculum in full depth.  Students need to attend an extra class every week along with two Maths advanced classes. Each class is 2 hours long with a 10-minute break in between. Students are motivated to keep their assessments up to date on google classroom and parents receive report cards every term containing detailed statistics of their children's test scores. Students can ask our teachers to help them personally with their school homework and assessments before/after class hours.

Weekly Course Schedule

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Mathematics Syllabus

Mathematical Induction


  • Using mathematical induction for series
  • Proving divisibility by mathematical induction



  • Directed intervals and vectors
  • Components and column vectors
  • The dot product (or scalar product)
  • Geometric problems
  • Projections
  • Applications to physical situations

Motion and Rates

  • Average velocity and speed
  • Velocity and acceleration as derivatives
  • Integrating with respect to time
  • Rates and differentiation
  • Review of related rates
  • Rates and integration

Projectile Motion


  • Projectile motion — the time equations
  • Projectile motion — the equation of path

Trigonometric Equations


  • Equations involving compound angles
  • The sum of sine and cosine functions
  • Using the t-formula to solve equations

Further Calculus


  • Inverse trigonometric functions — differentiating
  • Inverse trigonometric functions — integrating
  • Further trigonometric integrals
  • Integration by substitution
  • Further integration by substitution
  • Volumes of rotation

Differential Equations

  • Differential equations
  • Slope fields
  • Separable differentiable equations
  • y ' = g(y ) and the logistic equation
  • Applications of differential equations

Series and finance

  • Applications of APs and GPs
  • The use of logarithms with GPs
  • Simple and compound interest
  • Investing money by regular instalments
  • Paying off a loan

Displaying and Interpreting Data

  • Displaying data
  • Grouped data and histograms
  • Quartiles and interquartile range
  • Bivariate data
  • Formulae for correlation and regression
  • Using technology with bivariate data

Continuous Probability Distributions

  • Relative frequency
  • Continuous distributions
  • Mean and variance of a distribution
  • The standard normal distribution
  • General normal distributions
  • Applications of the normal distribution
  • Investigations using the normal distribution

Binomial Distributions

  • Binomial probability
  • Binomial distributions
  • Normal approximations to a binomial
  • Sample proportions


Parents Say

Our Students'


Hari H.

Krishna S.

Kate K.

Harsha G.

Alokshi A.

Amol Kumar

My child loved the tutoring. He had no interest in science when he started but he now enjoys it. Shariq made the subject really interesting by showing students videos and doing activities in class. 

Alvin White

Great place for study. students can come anytime and study in the study rooms and also ask questions to teachers. Sai and his team is extremely helpful.

Yousef Mohammed

Rate 5 stars. Nice campus and learning environment. Students are taught several practical based things apart from regular academics.

Tanishka Reddy

Flexible teaching style. Teachers understood that my child was able to catch things fast and already knew the content so they promoted him to the next class and taught him the full syllabus. My son enjoyed his experience.

Sameer Reddy

Received lot of study material for practice. Online quizzes and tests were pretty helpful. Certainly recommend.

Kiran Badekar

Very good coaching center. Nice staff and location.

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Test Yourself


Max Marks


Further Calculus

Series and Finance

Differential equations​

Motion and rates

Projectile motion











Let's do this!