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YEAR 12

ADVANCED MATHEMATICS

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Our Objective

The year 12 Advanced Mathematics program at Cosmos aims at helping students understand all the concepts in advanced 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 advanced Mathematics syllabus as per the latest NSW curriculum in full depth.  Students need to attend two classes every week along with an optional doubt clearing and extra practice class every Sunday. 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 before/after class hours. 

Year 12 Maths Tutoring Program

Weekly Course Schedule

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Resources

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Timetable

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Mathematics Syllabus

Sequences and series


Subtopics:

  • Sequences and how to specify them
  • Arithmetic sequences
  • Geometric sequences
  • Solving problems involving APs and GPs
  • Adding up the terms of a sequence
  • Summing an arithmetic series
  • Summing a geometric series
  • The limiting sum of a geometric series
  • Recurring decimals and geometric series




Graphs and equations


Subtopics:

  • The sign of a function
  • Vertical and horizontal asymptotes
  • A curve‐sketching menu
  • Solving inequations
  • Using graphs to solve equations and inequations
  • Review of translations and refl ections
  • Dilations
  • Combinations of transformations
  • Trigonometric graphs




Curve‐sketching using the derivative


  • Increasing, decreasing and stationary at a point
  • Stationary points and turning points
  • Second and higher derivatives
  • Concavity and points of infl ection
  • Systematic curve sketching with the derivative
  • Global maximum and minimum
  • Applications of maximisation and minimisation
  • Primitive functions




Integration


Subtopicss:

  • Areas and the defi nite integral
  • The fundamental theorem of calculus
  • The defi nite integral and its properties
  • Challenge – proving the fundamental theorem
  • The indefi nite integral
  • Finding areas by integration
  • Areas of compound regions
  • The trapezoidal rule
  • The reverse chain rules




The exponential and logarithmic functions


Subtopics:

  • Review of exponential functions base e
  • Differentiation of exponential functions
  • Applications of differentiation
  • Integration of exponential functions
  • Applications of integration
  • Differentiation of logarithmic functions
  • Applications of differentiation of log e x
  • Integration of the reciprocal function
  • Applications of integration of 1 / x
  • Calculus with other bases




The trigonometric functions


Subtopics:

  • The behaviour of sin x near the origin
  • Differentiating the trigonometric functions
  • Applications of differentiation
  • Integrating the trigonometric functions
  • Applications of integration




Motion and rates


  • Average velocity and speed
  • Velocity and acceleration as derivatives
  • Integrating with respect to time
  • Rates and differentiation
  • Rates and integration
  • Exponential growth and decay




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




Working with time


  • Units of time
  • Timetables
  • Latitude and longitude
  • Time zones
  • Time difference and local time




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





What

Parents Say

Our Students'

Results

Alice M.

Richa S.

Yash B.

Shree L.

Viraj K.

Alok K.

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

Topic

Max Marks

Questions

Sequences and Series

Graphs and Equations

Continuous probability distributions

Integration​

Trigonometric Equations

50

50

50

50

50

10

10

10

10

10

Let's do this!