This course develops competencies in skills and strategies ranging from simple familiar to complex unfamiliar, in Unit 3 and Unit 4 Specialist Mathematics.
What you will learn
Following all QCAA syllabus objectives, students studying Specialist Mathematics Year 12 will learn about:
- Mathematical induction
- Vectors and matrices
- Complex numbers
- Integration and applications of integration
- Rates of change and differential equations
- Statistical inference
A full course framework and curriculum included in this course is shown below.
Who this course is for
This course is for students studying year 12 Specialist Mathematics – or a high-level unit mathematics, who wish to excel in mathematics exams and optimise their ATAR. Teaching institutions and individual teachers will also find this course an excellent teaching and learning tool.
Course structure
The Specialist Mathematics year 12 course includes lectures and tutorials that deliver theoretical content and concepts, as well as demonstrates detailed workings that you require to solve a variety of problems – ranging from simple familiar to complex unfamiliar, in Unit 3 and Unit 4 subject areas. Where useful or required, the course demonstrates how to use the graphics calculator for problem solution.
Course Curriculum
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Mathematical induction
Welcome to Proof By Mathematical Induction
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Welcome to Proof By Mathematical Induction• Module Introduction
Mathematical induction
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Mathematical induction• Initial statement
• Inductive process
• Prove summation results
• Prove divisibility results
Vectors & matrices
Welcome to Vectors and Matrices
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Welcome to Vectors and Matrices• Module Introduction
Algebra of vectors in 3-dimensional space
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Algebra of vectors in 3-dimensional space• Review vectors in 2-dimensional space
• Extend vectors from 2-dimensional space to 3-dimensional space
• Consider the altitude angle
• Simple proofs in 3-dimensional space
Vector and Cartesian equations
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Vector and Cartesian equations• Cartesian co-ordinates for 3-dimensional space
• Equation of a sphere
• Vector equation of a curve - involving a parameter
• Conversion of a 2-dimensional vector equation to Cartesian form
• Equation of a straight line: vector, parametric and Cartesian form
• Position of particles – vector function of time
• Vector (cross) product, and its application to area
• Cartesian and vector equation of a plane
Systems of linear equations
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Systems of linear equations• Gaussian elimination
• Matrix algebra, including the use of technology
• Geometric interpretation of a solution for a set of simultaneous equations
Applications of matrices
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Applications of matrices• Modelling using matrices
• Dominance matrices
• Leslie matrices
Vector calculus
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Vector calculus• Vector position as a function of time
• Cartesian equation of the path of a particle: circle, ellipse and hyperbola
• Differentiate a vector function with respect to time
• Integrate a vector function with respect to time
• Motion equation of a particle travelling in a straight line – constant and variable acceleration
• Projectile and circular motion
Complex numbers
Welcome to Complex Numbers 2
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Welcome to Complex Numbers 2• Module Introduction
Cartesian forms
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Cartesian forms• Review: real and imaginary parts of a complex number
• Review: Cartesian form
• Review: algebra of complex numbers
The complex plane – Argand diagrams
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The complex plane – Argand diagrams• Straight line subsets in the complex plane
• Circle subsets in the complex plane
Roots of complex numbers
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Roots of complex numbers• Calculate the nth root of unity
• Locate the nth root of unity on the unit circle
• Calculate the nth root of a complex number
• Locate the nth root of a complex number on an Argand diagram
Factorisation of polynomials
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Factorisation of polynomials• Factor theorem
• Remainder theorem
• Polynomial division in the complex plane
• Conjugate roots of a polynomial with real coefficients
• Solution of a polynomial equation to order 4
Integration & applications of integration
Welcome to Integration and Applications of integration
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Welcome to Integration and Applications of integration• Module Introduction
Integration techniques
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Integration techniques• Integration using trigonometric identities
• Integration using substitution
• Integration with the reciprocal function
• Integration using partial fractions
• Differentiation and integration using inverse trigonometric functions
• Integration by parts
Application of Integral Calculus
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Application of Integral Calculus• Area between curves representing given functions
• Volume of solids of revolution
• Simpson’s rule: numerical method of integration
• Probability density function for the exponential random variable
Rates of change & differential equations
Welcome to Rates of Change and Differential Equations
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Welcome to Rates of Change and Differential Equations• Module Introduction
Rates of Change
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Rates of Change• Implicit differentiation
• Related rates
• Solution of first order differential equations
• Separation of variables
• Slope fields of a first order differential equation
• Logistic equations in practical scenarios
Modelling Motion
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Modelling Motion• Momentum, force, resultant force, action and reaction
• Constant and non-constant force
• Concurrent forces and motion
• Straight line motion for constant and non-constant acceleration
• Simple harmonic motion
Statistical inference
Welcome to Statistical Inference
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Welcome to Statistical Inference• Module Introduction
Sample Means
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Sample Means• Sample mean: random variable
• Simulation: repeated random sampling
• Approximate standard normality for large samples – n greater than 30
Confidence Intervals For Means
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Confidence Intervals For Means• Interval estimate for a random variable parameter
• Confidence interval for the population mean
• Simulation using technology – comparison of confidence intervals for the sample mean
• Estimation of the population mean and standard deviation using the sample mean and standard deviation
$930.00Enrol Now This Course Includes:
This Course Includes:
- 37 lectures
- 165 tutorials
- Notes for key learning concepts
- Graphics calculator applications
- 37 lectures
- 165 tutorials
- Notes for key learning concepts
- Graphics calculator applications
2 STUDENTS ENROLLED
