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VCE Mathematics: Specialist Mathematics

Aim

Specialist Mathematics Units 1-4 focus on advanced mathematical concepts, including complex numbers, vectors, calculus, differential equations, and statistical inference. These units enhance students' mathematical reasoning, proof, and problem-solving skills. Designed to be taken alongside or after Mathematical Methods Units 3 and 4, Specialist Mathematics prepares students for further studies in STEM fields and other areas requiring strong mathematical foundations. The course covers theoretical and practical applications, fostering a deep understanding of mathematical structures and their use in various contexts


Prior Learning:

Prerequisites for Units 1 and 2: Successful completion of the Pre-Methods elective. and/OR Strong results in High level mathematics class. 

Prerequisites for Units 3 and 4: Successful completion of Units 1 and 2 Specialist Mathematics.


NOTE: Specialist Mathematics MUST be undertaken in conjunction with Mathematical Methods.


Study design 2023-2027 (word doc)


Assessments

Satisfactory completion 

- Demonstrated achievement of the set of outcomes.


Outcome 1

Define and Explain Key Concepts

  • Define and explain key concepts from the areas of study.

  • Apply a range of related mathematical routines and procedures to solve practical problems.

Outcome 2

Apply Mathematical Processes

  • Apply mathematical processes in practical, non-routine contexts.

  • Analyse and discuss the applications of mathematics in various situations, using investigative modelling or problem-solving approaches.

Outcome 3

Use Technology and Computational Thinking

  • Use computational thinking and the functionalities of technology (numerical, graphical, symbolic, and statistical).

  • Develop mathematical ideas, produce results, and perform analysis in practical situations requiring investigative modelling or problem-solving techniques.

Assessment of satisfactory completion and weightings

Units 1 and 2:

Individual school decision on the levels of achievement.


Unit 3:  

School assessed coursework (20%)


Unit 4:  

School assessed coursework (20%)


Units 3 and 4:  

End-of-year examination 1 (20%)

End-of-year examination 2 (40%)

UNIT 1

UNIT 2

  • Algebra and Structure

    • Polynomial and rational functions.

    • Complex numbers in rectangular and polar forms.

    • Algebraic manipulation and simplification.

  • Functions, Relations, and Graphs

    • Graphical representation of functions.

    • Inverse functions and transformations.

    • Modelling with functions.

  • Calculus

    • Introduction to limits and continuity.

    • Differentiation of polynomial and simple transcendental functions.

    • Applications of differentiation: tangents, normals, and optimisation.

  • Vectors

    • Introduction to vectors in two and three dimensions.

    • Operations with vectors: addition, subtraction, scalar multiplication.

    • Applications of vectors in geometry and physics.

  • Algebra and Structure

    • Further exploration of complex numbers.

    • Solving polynomial equations.

    • Sequences and series, including arithmetic and geometric progressions.

  • Functions, Relations, and Graphs

    • Further study of functions and their graphs.

    • Parametric equations and their applications.

    • Polar coordinates and graphing.

  • Calculus

    • Integration of polynomial and simple transcendental functions.

    • Applications of integration: areas, volumes, and kinematics.

    • Techniques of integration: substitution and integration by parts.

  • Mechanics

    • Kinematics and dynamics of particles.

    • Newton’s laws of motion.

    • Applications of calculus to motion.


UNIT 3

UNIT 4

  • Functions and Graphs

    • Advanced study of functions: hyperbolic functions, implicit functions.

    • Further transformations and graphing techniques.

    • Applications of functions in modelling real-world scenarios.

  • Algebra

    • Complex numbers: advanced operations, De Moivre’s Theorem.

    • Polynomial equations: roots and factor theorem.

    • Advanced sequences and series.

  • Calculus

    • Advanced differentiation: higher-order derivatives, implicit differentiation.

    • Applications of differentiation: curve sketching, related rates, and optimisation problems.

    • Differential equations: solving first-order differential equations.

  • Vectors

    • Vector calculus: dot product, cross product.

    • Lines and planes in three-dimensional space.

    • Applications of vectors to geometry and physics.

  • Calculus (Advanced)

    • Techniques of integration: partial fractions, trigonometric integrals.

    • Applications of integration: complex areas, volumes of solids of revolution.

    • Solving differential equations: second-order differential equations, applications to motion and growth models.

  • Mechanics

    • Advanced kinematics and dynamics.

    • Circular motion and oscillations.

    • Applications of mechanics in engineering and physics.

  • Probability and Statistics

    • Probability distributions: binomial, normal, and Poisson distributions.

    • Statistical inference: hypothesis testing, confidence intervals.

    • Applications of probability and statistics in various fields.


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