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2019

 
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VCE Mathematics

Specialist Mathematics Unit 3 and 4

Prerequisites

Successful completion of Mathematical Methods Units 1 and 2. It is also strongly recommended that students have successfully completed Specialist Mathematics Units 1 and 2. Mathematical Methods Units 3 and 4 must be studied concurrently or have been successfully completed.

Course Description

Specialist Mathematics is the most challenging of the VCE Mathematics courses. It expands on many topics that are covered in Mathematical Methods Units 3 and 4 and explores additional topics such as proof, vectors, mechanics, complex numbers, differential equations and statistical prediction.

The appropriate use of CAS technology to support and develop the learning process is incorporated throughout the course.

Areas of Study

Algebra

  • Rational functions.
  • Complex numbers.
  • Proofs for integral powers.

Calculus

  • Differential and integral calculus.
  • Differential equations.
  • Kinematics.

Functions and Graphs 

  • Absolute value functions.
  • ​Reciprocal functions.
  • Simple quotient functions.
  • Circular and inverse circular functions.

Mechanics

  • Equations of motion.
  • Motion of a body.
  • Vector proofs.

Probability and Statistics

  • Linear combinations of random variables. 
  • Sample means.
  • Confidence intervals. 
  • Hypothesis testing.

Vectors

  • 2 and 3D vectors.
  • Vector calculus.

Assessment

Outcomes Assessment Tasks Marks Allocated
(school-assessed coursework)

Students demonstrate satisfactory completion of all three outcomes in each assessment task.

  • Define and explain key terms and concepts as specified in the content of the areas of study and apply a range of related mathematical routines and procedures.
  • Apply processes in non-routine contexts and analyse and discuss these applications.
  • Select and appropriately use numeric, graphic, and symbolic and statistical technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.

Application task (Unit 3)

50

Modelling or problem solving task 1 (Unit 4)

25
Statistical and probability modelling or problem solving task 2 (Unit 4) 25
Total Marks 100

Overall Final Assessment

Graded Assessment Title Assessment Exam Duration Contribution to Study Score (%)
1 Units 3 and 4 Coursework School-assessed   34
2

Written Examination 1

November 1 hour 22
3 Written Examination 2 November 2 hours 44

 

Reproduced by permission of the Victorian Curriculum and Assessment Authority, Victoria, Australia: www.vcaa.vic.edu.au