Specialist Mathematics
Unit 1 & 2
Course Description
Specialist Mathematics Units 1 and 2 provide a course of study for students who wish to undertake an in-depth study of mathematics, with an emphasis on concepts, skills and processes related to mathematical structure, modelling, problem solving and reasoning. This study has a focus on interest in the discipline of mathematics in its own right and investigation of a broad range of applications, as well as development of a sound background for further studies in Mathematical Methods Unit 3 and/or Specialist Mathematics Unit 3. The learning of Mathematical processes and theories must be accompanied by an increase in Thinking Mathematically, not just the mere application of rules.
Mathematical Methods Units 1 and 2 and Specialist Mathematics Units 1 and 2, must be taken in conjunction, providing a comprehensive preparation for Specialist Mathematics Units 3 and 4.
The areas of study for this course are:
Unit 1
Algebra, number and structure - Proof and number - introduction to principles of proof including propositions and quantifiers, examples and counter-examples, direct proof, proof by contradiction, and proof using the contrapositive and mathematical induction, simple proofs involving, for example, divisibility, sequences and series, inequalities and irrationality. Logic and algorithms - Boolean algebras - binary number systems tautologies, validity and proof patterns and the application of these to proofs in natural language and laws and properties of Boolean algebra, the algebra of sets and propositions. Complex numbers - definition and properties of the complex numbers C, arithmetic, modulus of a complex number, the representation of complex numbers as points on an argand diagram, general solution of quadratic equations, with real coefficients, of a single variable over C and conjugate roots
Discrete mathematics - Matrices - matrix notation, dimension and the use of matrices to represent data, matrix operations and algebra, determinants and matrix equations, and simple applications.
Space and measurement - Transformations- points in the plane, coordinates and their representation as 2 × 1 matrices, invariance of properties under transformation, and the relationship between the determinant of a transformation matrix and the effect of the linear transformation on the area of a bounded region of the plane.
Unit 2
Data analysis, probability & statistics-Simulation, sampling and sampling distributions - introduction to random variables for discrete distributions, distinction between a population parameter and a sample statistic and use of the sample statistics mean, concept of a sampling distribution and its random variable, distribution of sample means and proportions considered empirically, including comparing the distributions of different size samples from the same population in terms of centre and spread.
Space and measurement - Trigonometry- proof and application of the Pythagorean identities; the angle sum, difference and double angle identities and the identities for products of sines and cosines expressed as sums and differences.Proof and application of other trigonometric identities. Vectors in the plane - representation of plane vectors as directed lines segments, examples involving position, displacement and velocity magnitude and direction of a plane vector, and unit vectors geometric representation.
Functions, relations and graphs - interpreting graphical representations of data such as daily UV levels or water storage levels over time, graphs of simple reciprocal functions, including those for sine, cosine and tangent, locus definition and construction in the plane of lines, parabolas, circles, ellipses and hyperbolas.
Outcomes - On completion of this unit students will be able to:
On the completion of this unit the student should be able to define and explain key concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures.
On the completion of this unit the student should be able to apply mathematical processes, with an emphasis on general cases, in non-routine contexts, and analyse and discuss these applications of mathematics.
On the completion of this unit the student should be able to select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches
Assessment Tasks
Unit 1
Proof and number Test
Logic and algorithms Test
Complex Numbers Test
Matrices & Transformation Test
Semester Exam 1 (CAS Inactive)
Semester Exam 2 (CAS Active)
Unit 2
Data analysis and probability Test
Trigonometry & Circular Functions Test
Vectors Analysis Task
Functions & Graphs Application Task
Semester Exam 1 (CAS Inactive)
Semester Exam 2 (CAS Active)
Pathways
Unit 3 & 4 Specialist Mathematics
Textbook requirements:
Included in School Bundle
Resources/Requirements:
School laptop provided in School Bundle
A4 Exercise Book & pens
CAS calculator (TI Nspire) highly recommended (Available to rent, lease to own or purchase on the book list)
Career Pathways
Tertiary courses that require a strong mathematical component, including:
Statistics and Actuary work, Physical Sciences, Engineering and Mathematical Sciences, Medical Sciences.
Some important jobs for the future that rely on a strong background in Mathematics are: Environmental Engineer, Renewable Energies Engineer, Mechatronic Engineer, Statistician and Mathematician.
Note: There are many courses that require Maths Methods OR Specialist Maths, but in fact very few that require Specialist Maths on its own.