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VCE Specialist Mathematics (SM)
Specialist mathematics focuses on more advanced mathematical techniques and problem solving skills. The content requires not only prior knowledge from unit 1&2 specialist mathematics, but also knowledge from unit 3&4 maths methods. Therefore, VCAA requires students who wish to undertake units 3&4 specialist maths to have either completed units 3&4 maths methods or are simultaneously studying both subjects. The subject itself is considered to have a high level of difficulty generally scaling up the study score by 7-12 marks.
VCE SM Study Design:
Function and Relation:
● Graphs of rational functions of low degrees including asymptotic behaviours and natures of stationary points
● Absolute value functions
● Graphs of circular functions and their respective inverse functions
● Graphs of reciprocal circular functions
● Compound and double angle formulas and trigonometric identities
● Graphs of quotient functions
Vector:
● Addition and subtraction of vectors
● Magnitude of vectors
● Resolution of vectors
● Linear dependence and independence of vectors
● Scalar product and angle between vectors
● Parallel and perpendicular vectors
● Vector proofs of geometric results
Vector Calculus:
● Position of vectors as a function of time
● Sketching path of vectors
● Differentiation and antidifferentiation of a vector function
Complex Number:
● Number sets in a complex plane in the form of z=x+yi (C)
● Use of argand diagram
● Addition, subtraction, multiplication and division of complex numbers
● Polar form of complex numbers
● Use of De Moivre’s theorem for proof of integral powers and roots of complex numbers in polar form
● Nth roots of unity
● Factors of complex polynomials
● Factorisation of polynomial functions over C
● Solving polynomial functions over C
Calculus:
● Derivatives of inverse circular functions
● Second derivatives and application of second derivatives
● Application of chain rule in related rates of change and implicit differentiation
● Advanced techniques of anti differentiation including:
□ Anti-differentiation of 1/x to obtain loge| x |
□ Antidifferentiation by recognition using inverse circular functions
□ Use of ‘u’ substitution to antidifferentiate expressions
□ Use of the trigonometric identities in antidifferentiation
□ Use of partial fractions in antidifferentiation
● Relationship between functions and their antiderivatives
● Application of integration including areas bounded by curves, arc lengths and volumes of solids of revolution
Differential Equations:
● Application of differential equations in context of real life scenarios
● Verification of differential equations using slope fields
● Solution of differential equations
● Use of Euler’s method
Kinematics:
● Application of differentiation and antidifferentiation in the context of displacement, velocity and acceleration
● Derivative forms of acceleration
● Analysis of velocity-time graphs
Mechanics:
● Momentum and change of momentum
● Newton’s laws of motion and application of Newton’s law
● Equations of motion using weighted particles
● Weighted particles under equilibrium
Probability and Statistics:
● Linear combinations of random variables
● Independent random variables under normal distributions
● Concept of sample mean
● Simulation of random sampling
● Determination of confidence intervals and approximation of confidence intervals
● P values of hypothesis testing
● Formulation of null and alternative hypothesis
● Errors in hypothesis testing
SM SACs:
Unit 3 SACs contributes 17% to a students final study score and is composed of 3 outcomes. Unit 4 SACs also contributes 17% (34% in total for school-based assessments) and is composed of 3 outcomes. There will be at least 1 major problem solving assessment and at least 1 problem solving or modelling task based on probability and statistics or mechanics.
Final Exams:
The final exams contribute 66% of a students final study score and are composed of exam 1 (22%) and exam 2 (44%).
Exam 1 is composed of around 10 short answer questions with no access to notes or calculators.
Exam 2 is composed of 20 multiple choice and around 4 extended response style questions. Students are permitted 1 bound reference and both a CAS and scientific calculator exam 2.
SM Past Exam:
WILL provides free VCE SM past exam papers, all you need to do is contact us (via WeChat or Email) to claim it for free.
http://www.willeducationau.com/