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.

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