VCE Specialist Unit 4 Skills () « back to units

The skills below are aligned with the VCE Specialist Mathematics Study Design 2023-2027. Skills are organised into key areas: Integral Calculus Advanced, Differential Equations, Vector Calculus & Kinematics, and Statistics & Inference Advanced. To master a skill, you will have to gain 10 stars.

There are 3 levels to each skill,

  1. Easy: A star will be taken away if you get 3 consecutive wrong answers.
  2. Medium: A star will be taken away if you get 2 consecutive wrong answers.
  3. Hard: A star will be taken away on each wrong answer.

Most skills have multiple types of questions with varying difficulties. If you keep getting wrong answers, the system may give you the simplest question to answer. The idea is to have you master these skills with a ground up approach. If you get an answer wrong, you can read the solution and helpful tips that briefly explain the skill/topic you are practising.

All the best with your VCE Specialist Unit 4. If you see any issue, please do report it by clicking the red button at bottom left of this page.

  1. Integral Calculus Advanced

    1. Integration by parts
    2. Advanced substitution
    3. Partial fractions integration
    4. Trigonometric substitution
    5. Trigonometric integrals
    6. Volumes of revolution (disk/washer)
    7. Volumes of revolution (shell method)
    8. Surface area of revolution
    9. Arc length
    10. Improper integrals
    11. Reduction formulas
    12. Integration strategy
    13. Applications of integration
    14. Numerical integration
    15. Volumes of revolution (y-axis)

  2. Differential Equations

    1. Separation of variables
    2. Initial conditions
    3. Exponential growth
    4. Exponential decay
    5. Newton's law of cooling
    6. Logistic equation
    7. Slope fields
    8. Euler's method
    9. Euler's method with pseudocode
    10. Mixing problems
    11. Radioactive decay
    12. Population dynamics
    13. Homogeneous first-order DEs
    14. Integrating factor
    15. Second-order DEs
    16. Modelling with DEs

  3. Vector Calculus & Kinematics

    1. Vector functions of t
    2. Differentiation of vector functions
    3. Integration of vector functions
    4. Position, velocity, acceleration
    5. Speed and distance
    6. Straight-line motion
    7. Projectile motion (2D)
    8. Projectile motion (advanced)
    9. Circular motion
    10. Tangent and normal vectors
    11. Curvature
    12. Parametric motion
    13. Relative motion
    14. Newton's laws in vector form
    15. Work and energy
    16. Collision and momentum
    17. Collision problems
    18. Velocity-time graphs

  4. Statistics & Inference Advanced

    1. Linear combinations of random variables
    2. Distribution of sample mean
    3. Central Limit Theorem
    4. Confidence intervals (sigma known)
    5. Confidence intervals (sigma unknown)
    6. Hypothesis testing (one-tailed)
    7. Hypothesis testing (two-tailed)
    8. p-values
    9. Type I and II errors
    10. Power of a test
    11. Proportion testing
    12. Chi-squared test
    13. Markov chains: transition matrices
    14. Markov chains: state diagrams
    15. Markov chains: steady state
    16. Markov chains: n-step
    17. Pseudocode for statistical simulation
    18. Interpreting results
    19. Experimental design
    20. Comparing two populations
    21. Statistical inference review
    22. Continuous random variable PDFs
    23. Sample size determination
    24. Confidence interval interpretation

The Final Unit

Unit 4 is where everything comes together. These 73 skills represent the culmination of VCE Specialist Mathematics, directly preparing you for both technology-free and CAS-allowed exams.

What Makes Unit 4 Special?

Exam 1 Focus

Technology-free integration and differentiation drills

Exam 2 Mastery

Extended response questions worth 8-12 marks

Real Applications

Mechanics and physics integration throughout

Statistics

Brand new topic area - hypothesis testing mastery

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