Unit 4: Integration, DEs, Kinematics & Statistics
VCE Specialist Mathematics Study Design 2023-2027
73 Skills • 3 Levels Each
Units 3 & 4 (Exam-Assessed)
Unit 4 Skill Map
Integral Calculus Advanced, Differential Equations, Vector Calculus & Kinematics, and Statistics & Inference Advanced.
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Integral Calculus Advanced
15 skills
Integration by parts21400
Advanced substitution21401
Partial fractions integration21402
Trigonometric substitution21403
Trigonometric integrals21404
Volumes of revolution (disk/washer)21405
Volumes of revolution (shell method)21406
Surface area of revolution21407
Arc length21408
Improper integrals21409
Reduction formulas21410
Integration strategy21411
Applications of integration21412
Numerical integration21413
Volumes of revolution (y-axis)21414
Differential Equations
16 skills
Separation of variables21430
Initial conditions21431
Exponential growth21432
Exponential decay21433
Newton's law of cooling21434
Logistic equation21435
Slope fields21436
Euler's method21437
Euler's method with pseudocode21438
Mixing problems21439
Radioactive decay21440
Population dynamics21441
Homogeneous first-order DEs21442
Integrating factor21443
Second-order DEs21444
Modelling with DEs21445
Vector Calculus & Kinematics
18 skills
Vector functions of t21450
Differentiation of vector functions21451
Integration of vector functions21452
Position, velocity, acceleration21453
Speed and distance21454
Straight-line motion21455
Projectile motion (2D)21456
Projectile motion (advanced)21457
Circular motion21458
Tangent and normal vectors21459
Curvature21460
Parametric motion21461
Relative motion21462
Newton's laws in vector form21463
Work and energy21464
Collision and momentum21465
Collision problems21466
Velocity-time graphs21467
Statistics & Inference Advanced
24 skills
Linear combinations of random variables21500
Distribution of sample mean21501
Central Limit Theorem21502
Confidence intervals (sigma known)21503
Confidence intervals (sigma unknown)21504
Hypothesis testing (one-tailed)21505
Hypothesis testing (two-tailed)21506
p-values21507
Type I and II errors21508
Power of a test21509
Proportion testing21510
Chi-squared test21511
Markov chains: transition matrices21512
Markov chains: state diagrams21513
Markov chains: steady state21514
Markov chains: n-step21515
Pseudocode for statistical simulation21516
Interpreting results21517
Experimental design21518
Comparing two populations21519
Statistical inference review21520
Continuous random variable PDFs21521
Sample size determination21522
Confidence interval interpretation21523