Unit 4: Integration, DEs, Kinematics & Statistics

VCE Specialist Mathematics Study Design 2023-2027

69 Core Skills + 4 Extension 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

14 core + 4 extension

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 Curvature and acceleration components21460 Parametric motion21461 Relative motion21462 Velocity-time graphs21467

Extension mechanics

Newton's laws in vector form21463 Work and energy21464 Collision and momentum21465 Collision problems21466