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 First-order linear DEs21431 Slope fields: analysis and stability21432 Euler's method: accuracy and error21433 Second-order homogeneous DEs21434 Applications of DEs21435 Slope fields: basics21436 Euler's method: basics21437 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