Terminale Mathematics — General Sciences (GS)

Terminale Mathematics — General Sciences (GS)

Selected analysis, probability and complex-plane methods, taught through twelve linked lessons. This is a bounded written self-paced course, using the 2025–26 CRDP reference year. Official 2026–27 alignment has not been verified. It does not replace the complete school programme or establish official examination readiness.

Who this is for

• English-reading Terminale GS learners revising the stated scope
• Independent learners willing to attempt questions before opening keys

Before you begin

• Confident arithmetic with fractions and signed numbers
• Solving linear and quadratic equations; basic function notation
• A calculator for optional decimal checks; paper for working

Outcomes

• Justify a unique root and construct a restricted inverse
• Differentiate, analyse curvature, and solve logarithmic/exponential models
• Evaluate selected definite integrals and distinguish signed area from geometric area
• Count selections and calculate conditional probabilities and random-variable moments
• Use complex numbers to describe distance, rotation and direct similitude

Included

• Written lessons with original worked examples
• Practice and explained answer keys
• Topic checks and an original capstone
• 12-question practice quiz
• Compact revision/reference pack

Scope boundaries

• Remaining annual-school units: sequences; inverse trigonometric functions; first- and second-order differential equations; spatial vector products, planes and lines, parallelism and distances
• Not developed fully here: general rational integration decompositions, extensive complex-locus proofs and compositions of many transformations
• Trigonometric and inverse-trigonometric integration are outside this course and excluded from the cited final-exam selection
• Complete official programme or past-paper collection
• Video, live coaching, official grading, certification or accreditation

Course outline

1. Functions and local change
   • Continuity and locating a unique root
   • Inverse functions with honest domains
   • Derivatives, curvature and indeterminate limits
2. Logarithms, exponentials and accumulation
   • Natural logarithms: domain before algebra
   • Exponential models and rates
   • Definite integrals and area
   • Choose an integration technique
3. Counting and uncertainty
   • Counting unordered selections
   • Conditional probability and reverse questions
   • Discrete random variables and risk
4. Complex-plane methods
   • Complex numbers as plane geometry
   • Dilations and direct similitudes

The revision pack is a compact companion. Read the full explanations, complete the practice, and then use the pack for retrieval practice. All datasets and scenarios are invented for learning.