France Terminale Technological track — common core

1. Philosophy (technological track)

Art · Justice · Freedom · Nature · Religion · Technology · Truth · Perspectives and method

• Philosophy of Art: What Is Art, and Why Does It Matter? – The philosophy of art (part of aesthetics) asks: what is art, what is beauty, is taste only personal, what makes a creator, and can art show truth? Answers have changed from "art copies nature" to "art expresses feeling" to "the idea is the art".
• Political Philosophy: The State, Power and Justice – Political philosophy asks big questions about living together: Why do we need a state? What makes power rightful (legitimate)? What is justice? How much freedom and equality should people have? Social contract thinkers (Hobbes, Locke, Rousseau) explain the state as an agreement. Plato and Aristotle described the ideal state and the forms of government; Cicero saw the republic as the people's shared property under law. Rawls, Mill and thinkers from many traditions (Confucius, Kautilya, Ubuntu) help us weigh liberty, equality, property and community.
• Free Will, Determinism and Freedom – Free will is the power to choose our actions ourselves. Determinism says every event, including every choice, is fixed by earlier causes. Hard determinists say free will is an illusion; libertarians say some choices are not fixed; compatibilists say a choice is free when it comes from your own reasons and no one forces you. Aristotle separated voluntary from forced acts, and noticed weakness of will. Kant linked freedom to autonomy: obeying a rational law you give yourself. In society, freedom needs laws so that each person's freedom fits with everyone else's.
• Philosophy of Nature: Nature, Culture and Human Nature – Philosophers use the word "nature" in three ways: everything that grows by itself, the basic character of a thing (human nature), and a model to copy. Culture is what people add: language, tools, rules. Thinkers also ask how humans differ from animals, and what we owe to nature.
• Philosophy of Technology: What Tools Do to Us – Technology is how humans make tools to change the world. Philosophers ask: do tools only extend our power, or do they also change how we see nature and ourselves? Is technical progress always real progress? Do we control our machines, or do they shape us? And where is the line between human and machine?
• Epistemology: What Is Knowledge? – Epistemology is the part of philosophy that asks what knowledge is, how we get it and how sure we can be. A classic answer: knowledge is a belief that is true and well justified (justified true belief), although lucky cases (Gettier cases) show this may not be enough. Knowledge comes from reason (rationalism) and from experience through the senses (empiricism); Kant argued we need both. Theories of truth include correspondence (matches the facts), coherence (fits with other beliefs) and pragmatic (works in practice). Scepticism reminds us that senses and reasoning can mislead, so we test, check sources and stay open to correction.

2. History — totalitarianism, wars and democracy

Rise of totalitarian regimes and war · The world since 1945 · France since 1945: politics and society

• Totalitarianism – A totalitarian regime is a one-party state that tries to control every part of life — politics, the economy, the media, schools and even people's thoughts — using one leader, propaganda and terror. After the First World War and the 1929 depression, such regimes arose in Fascist Italy (1922), Stalin's Soviet Union (late 1920s) and Nazi Germany (1933). Their aims and ideas differed, but their methods were alike, and their rise helped lead to the Second World War.
• The Cold War (1945–1991) – The Cold War was a long contest (1945–1991) between two superpowers: the USA with its Western allies (capitalism, multi-party elections) and the USSR with its Eastern allies (communism, one-party rule). They never fought each other directly. Instead they formed rival alliances (NATO, Warsaw Pact), raced to build nuclear weapons and reach space, backed opposite sides in proxy wars (Korea, Vietnam, Afghanistan) and came close to nuclear war in Cuba in 1962. Many new nations, led by India and others, stayed non-aligned. Détente eased tension in the 1970s. Reforms in the USSR, the fall of the Berlin Wall (1989) and the break-up of the USSR (1991) ended it.
• The Fifth Republic of France – France today lives under the Fifth Republic, born in 1958 after the weak Fourth Republic and the Algerian crisis. General de Gaulle came back as leader. The new constitution gave the President strong powers, and from 1962 citizens elect the President directly. Deputies are chosen by a two-round majority vote. Power then moved between left and right (alternation), and sometimes the President and Prime Minister came from rival camps (cohabitation).

3. Geography — globalisation, unequal connections

Seas and oceans in globalisation · Uneven territorial dynamics · Places of French influence

• Seas and Oceans in Globalisation: Ships, Ports, Cables and Sea Law – Oceans cover about 71% of Earth and carry about 80% of world trade by volume. Container ships follow lanes between big ports and squeeze through straits and canals. Cables on the seabed carry almost all data between continents. Under the law of the sea, a coastal state controls a 12 nautical mile territorial sea and uses resources in a 200 nautical mile exclusive economic zone (EEZ), while ships of all states may sail the high seas. Seas also regulate climate, feed people and need protection.
• The Making of a Global World – People, goods, ideas and germs have moved across the world for thousands of years: on the silk routes, with food crops like potato and maize, and with diseases like smallpox. Between 1815 and 1914 the world economy grew through three flows: goods, labour and capital, helped by railways, steamships and refrigerated ships. Colonies paid a price: rinderpest in Africa and indentured labour from India. After the First World War came mass production in the USA and then the Great Depression of 1929, which hit India's farmers hard. After 1945, the Bretton Woods system, the IMF and the World Bank rebuilt the world economy.

4. Mathematics (2019 programme)

Sets and logic · Algorithms and programming (not STD2A) · Geometry activities (STD2A) · Quick-fire skills · Sequences · Exponential functions · Common logarithm · Reciprocal function · Two-variable statistics · Conditional probability and random variables · Study themes

• Sets: Representation, Types, Subsets, Venn Diagrams and Operations – A set is a well-defined collection of different objects. We write it in roster form {2, 4, 6} or set-builder form {x : x is even}. Sets can be empty, finite, infinite or equal. If every element of B is in A, B is a subset of A (B ⊂ A); a set with n elements has 2ⁿ subsets. Intervals like (a, b) and [a, b] are subsets of real numbers. The universal set U holds everything under study. With Venn diagrams we see union A ∪ B, intersection A ∩ B, difference A − B and complement A′ = U − A.
• Python Basics: Modes, Variables, Data Types and Operators – Python runs in interactive mode (one line at a time) or script mode (a saved .py file). Blocks are shown by indentation. Variables are names tied to values; every value has a data type, and some types are mutable. Operators build expressions that Python works out by precedence. input() reads text, int()/float()/str() convert types, and debugging fixes syntax, runtime and logical errors.
• Getting Started with Python – Python is a high-level, free and open-source, interpreted, portable, case-sensitive language that is easy to read. You can run it in interactive mode (type after the >>> prompt and see the result at once) or script mode (save code in a .py file and run it). Python's character set includes letters, digits, special symbols, whitespace and all Unicode characters. The smallest units of a program are tokens: keywords, identifiers, literals, operators and punctuators. A variable is a name that refers to a value; in an assignment the right side (r-value) is evaluated first and stored in the left side (l-value). Comments start with # and are ignored by Python.
• Python Revision for Class 12: Everything from Class 11 in One Place – Class 12 builds on Class 11 Python. You must know tokens (keywords, identifiers, literals, operators, punctuators), data types (int, float, bool, str, list, tuple, dict), which types are mutable (can change in place) and which are immutable, operator precedence, if-elif-else, for and while loops with break and continue, string slicing, and the main methods of lists, tuples and dictionaries.
• Conic Sections (Class 11): Circle, Parabola, Ellipse and Hyperbola – Cutting a double cone with a plane gives a circle, an ellipse, a parabola or a hyperbola; a cut through the vertex gives a point, a line or a pair of lines (degenerate conics). Circle: (x − h)² + (y − k)² = r². Parabola y² = 4ax: focus (a, 0), directrix x = −a, latus rectum 4a, e = 1. Ellipse x²/a² + y²/b² = 1 (a > b): c² = a² − b², foci (±c, 0), e = c/a < 1, latus rectum 2b²/a, PF₁ + PF₂ = 2a. Hyperbola x²/a² − y²/b² = 1: c² = a² + b², e = c/a > 1, latus rectum 2b²/a, |PF₁ − PF₂| = 2a.
• Mental Maths: Fast Everyday Calculation Skills – Mental maths means doing routine calculations quickly and correctly in your head or with a few lines. Compare two numbers by difference or by ratio. Write a percent change as a factor: +20% is × 1.2, −20% is × 0.8. Successive changes multiply their factors, so +20% then −20% gives × 0.96, not × 1. To undo +p% use the reciprocal factor. Know powers of ten and unit conversions, the special products (a + b)² = a² + 2ab + b² and (a + b)(a − b) = a² − b², how to make one letter the subject of a formula, and that a product is zero only if a factor is zero.
• Sequences and Series: AP, GP, AM and GM – A sequence is a list of numbers in a definite order: a₁, a₂, a₃, … A series is what we get when we add the terms. In an arithmetic progression (AP) we add the same number d each time; aₙ = a + (n − 1)d and Sₙ = n/2[2a + (n − 1)d]. The arithmetic mean (AM) of a and b is (a + b)/2; n AMs between a and b use d = (b − a)/(n + 1). In a geometric progression (GP) we multiply by the same number r each time; aₙ = arⁿ⁻¹ and Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1. If |r| < 1 the terms shrink and the infinite sum is S∞ = a/(1 − r). The geometric mean (GM) of two positive numbers a and b is √(ab), and n GMs between them use r = (b/a)^(1/(n+1)). For positive a and b, AM ≥ GM, with equality only when a = b.
• Exponential Functions – An exponential function has the form y = a·bˣ, where a ≠ 0 is the starting value and b > 0, b ≠ 1 is the growth factor. If b > 1 it grows; if 0 < b < 1 it decays. Each step of 1 in x multiplies y by b (a constant ratio), unlike a linear function which adds a constant. The graph of y = bˣ passes through (0, 1), has domain all real numbers, range y > 0, and the x-axis as a horizontal asymptote. The general form y = a·b^(k(x − d)) + c stretches, reflects and shifts it.
• Logarithms – A logarithm tells you the power you need. log_b x = y means b^y = x. So log₂ 8 = 3 because 2³ = 8. Logs turn multiplying into adding: log(ab) = log a + log b, log(a/b) = log a − log b, log(aⁿ) = n log a. Base 10 is the common log, base e is the natural log (ln). Any base can be changed: log_b x = log x ÷ log b.
• Functions: Composite, Inverse and Standard Graphs – A function is a rule that gives exactly one output for each allowed input. The allowed inputs are the domain; the outputs are the range. Two functions can be joined: g(f(x)) means do f first, then g. An inverse function f⁻¹ undoes f, and its graph is the mirror image of the graph of f in the line y = x. Only one-to-one functions have an inverse.
• Linear Regression and the Least Squares Line – Linear regression finds the straight line ŷ = a + bx that best follows paired data (x, y). A residual is the gap between a real point and the line: e = y − ŷ. The least squares line makes the sum of squared residuals as small as possible. Its slope is b = Sxy ÷ Sxx and it always passes through the mean point (x̄, ȳ). We use it to predict y from x, but only inside the data range, and a strong link does not prove that x causes y.
• Binomial Distribution – Repeat the same yes/no trial n times, independently, with the same chance of success p each time. The number of successes X follows the binomial distribution B(n, p): P(X = k) = ⁿCₖ pᵏ qⁿ⁻ᵏ with q = 1 − p. Its mean is np and its variance is npq.
• Mathematical Modelling: Using Maths to Describe the Real World – A mathematical model is an equation, graph or table that describes a real situation in a simple way. The modelling cycle: understand the real problem → choose variables and make assumptions → build a model (for example linear, quadratic or exponential) → solve and predict → check the answer against real data → improve the model or state its limits. No model is perfect; a good one is simple and close enough to be useful.

5. Modern languages A and B

Identities and exchanges · Private and public space · Art and power · Citizenship and virtual worlds · Fiction and reality · Science, innovation and responsibility · Diversity and inclusion · Territory and memory · Language activities

Coming soon

6. Moral and civic education (2024) — democratic life

Principles and spaces of democratic debate · Deliberation in institutions

• Democracy – Democracy is rule by the people. People choose their rulers in free and fair elections, each adult has one vote of equal value, and the government must follow the law and respect rights. Democracy can be direct or representative. India has old democratic roots and today uses a parliamentary system, while the USA uses a presidential system. Poverty, illiteracy, corruption and inequality are its main challenges.
• Outcomes of Democracy – Democracy is judged by what it delivers. It gives an accountable, responsive and legitimate government, and it is best at protecting dignity and freedom. On economic growth it is about as good as dictatorship. It has not done enough to cut inequality and poverty. It handles social differences well when majority and minority keep changing.