Comprehensive French Language and Algebra Revision Notes

Temporal Vocabulary and Date Formatting in French

Effective communication in French regarding time involves mastering the various terms for days, weeks, and relative timing. Today is represented by the word aujourd'hui, while yesterday is hier and tomorrow is demain. The word for day is le jour, and the week is la semaine, whereas the weekend is le weekend. To indicate that a period of time is upcoming, one uses prochain for masculine nouns or prochaine for feminine nouns, such as next week which is la semaine prochaine or next weekend which is le weekend prochain. Conversely, to refer to the past, one uses dernier for masculine or dernière for feminine, resulting in terms like last week, la semaine dernière, and last weekend, le weekend dernier. For specific past dates, the day before yesterday is expressed as avant-hier. When writing the date, the structure often follows a pattern such as C'est mardi le 31 mars 2026. In spoken French, this is read as C'est mardi le trente et un mars deux mille vingt-six. It is important to note that for the first day of the month, the term premier or 1er is used, but for all subsequent days, cardinal numbers like deux are used.

Conventions for Recurrent Events and Greetings

Daily routines and recurring events are expressed through specific phrasing in French. If one wishes to say they attend school on specific days, they might say Je suis à l'école lundi et jeudi, which translates to I am at school on Monday and Thursday. When using the name of the day directly, the preposition on is omitted. However, to indicate a recurring event on every instance of a specific day, such as Every Monday, one says le lundi or tous les lundis. The phrase for every day is tous les jours. When saying goodbye to someone with the intention of seeing them on a specific day, the preposition à is used before the day, such as À jeudi for See you on Thursday or À demain for See you tomorrow. Other vocabulary related to personal milestones include anniversaire, which means birthday or anniversary.

Irregular Nouns and Professional Gender Rules

French grammar distinguishes between masculine and feminine nouns, particularly in the context of people and professions. While many nouns change by adding an e to the masculine form—such as un gérant becoming une gérante for a manager, or un commerçant becoming une commerçante for a shopkeeper—there are several irregular cases. Some professions remain identical in form regardless of gender, such as un/une principal for a principal, un/une médecin for a doctor, un/une soldat for a soldier, and un/une facteur for a postman. Other nouns follow specific suffix transformations. Nouns ending in -teur often change to -trice in the feminine, like un directeur becoming une directrice for a director or un traducteur becoming une traductrice for a translator. Nouns ending in -eur typically change to -euse, such as un chanteur becoming une chanteuse for a singer, un coiffeur becoming une coiffeuse for a hairdresser, and un serveur becoming une serveuse for a server. However, exceptions exist where the form remains unchanged despite the gender, such as un/une professeur for a teacher or un/une ingénieur for an engineer. Nouns ending in -er change to -ère, like un conseiller becoming une conseillère for a counsellor or un infirmier becoming une infirmière for a nurse. Nouns ending in -ien change to -ienne, such as un technicien becoming une technicienne for a technician or un mécanicien becoming une mécanicienne for a mechanic.

Numbers, Months, and Seasonal Transitions

Counting in French is essential for daily transactions and date keeping. The numbers from zero to ten are zéro, un (masculine) or une (feminine), deux, trois, quatre, cinq, six, sept, huit, neuf, and dix. The numbers from eleven to twenty are onze, douze, treize, quatorze, quinze, seize, dix-sept, dix-huit, dix-neuf, and vingt. The months of the year are recognized as janvier, février, mars, avril, mai, juin, juillet, août, septembre, octobre, novembre, and décembre. To specify being born in a certain month, one can say Je suis né(e) en janvier or Je suis né(e) au mois de janvier. Seasons also have specific prepositional markers: summer is L'été (en été), autumn is L'automne (en automne), and winter is L'hiver (en hiver). Because these start with vowels, they use en. Spring is le printemps, and because it starts with a consonant, it uses the prepositional phrase au printemps.

Definite Articles and Noun Gender Indicators

French nouns and articles must agree in gender and number. The definite article, equivalent to the English the, has four forms: le for masculine singular, la for feminine singular, l' for singular nouns starting with a vowel, and les for plural nouns of either gender. Examples include le chien, la chienne, l'amie, and les chiens. Indefinite articles, equivalent to a or an, include un for masculine, une for feminine, and des for plural, which means some. While it is generally true that nouns ending in e are feminine and those ending in a consonant are masculine, several suffixes provide clearer clues. Masculine suffixes include -age (except une image or une page), -asme, -isme, -acle, -ment, and -eau (except l'eau, which is feminine). Other masculine exceptions include un lycée, un ingénieur, un plastic, un kiosque, and un pilote. Typical feminine endings include -ade, -ance, -ation, -oire, -ure, -ence, -ette, -que, -ie, -sion, and -ssion, with exceptions like la fin and la météo.

Classroom Vocabulary and Equipment

Describing an educational environment requires specific terminology for classroom objects and fixtures. Common structural elements include le mur for the wall, le plancher for the floor, and le plafond for the ceiling. Technological tools include l'ordinateur or portable for a computer or laptop, a baladeur for a personal player, a tableau blanc interactif for an interactive whiteboard, and le lecteur CD/MP3. General school supplies include le pupitre for the desk, le stylo for the pen, le crayon for the pencil, le feutre for the marker, and le taille-crayon for the pencil sharpener. Organization is handled by tools such as les ciseaux for scissors, le livre for a book, le cahier for an exercise book, le papier for paper, le classeur for a file, and le dictionnaire for a dictionary. Students carry their belongings in a sac à dos or a cartable and must complete les devoirs or l'exercice. Other classroom furniture and items include la fenêtre for the window, la porte for the door, la calculatrice for the calculator, la chaise for the chair, la table for the table, la gomme for the rubber or eraser, la règle for the ruler, la trousse for the pencil case, la boîte for the box, and la poubelle for the bin.

French Pronunciation and Punctuation

French pronunciation requires attention to spelling and letters. A capital letter is referred to as Majuscule, while a small letter is a Minuscule. When spelling, double letters are noted as deux followed by the letter, such as deux ss or deux tt. In electronic communications, an email address is an adresse électronique or le courriel, featuring an arobase (@), a point (.), and an espace for a space. French vowels are a, e, i, o, and u. Phonetic rules dictate that certain consonants at the end of words remain silent, such as the t in salut, the c and s in blanc or divers, and the t in vert or petit. However, adding an e to the end of a word allows the preceding consonant to be pronounced, as seen in the transition from petit to petite or grand to grande. Vowel combinations create specific sounds: eu sounds like /oe/ as in professeur, ou sounds like /u/ as in bonjour, and oi sounds like /wa/ as in toi or moi. The combination in sounds like /un/, and en/an are nasalized as in onze or ans. Note that the letter j is pronounced /zh/ as in bonjour, and ch is pronounced /sh/ as in chat or chien.

Diacritics and Manners in French

The French language utilizes several accent symbols placed over vowels to alter sound or distinguish meaning. L'accent aigu (é) is the acute accent found only on top of the letter e, as in télévision. L'accent grave (à, è, ù) is found in words like père and mère. L'accent circonflexe (â, ê, î, ô, û) can stretch the sound of a letter and appears in words like âge, hôpital, and fenêtre; it can also distinguish between words that are spelled similarly. Le tréma (ë, ï) is used to separate vowel sounds, as in Noël. La cédille (ç) is the only accent found below a consonant, specifically the c, changing its sound to an s when followed by a, o, or u, as in français or garçon. L'apostrophe (') indicates that a letter has been dropped and replaced, as in aujourd'hui. Polite interactions involve greetings like Bonjour for good day, Bonne journée for have a good day, and Comment allez-vous? for the formal how are you? Responses include bien for good and pas mal for not bad. Manners are expressed through s'il vous plaît for please, merci for thank you, and de rien or je vous en prie for you're welcome. Situational etiquette includes félicitations for congratulations, bonne chance for good luck, and excusez-moi or pardonnez-moi for excuse me.

Algebra and Mathematical Operations

Mathematics revision covers fundamental algebraic concepts and the simplification of expressions. Algebra is defined as a branch of mathematics that uses letters to represent and solve problems. The order of operations follows BODMAS, standing for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. When expanding brackets, multiplication is distributed across the terms inside, such as $10t - 8(3 - t) = 10t - 24 + 8t = 18t - 24$. Another example involves distribution and subtraction: $-5(2x - 11y) = -10x^2 + 55xy$. Simplification of terms requires combining like variables, such as $8x + x + 7x = 16x$ and $2a + 3a = 5a$. When multiplying variables, indices are used, as in $n \times n = n^2$ or $x \times x = x^2$.

Advanced Algebraic Simplification and Polynomials

Mathematical problems involving multiple variables and signs require careful calculation of coefficients. For instance, in a problem dated March 16, 2026, simplifying the expression involving s and a resulted in $20s - 10s - 3s + 11a + 8a + 9a = 7s + 28a$. Other operations include division of algebraic terms such as $15m^2 \div 5m = 3m$. Expanding more complex expressions like $(x + 4)(x - 8)$ involves distributed multiplication resulting in $x^2 - 4x - 32$. Constant numerical expressions can also be simplified using BODMAS, such as $5 + (3 - 3) \times 5 = 5$, because the calculation within the brackets results in zero. In a different example involving y, the term $17y - (5y \times 2)$ simplifies to $17y - 10y$ which equals $7y$. For expressions with multiple sign changes, such as $-(a + b)$, the result is $-a - b$, and $-5(a - b)$ results in $-5a + 5b$. The specific expression $12f - 5f - 3f - 4f + 4d - 4d$ simplifies to $0f + 0d = 0$.