Luxembourg General Secondary School Leaving Exam (Bac Général)

In a formal French letter to the director of a department, when you do not know whether the post is held by a man or a woman, which salutation and closing formula are standard?

• A'Cher Monsieur le Directeur,' and 'Bien cordialement.'
• B'À qui de droit,' and 'Veuillez agréer mes salutations distinguées.'
• C'Madame la Directrice, Monsieur le Directeur,' and 'Je vous prie d'agréer, Madame la Dire…
• D'Madame, Monsieur,' and 'Amitiés.'

What is the defining structural objective of a synthesis note (la note de synthèse) in administrative and business communication?

• ATo defend the writer's own position on the issue with arguments and a personal conclusion.
• BTo summarize each document separately, one after the other, in the order in which they ap…
• CTo produce a concise, objective and structured synthesis of a dossier of documents withou…
• DTo comment on and critique the style and reliability of each author.

In commercial German correspondence (kaufmännischer Schriftverkehr), which formal opening is standard when contacting a company or business partner whose individual recipient name is unknown?

• A'Liebe Kolleginnen und Kollegen!' followed by an exclamation mark and a capitalized first…
• B'Hallo zusammen,' followed by a comma and a lowercase first word.
• C'Sehr geehrte Damen und Herren!' followed by an exclamation mark and a capitalized first…
• D'Sehr geehrte Damen und Herren,' followed by a comma, continuing the first body sentence…

In German commercial law and business documentation, what is an 'Auftragsbestätigung'?

• AA formal written confirmation sent by the seller accepting a buyer's purchase order and e…
• BA reminder notice sent to a debtor demanding immediate payment of an overdue invoice.
• CA customs declaration certifying the geographical origin of exported industrial machinery.
• DA letter of recommendation testifying to an employee's professional conduct.

In international business English, what does the Incoterm 'FOB' (Free on Board, followed by named port of shipment) specify regarding risk and cost transfer?

• AThe seller pays all freight, insurance, and import customs duties directly to the buyer's…
• BThe seller delivers the goods on board the vessel nominated by the buyer; risk of loss or…
• CThe buyer assumes all risks and costs from the moment the goods leave the seller's factor…
• DThe shipping company assumes unlimited legal liability for market price fluctuations duri…

Which sentence is grammatically correct in standard written English?

• AIf the company would have invested earlier, it would have avoided the losses.
• BIf the company had invested earlier, it would avoid the losses last year.
• CIf the company had invested earlier, it would have avoided the losses.
• DIf the company invested earlier, it would have avoided the losses.

Which French grammatical rule governs the agreement of the past participle (participe passé) when used with the auxiliary verb 'avoir'?

• AThe past participle always agrees in gender and number with the grammatical subject of th…
• BThe past participle never agrees under any circumstances when conjugated with 'avoir'.
• CThe past participle agrees in gender and number with the direct object (COD) only if the…
• DThe past participle agrees with the indirect object (COI) regardless of its position in t…

In German syntax, what is the required position of the finite verb in a subordinate clause introduced by a subordinating conjunction such as 'weil', 'dass', or 'obwohl'?

• AImmediately in the second position (V2) following the conjunction.
• BAt the very beginning of the subordinate clause before the subject.
• CAt the very end of the subordinate clause (Nebensatz-Verb-Endstellung).
• DDirectly after the subject, as in a main clause (…, weil ich will die Prüfung bestehen).

In formal German reported speech (indirekte Rede), how should Herr Weber's statement 'Ich bin krank' be reported?

• AHerr Weber sagte, er sei krank.
• BHerr Weber sagte, er ist krank gewesen.
• CHerr Weber sagte, er wäre krank gewesen.
• DHerr Weber sagte, ich bin krank.

In a French argumentative essay, which connector introduces a concession, acknowledging an opposing point before the writer restates their own position?

• APar conséquent
• BCertes (… mais …)
• CEn effet
• DDe plus

In commercial correspondence, what is a 'letter of credit' (lettre de crédit documentaire / Akkreditiv)?

• AAn informal recommendation letter written by an accountant praising a firm's creditworthi…
• BA bank loan granted to the exporter to finance production before the goods are shipped.
• CA binding payment undertaking issued by a bank on behalf of an importer (buyer), promisin…
• DA certificate issued by customs authorities authorizing tariff-free duty exemption.

Which sentence correctly uses the present perfect in standard British English?

• AWe have signed the contract yesterday, so the project can start.
• BWe sign the contract already, so the project can start now.
• CWe have signed the contract, so the project can start now.
• DWe have sign the contract, so the project can start now.

Which form correctly completes the French sentence 'Bien qu'il ___ toute la nuit, le match a commencé à l'heure ce matin.' (verb: pleuvoir)?

• Aait plu
• Ba plu
• Cpleuve
• Davait plu

In German corporate governance, what is the function of the 'Handelsregister' (commercial register)?

• AA public register providing legal disclosure and publicity regarding registered businesse…
• BA land register (Grundbuch) recording who owns each plot of real estate and which mortgag…
• CA municipal record of trade notifications (Gewerbeanmeldung) used to authorize the start…
• DAn internal share register kept by the company and open only to its shareholders.

What is the primary linguistic function of the subjunctive mood (le subjonctif) in French professional and legal writing?

• ATo express subjective attitudes, uncertainty, doubt, obligation, or necessity (e.g., 'Il…
• BTo state objective historical facts with absolute chronological certainty.
• CTo formulate direct commands in the imperative second-person plural.
• DTo conjugate conditional hypotheses in the past anterior tense.

Which sentence correctly expresses in German that the invoice has to be paid by Friday (passive voice with a modal verb)?

• ADie Rechnung muss bis Freitag bezahlt worden.
• BDie Rechnung muss bis Freitag bezahlen werden.
• CDie Rechnung muss bis Freitag bezahlt werden.
• DDie Rechnung wird bis Freitag bezahlt müssen.

In commercial sales contracts, what is the meaning of the clause 'salvo errore et omissione' (S.E.e.O. / S.E.O. / errors and omissions excepted)?

• AA guarantee that the prices quoted remain valid for a fixed period.
• BA reservation indicating that the issuer may correct clerical, typographical or calculati…
• CAn agreement granting the buyer the right to cancel an order without penalty after delive…
• DA clause transferring ownership before payment is received by the seller.

A company wants a single matrix that combines its internal strengths and weaknesses with the opportunities and threats in its environment. Which strategic analysis tool should it use?

• ASWOT analysis
• BPESTEL analysis
• CPorter's five forces
• DThe BCG growth-share matrix

Which article correctly completes the sentence in standard written German: 'Wegen ___ schlechten Wetters wurde der Ausflug verschoben.'?

• Adem
• Bden
• Cder
• Ddes

In German business and employment communication, what is an 'Abmahnung'?

• AA formal written disciplinary warning issued by an employer notifying an employee of a sp…
• BA congratulatory letter awarding an annual performance bonus.
• CA formal notification announcing an employee's election to the works council.
• DAn official certificate confirming completion of vocational apprenticeship training.

A business takes out a loan of €50,000 at an annual compound interest rate of 4.0% for 3 years, with interest compounded annually. What is the total compound amount (principal + interest) due at the end of year 3?

• A€56,000.00
• B€56,243.20
• C€52,000.00
• D€6,243.20

A commercial company requires an annual constant annuity repayment of a = €10,000 on a loan at an annual interest rate i = 5.0% over n = 5 years. What is the present value (initial loan principal borrowed) V0? (Formula: V0 = a * [1 - (1 + i)^(-n)] / i)

• A€43,294.77
• B€50,000.00
• C€37,907.87
• D€45,459.51

A manufacturing firm produces q units of a product with a total cost function C(q) = 2q^2 + 40q + 5000 and total revenue function R(q) = 200q. At what production quantity q is profit Π(q) maximized?

• Aq = 80 units
• Bq = 100 units
• Cq = 50 units
• Dq = 40 units

A firm has fixed costs of FC = €60,000 per month. Each unit of product sells for P = €150 and has a unit variable cost of VC = €90. What is the break-even point in units (seuil de rentabilité en volume)?

• A400 units
• B1,000 units
• C667 units
• D2,500 units

A sample of five monthly sales figures (in thousands of euros) is recorded as: 12, 15, 18, 22, 28. What is the sample mean (moyenne) and median (médiane) of this dataset?

• AMean = 18.0 and Median = 19.0
• BMean = 19.0 and Median = 15.0
• CMean = 19.0 and Median = 18.0
• DMean = 23.75 and Median = 22.0

A €10,000 loan at 5% annual interest is repaid over 3 years by constant annual payments (annuités constantes) of €3,672.09. How much interest is paid in the second year?

• A€500.00
• B€333.33
• C€341.40
• D€3,330.69

In statistics, what does a Pearson correlation coefficient of r = -0.92 between advertising expenditure and product return rate indicate?

• AA strong negative linear relationship (as advertising expenditure increases, the product…
• BA weak positive relationship with no practical predictive value.
• CA calculation error, because correlation coefficients cannot be negative.
• DThat advertising expenditure causes exactly 92% of all customer purchases.

In linear programming, a business seeks to maximize profit Z = 30x + 40y subject to the constraints: x + 2y ≤ 16, 2x + y ≤ 14, x ≥ 0, y ≥ 0. What are the coordinates of the optimal vertex (corner point) and the maximum profit Z?

• A(x = 7, y = 0) with maximum profit Z = €210
• B(x = 0, y = 8) with maximum profit Z = €320
• C(x = 5, y = 5) with maximum profit Z = €350
• D(x = 4, y = 6) with maximum profit Z = €360

A production line fills cereal boxes with a target weight of 500 grams. The filling process follows a normal distribution with mean μ = 500 g and standard deviation σ = 5 g. What proportion of boxes is expected to weigh between 490 g and 510 g?

• AApproximately 68.27% (within ±1 standard deviation)
• BApproximately 99.73% (within ±3 standard deviations)
• CApproximately 95.45% (within ±2 standard deviations)
• DExactly 50.00%

An office equipment asset is purchased on January 1 for €20,000 with an estimated useful life of 5 years and zero salvage value. Under the straight-line depreciation method (amortissement linéaire), what is the annual depreciation charge and the Net Book Value (valeur nette comptable / VNC) at the end of Year 3?

• AAnnual depreciation = €5,000; VNC at end of Year 3 = €5,000
• BAnnual depreciation = €4,000; VNC at end of Year 3 = €8,000
• CAnnual depreciation = €4,000; VNC at end of Year 3 = €12,000
• DAnnual depreciation = €2,000; VNC at end of Year 3 = €14,000

A financial manager calculates the Net Present Value (NPV / VAN) of an investment project requiring an initial outlay of €100,000 that generates cash flows of €40,000 at the end of Year 1, €50,000 at Year 2, and €60,000 at Year 3, discounted at a cost of capital of 10%. What is the NPV of this project?

• A€22,764.84 (the project is financially viable since NPV > 0)
• B€50,000.00 (the undiscounted net profit)
• C-€12,450.00 (the project must be rejected)
• D€150,000.00 (the gross nominal cash flow)

The demand equation for a consumer good is P(q) = 120 - 2q. What is the total revenue function R(q) and the marginal revenue MR(q)?

• AR(q) = 120q - q^2 and MR(q) = 120 - 2q
• BR(q) = 120q - 2q^2 and MR(q) = 120 - 4q
• CR(q) = 60q - q^2 and MR(q) = 60 - 2q
• DR(q) = 120 - 2q and MR(q) = -2

A commercial inventory manager uses the Economic Order Quantity (EOQ / Wilson formula) Q* = √((2 * D * S) / H). If annual demand is D = 10,000 units, fixed order cost is S = €50 per order, and annual holding cost per unit is H = €4, what is the optimal order quantity Q*?

• A250 units
• B1,000 units
• C2,500 units
• D500 units

What is the compound annual growth rate (CAGR / taux de croissance annuel moyen) of a company whose annual revenue grew from €1,000,000 in Year 0 to €1,440,000 in Year 2?

• A44.0% per year
• B22.0% per year
• C14.4% per year
• D20.0% per year

In a probability tree diagram for a two-stage quality inspection, 5% of manufactured items are defective (P(D) = 0.05). If an item is defective, an optical sensor detects it with 98% probability (P(S+|D) = 0.98). If an item is non-defective, the sensor incorrectly flags it with 2% probability (P(S+|D^c) = 0.02). What is the total probability P(S+) that an item is flagged by the sensor?

• A0.0680 (or 6.8%)
• B0.0490 (or 4.9%)
• C0.0500 (or 5.0%)
• D0.0190 (or 1.9%)

A retail bank offers a nominal annual interest rate of 6.0% compounded monthly. What is the effective annual interest rate (taux effectif annuel)? (Formula: i_eff = (1 + r/m)^m - 1)

• AExactly 6.00%
• BApproximately 6.09%
• C0.50%
• DApproximately 6.17%

A company models the depreciation of its delivery vehicle fleet using an exponential decay model V(t) = V0 * e^(-0.15t), where t is measured in years. If the initial fleet value is V0 = €200,000, what is the estimated fleet value after t = 4 years? (Take e^(-0.60) ≈ 0.5488)

• A€80,000
• B€109,760
• C€120,000
• D€54,880

In descriptive statistics, what does the interquartile range (IQR = Q3 - Q1 / écart interquartile) represent in a box plot (boîte à moustaches)?

• AThe difference between the maximum and minimum observations in the entire sample.
• BThe ratio of the standard deviation to the arithmetic mean.
• CThe spread of the middle 50% of the dataset, providing a measure of dispersion resistant…
• DThe square root of the variance of the upper decile.

A production process produces components with an average failure rate of λ = 2 failures per day, following a Poisson distribution P(X = k) = (e^(-λ) * λ^k) / k!. What is the probability of observing exactly 0 failures on a given day? (Take e^(-2) ≈ 0.1353)

• A0.1353 (or 13.53%)
• B0.2707 (or 27.07%)
• C0.8647 (or 86.47%)
• D0.1804 (or 18.04%)

Under a loan repaid by constant principal amortization (amortissement constant) of a €60,000 loan over 5 years at 5% annual interest, what is the total payment (annuity = principal + interest) due at the end of the first year?

• A€13,858 (Constant annuity method)
• B€12,000 (Principal only)
• C€18,000 (Principal = €15,000 and Interest = €3,000)
• D€15,000 (Principal = €12,000 and Interest = €3,000)

Under the Luxembourg Standard Chart of Accounts (Plan Comptable Normalisé - PCN), what is the fundamental accounting equation that governs the Balance Sheet (le Bilan)?

• ATotal Assets = Total Revenues minus Total Operating Expenses
• BTotal Assets (Actif) = Total Liabilities and Equity (Passif: Capitaux Propres + Dettes)
• CTotal Equity = Bank Cash Balances minus Accounts Payable
• DTotal Assets + Total Revenues = Total Liabilities + Total Depreciation

In the Luxembourg PCN, which account class groups the enterprise's Operating Expenses (Charges) and which class groups Operating Revenues (Produits)?

• AClass 6 records Expenses (Charges) and Class 7 records Revenues (Produits).
• BClass 1 records Expenses and Class 2 records Revenues.
• CClass 4 records Expenses and Class 5 records Revenues.
• DClass 7 records Expenses and Class 6 records Revenues.

A Luxembourg business subject to standard VAT sells merchandise for €10,000 excluding tax (HTVA). What is the standard Luxembourg Value Added Tax (TVA) rate applicable in 2026, and what is the total invoice amount including tax (TTC)?

• AStandard rate is 17%; TVA = €1,700 and Total TTC = €11,700
• BStandard rate is 21%; TVA = €2,100 and Total TTC = €12,100
• CStandard rate is 15%; TVA = €1,500 and Total TTC = €11,500
• DStandard rate is 19%; TVA = €1,900 and Total TTC = €11,900

Under Luxembourg corporate law (Loi du 10 août 1915 sur les sociétés commerciales, telle que modifiée), what is the statutory minimum share capital required to incorporate a public limited company (Société Anonyme - SA)?

• A€12,000
• B€1
• C€100,000
• D€30,000

What is the statutory minimum share capital required to incorporate a standard private limited liability company (Société à Responsabilité Limitée - SARL) in Luxembourg?

• A€30,000 with 50% paid up upon incorporation.
• B€6,000 paid up annually over five years.
• C€1 with mandatory civil liability bond.
• D€12,000 fully subscribed and paid up upon incorporation.

In financial analysis, how is the Current Ratio (ratio de liquidité générale) calculated, and what does it measure?

• ATotal Equity / Total Debt; it measures the long-term solvency ratio.
• BCurrent Assets / Current Liabilities; it measures a company's ability to cover its short-…
• CNet Profit / Total Assets; it measures the return on investment (ROA).
• DOperating Cash Flow / Depreciation; it measures capital expenditure reinvestment.

A trading enterprise records the following inventory transactions: beginning inventory of 100 units at €10; purchase of 200 units at €13; and sale of 150 units. Under the First-In, First-Out (FIFO / PEPS) method, what is the cost of goods sold (COGS) and the value of ending inventory?

• ACOGS = €1,800 and Ending Inventory = €1,800
• BCOGS = €1,950 and Ending Inventory = €1,650
• CCOGS = €1,650 and Ending Inventory = €1,950
• DCOGS = €1,500 and Ending Inventory = €2,100