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Cameroon BEPC - independent subject foundations study materials
Cameroon BEPC - independent subject foundations study resources

Cameroon BEPC - independent subject foundations practice questions

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Question 1Lower-secondary number, algebra, geometry and data

Simplify the square root expression: $A = \sqrt{75} - 2\sqrt{27} + \sqrt{48}$. What is the resulting exact value?

  1. $5\sqrt{3}$
  2. $3\sqrt{3}$ Correct answer.
  3. $\sqrt{3}$
  4. $7\sqrt{3}$

Explanation

Factoring each radicand by perfect squares: $\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$; $2\sqrt{27} = 2\sqrt{9 \times 3} = 2(3\sqrt{3}) = 6\sqrt{3}$; $\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$. Combining the terms yields $A = 5\sqrt{3} - 6\sqrt{3} + 4\sqrt{3} = (5 - 6 + 4)\sqrt{3} = 3\sqrt{3}$.

Question 2Lower-secondary number, algebra, geometry and data

Rationalize the denominator of the fraction $F = \frac{6}{\sqrt{5} - 1}$. What is the simplified expression?

  1. $\frac{6(\sqrt{5} + 1)}{6}$
  2. $3(\sqrt{5} - 1)$
  3. $\frac{3(\sqrt{5} + 1)}{2}$ Correct answer.
  4. $\frac{3\sqrt{5} - 3}{4}$

Explanation

Multiplying the numerator and denominator by the conjugate $(\sqrt{5} + 1)$: $F = \frac{6(\sqrt{5} + 1)}{(\sqrt{5} - 1)(\sqrt{5} + 1)} = \frac{6(\sqrt{5} + 1)}{(\sqrt{5})^2 - 1^2} = \frac{6(\sqrt{5} + 1)}{5 - 1} = \frac{6(\sqrt{5} + 1)}{4}$. Simplifying by dividing numerator and denominator by 2 gives $\frac{3(\sqrt{5} + 1)}{2}$.

Question 3Lower-secondary number, algebra, geometry and data

Expand and simplify the algebraic expression: $E(x) = (2x - 3)^2 - (x + 1)(2x - 3)$.

  1. $2x^2 - 13x + 6$
  2. $4x^2 - 11x + 12$
  3. $2x^2 - 7x + 6$
  4. $2x^2 - 11x + 12$ Correct answer.

Explanation

Expanding $(2x - 3)^2 = 4x^2 - 12x + 9$. Expanding $(x + 1)(2x - 3) = 2x^2 - 3x + 2x - 3 = 2x^2 - x - 3$. Subtracting the two expressions: $E(x) = (4x^2 - 12x + 9) - (2x^2 - x - 3) = 4x^2 - 12x + 9 - 2x^2 + x + 3 = (4-2)x^2 + (-12+1)x + (9+3) = 2x^2 - 11x + 12$.

Question 4Lower-secondary number, algebra, geometry and data

Completely factorize the algebraic expression: $P(x) = (3x - 2)^2 - 16$.

  1. $3(x - 2)(3x + 2)$ Correct answer.
  2. $(3x - 6)(3x - 2)$
  3. $(3x + 2)(3x - 2)$
  4. $9(x - 2)(x + 2)$

Explanation

Using the difference of two squares identity $a^2 - b^2 = (a - b)(a + b)$ with $a = 3x - 2$ and $b = 4$: $P(x) = [(3x - 2) - 4][(3x - 2) + 4] = (3x - 6)(3x + 2)$. Factoring out 3 from the first binomial $(3x - 6) = 3(x - 2)$ gives $P(x) = 3(x - 2)(3x + 2)$.

Question 5Lower-secondary number, algebra, geometry and data

Solve the zero-product equation in $\mathbb{R}$: $(2x - 5)(3x + 4) = 0$.

  1. $S = \left\{ \frac{4}{3}, -\frac{5}{2} \right\}$
  2. $S = \left\{ -\frac{4}{3}, \frac{5}{2} \right\}$ Correct answer.
  3. $S = \left\{ \frac{5}{2}, \frac{4}{3} \right\}$
  4. $S = \left\{ -\frac{5}{2}, -\frac{4}{3} \right\}$

Explanation

A product of factors equals zero if and only if at least one factor is zero: $2x - 5 = 0 \implies 2x = 5 \implies x = 5/2$; or $3x + 4 = 0 \implies 3x = -4 \implies x = -4/3$. Thus the solution set is $S = \{-4/3, 5/2\}$.

Question 6Lower-secondary number, algebra, geometry and data

Solve the first-degree inequality in $\mathbb{R}$: $3x - 7 \le 5x + 5$.

  1. $S = ]-\infty, -6]$
  2. $S = [6, +\infty[$
  3. $S = [-6, +\infty[$ Correct answer.
  4. $S = ]-\infty, 6]$

Explanation

Subtracting $5x$ from both sides: $3x - 5x - 7 \le 5 \implies -2x - 7 \le 5$. Adding 7 gives $-2x \le 12$. Dividing both sides by $-2$ reverses the inequality symbol: $x \ge \frac{12}{-2} \implies x \ge -6$. In interval notation, $S = [-6, +\infty[$.

Question 7Lower-secondary number, algebra, geometry and data

Solve the system of two linear equations in $\mathbb{R} \times \mathbb{R}$: $$\begin{cases} 2x + 3y = 21 \\ 5x - y = 10 \end{cases}$$

  1. $(x, y) = (5, 3)$
  2. $(x, y) = (2, 5)$
  3. $(x, y) = (3, 4)$
  4. $(x, y) = (3, 5)$ Correct answer.

Explanation

From the second equation, express $y = 5x - 10$. Substitute into the first equation: $2x + 3(5x - 10) = 21 \implies 2x + 15x - 30 = 21 \implies 17x = 51 \implies x = 3$. Then $y = 5(3) - 10 = 15 - 10 = 5$. Thus $(x, y) = (3, 5)$. Checking: $2(3)+3(5)=6+15=21$ and $5(3)-5=10$.

Question 8Lower-secondary number, algebra, geometry and data

Let $ABC$ be a right-angled triangle at $A$ such that $AB = 8\text{ cm}$ and $AC = 6\text{ cm}$. Let $H$ be the orthogonal projection of $A$ on the hypotenuse $[BC]$. Calculate the length of the height $AH$.

  1. $4.8\text{ cm}$ Correct answer.
  2. $5.0\text{ cm}$
  3. $4.0\text{ cm}$
  4. $3.6\text{ cm}$

Explanation

By Pythagoras theorem, $BC = \sqrt{AB^2 + AC^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10\text{ cm}$. The area of triangle $ABC$ can be calculated in two ways: $\text{Area} = \frac{AB \times AC}{2} = \frac{BC \times AH}{2}$. Thus $AB \times AC = BC \times AH \implies 8 \times 6 = 10 \times AH \implies AH = \frac{48}{10} = 4.8\text{ cm}$.

Question 9Lower-secondary number, algebra, geometry and data

A triangle has side lengths $7\text{ cm}$, $24\text{ cm}$, and $25\text{ cm}$. According to the converse of Pythagoras' theorem (réciproque de Pythagore), what can be concluded?

  1. The triangle is isosceles because $25 - 24 = 1$.
  2. The triangle is right-angled because $7^2 + 24^2 = 49 + 576 = 625 = 25^2$. Correct answer.
  3. The triangle is obtuse because $25^2 > 7^2 + 24^2$.
  4. The triangle is equilateral because all side lengths are integers.

Explanation

Calculating the square of the longest side: $25^2 = 625$. The sum of the squares of the other two sides: $7^2 + 24^2 = 49 + 576 = 625$. Since $25^2 = 7^2 + 24^2$, by the converse of Pythagoras' theorem, the triangle is strictly right-angled.

Question 10Lower-secondary number, algebra, geometry and data

In a triangle $ABC$, point $M$ lies on $[AB]$ and point $N$ lies on $[AC]$ such that $(MN)$ is parallel to $(BC)$. Given $AB = 12\text{ cm}$, $AM = 4\text{ cm}$, and $BC = 15\text{ cm}$, what is the length of segment $[MN]$?

  1. $4\text{ cm}$
  2. $6\text{ cm}$
  3. $5\text{ cm}$ Correct answer.
  4. $7.5\text{ cm}$

Explanation

According to Thales' theorem: $\frac{AM}{AB} = \frac{AN}{AC} = \frac{MN}{BC}$. Substituting known values: $\frac{4}{12} = \frac{MN}{15} \implies \frac{1}{3} = \frac{MN}{15} \implies MN = \frac{15}{3} = 5\text{ cm}$.

Question 11Lower-secondary number, algebra, geometry and data

In triangle $RST$, point $P$ belongs to segment $[RS]$ and point $Q$ belongs to segment $[RT]$ in the same order. If $RP = 3\text{ cm}$, $RS = 7.5\text{ cm}$, $RQ = 4\text{ cm}$, and $RT = 10\text{ cm}$, are lines $(PQ)$ and $(ST)$ parallel?

  1. No, because $7.5 - 3 \neq 10 - 4$.
  2. No, because $3 \times 4 \neq 7.5 \times 10$.
  3. It is impossible to determine without knowing the angle at vertex $R$.
  4. Yes, because the ratios $\frac{RP}{RS} = \frac{3}{7.5} = 0.4$ and $\frac{RQ}{RT} = \frac{4}{10} = 0.4$ are equal in the same order. Correct answer.

Explanation

According to the converse of Thales' theorem (réciproque du théorème de Thalès), since the points $R, P, S$ and $R, Q, T$ are aligned in the same order and $\frac{RP}{RS} = \frac{3}{7.5} = \frac{2}{5} = 0.4$ while $\frac{RQ}{RT} = \frac{4}{10} = \frac{2}{5} = 0.4$, the ratios are equal, proving that $(PQ) \parallel (ST)$.

Question 12Lower-secondary number, algebra, geometry and data

In a right-angled triangle $EFG$ at $E$, the hypotenuse is $FG = 15\text{ cm}$ and $\cos(\widehat{EFG}) = 0.6$. Calculate the length of adjacent side $EF$ and the length of opposite side $EG$.

  1. $EF = 9\text{ cm}$ and $EG = 12\text{ cm}$ Correct answer.
  2. $EF = 12\text{ cm}$ and $EG = 9\text{ cm}$
  3. $EF = 6\text{ cm}$ and $EG = 9\text{ cm}$
  4. $EF = 10\text{ cm}$ and $EG = 11\text{ cm}$

Explanation

By definition, $\cos(\widehat{EFG}) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{EF}{FG} \implies EF = FG \times \cos(\widehat{EFG}) = 15 \times 0.6 = 9\text{ cm}$. Using Pythagoras theorem: $EG = \sqrt{FG^2 - EF^2} = \sqrt{15^2 - 9^2} = \sqrt{225 - 81} = \sqrt{144} = 12\text{ cm}$.

Question 13Lower-secondary number, algebra, geometry and data

Let $\alpha$ be an acute angle such that $\cos(\alpha) = \frac{4}{5}$. Calculate $\tan(\alpha)$.

  1. $\frac{4}{3}$
  2. $\frac{3}{4}$ Correct answer.
  3. $\frac{3}{5}$
  4. $\frac{5}{4}$

Explanation

Using the fundamental trigonometric identity $\cos^2(\alpha) + \sin^2(\alpha) = 1$: $\sin^2(\alpha) = 1 - \left(\frac{4}{5}\right)^2 = 1 - \frac{16}{25} = \frac{9}{25} \implies \sin(\alpha) = \frac{3}{5}$. Then $\tan(\alpha) = \frac{\sin(\alpha)}{\cos(\alpha)} = \frac{3/5}{4/5} = \frac{3}{4} = 0.75$.

Question 14Lower-secondary number, algebra, geometry and data

A student obtained the following grades on four test papers with coefficients (weights): Grade 8 (coeff 2), Grade 10 (coeff 3), Grade 12 (coeff 4), and Grade 16 (coeff 1). What is the weighted mean average (moyenne pondérée)?

  1. $11.50 / 20$
  2. $10.50 / 20$
  3. $11.00 / 20$ Correct answer.
  4. $12.00 / 20$

Explanation

The weighted sum of scores is: $(8 \times 2) + (10 \times 3) + (12 \times 4) + (16 \times 1) = 16 + 30 + 48 + 16 = 110$. The total sum of coefficients is $2 + 3 + 4 + 1 = 10$. The weighted mean is $\bar{x} = \frac{110}{10} = 11.00$.

Question 15Lower-secondary number, algebra, geometry and data

Consider the ordered statistical dataset of 8 scores: $5, 8, 9, 12, 14, 17, 19, 21$. What are the median (médiane) and the range (étendue) of this dataset?

  1. Median = 12 and Range = 16
  2. Median = 13.5 and Range = 21
  3. Median = 14 and Range = 15
  4. Median = 13 and Range = 16 Correct answer.

Explanation

With $N = 8$ (even), the median is the arithmetic mean of the 4th and 5th values: $\text{Median} = \frac{12 + 14}{2} = 13$. The range is the difference between the maximum and minimum values: $\text{Range} = 21 - 5 = 16$.

Question 16Lower-secondary number, algebra, geometry and data

In an orthonormal coordinate system $(O, \vec{i}, \vec{j})$, let points be $A(2, -1)$ and $B(-3, 4)$. What are the coordinates of vector $\vec{AB}$ and its exact Euclidean norm $\|\vec{AB}\|$?

  1. $\vec{AB}(-5, 5)$ and $\|\vec{AB}\| = 5\sqrt{2}$ Correct answer.
  2. $\vec{AB}(5, -5)$ and $\|\vec{AB}\| = 5\sqrt{2}$
  3. $\vec{AB}(-1, 3)$ and $\|\vec{AB}\| = \sqrt{10}$
  4. $\vec{AB}(-5, 5)$ and $\|\vec{AB}\| = 50$

Explanation

Vector coordinates: $\vec{AB} = (x_B - x_A, y_B - y_A) = (-3 - 2, 4 - (-1)) = (-5, 5)$. The norm is $\|\vec{AB}\| = \sqrt{(-5)^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$.

Question 17Lower-secondary number, algebra, geometry and data

In the Cartesian plane, find the coordinates of midpoint $I$ of line segment $[AB]$ where $A(6, -4)$ and $B(-2, 8)$.

  1. $I(4, 4)$
  2. $I(2, 2)$ Correct answer.
  3. $I(8, -12)$
  4. $I(2, 6)$

Explanation

The midpoint formula is $I\left(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2}\right) = I\left(\frac{6 + (-2)}{2}, \frac{-4 + 8}{2}\right) = I\left(\frac{4}{2}, \frac{4}{2}\right) = I(2, 2)$.

Question 18Lower-secondary number, algebra, geometry and data

Determine the reduced equation (équation réduite) of the straight line $(D)$ passing through points $A(1, 3)$ and $B(4, 9)$.

  1. $y = 2x + 3$
  2. $y = 3x$
  3. $y = 2x + 1$ Correct answer.
  4. $y = \frac{1}{2}x + \frac{5}{2}$

Explanation

Slope $m = \frac{y_B - y_A}{x_B - x_A} = \frac{9 - 3}{4 - 1} = \frac{6}{3} = 2$. The line has equation $y = 2x + p$. Substituting $A(1, 3)$: $3 = 2(1) + p \implies p = 3 - 2 = 1$. Thus $y = 2x + 1$. Checking $B(4, 9)$: $2(4) + 1 = 9$ (verified).

Question 19Lower-secondary number, algebra, geometry and data

In the plane, line $(D_1)$ has equation $y = -\frac{2}{3}x + 4$. What is the slope (coefficient directeur) of any line $(D_2)$ perpendicular to $(D_1)$?

  1. $-\frac{3}{2}$
  2. $-\frac{2}{3}$
  3. $\frac{2}{3}$
  4. $\frac{3}{2}$ Correct answer.

Explanation

Two non-vertical lines are perpendicular if and only if the product of their slopes equals $-1$: $m_1 \times m_2 = -1$. Here, $-\frac{2}{3} \times m_2 = -1 \implies m_2 = \frac{-1}{-2/3} = \frac{3}{2}$.

Question 20Lower-secondary number, algebra, geometry and data

A regular pyramid has a square base with side length $a = 6\text{ cm}$ and a height $h = 10\text{ cm}$. What is its volume $V$?

  1. $120\text{ cm}^3$ Correct answer.
  2. $360\text{ cm}^3$
  3. $60\text{ cm}^3$
  4. $180\text{ cm}^3$

Explanation

The area of the square base is $\text{Base} = a^2 = 6^2 = 36\text{ cm}^2$. The volume of a pyramid is $V = \frac{1}{3} \times \text{Base} \times h = \frac{1}{3} \times 36 \times 10 = 12 \times 10 = 120\text{ cm}^3$.

Question 21Lower-secondary number, algebra, geometry and data

A cone of revolution has a base radius $R = 6\text{ cm}$ and a height $H = 12\text{ cm}$. It is cut by a plane parallel to the base at a scale reduction factor $k = \frac{1}{2}$. What is the exact volume $V'$ of the small reduced cone?

  1. $72\pi\text{ cm}^3$
  2. $18\pi\text{ cm}^3$ Correct answer.
  3. $36\pi\text{ cm}^3$
  4. $144\pi\text{ cm}^3$

Explanation

The total volume of the initial cone is $V = \frac{1}{3}\pi R^2 H = \frac{1}{3}\pi (6^2)(12) = \frac{1}{3}\pi (36)(12) = 144\pi\text{ cm}^3$. Under a linear reduction factor $k = 1/2$, volumes are scaled by $k^3 = (1/2)^3 = 1/8$. Thus $V' = k^3 V = \frac{1}{8} \times 144\pi = 18\pi\text{ cm}^3$.

Question 22Lower-secondary number, algebra, geometry and data

Calculate the exact volume $V$ of a solid sphere of radius $r = 3\text{ cm}$.

  1. $12\pi\text{ cm}^3$
  2. $108\pi\text{ cm}^3$
  3. $36\pi\text{ cm}^3$ Correct answer.
  4. $27\pi\text{ cm}^3$

Explanation

The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$. Substituting $r = 3\text{ cm}$: $V = \frac{4}{3}\pi (3^3) = \frac{4}{3}\pi (27) = 4 \times 9\pi = 36\pi\text{ cm}^3$.

Question 23Lower-secondary number, algebra, geometry and data

A BEPC preparation manual initially priced at $25,000\text{ FCFA}$ receives a $20\%$ discount, after which a $5\%$ municipal tax is applied to the discounted price. What is the final price paid by the student?

  1. $21,250\text{ FCFA}$
  2. $20,000\text{ FCFA}$
  3. $22,500\text{ FCFA}$
  4. $21,000\text{ FCFA}$ Correct answer.

Explanation

Applying the $20\%$ discount: $\text{Discounted Price} = 25,000 \times (1 - 0.20) = 25,000 \times 0.80 = 20,000\text{ FCFA}$. Applying the $5\%$ tax to the discounted price: $\text{Final Price} = 20,000 \times (1 + 0.05) = 20,000 \times 1.05 = 21,000\text{ FCFA}$.

Question 24Lower-secondary number, algebra, geometry and data

A bag contains 4 red balls, 6 green balls, and 10 white balls, all identical to the touch. A ball is drawn at random. What is the probability of drawing a ball that is NOT white?

  1. $\frac{1}{2}$ (or $0.50$) Correct answer.
  2. $\frac{1}{4}$ (or $0.25$)
  3. $\frac{3}{10}$ (or $0.30$)
  4. $\frac{3}{5}$ (or $0.60$)

Explanation

Total number of balls $= 4 + 6 + 10 = 20$. The number of favorable outcomes (balls that are not white, i.e., red or green) is $4 + 6 = 10$. The probability is $P(\text{not white}) = \frac{10}{20} = \frac{1}{2} = 0.50$.

Question 25Lower-secondary number, algebra, geometry and data

Given the approximation $2.236 < \sqrt{5} < 2.237$, find the framing (encadrement) of the expression $A = 3\sqrt{5} - 4$.

  1. $6.708 < A < 6.711$
  2. $2.708 < A < 2.711$ Correct answer.
  3. $2.236 < A < 2.237$
  4. $0.708 < A < 0.711$

Explanation

Multiplying the inequality by $3 > 0$: $3 \times 2.236 < 3\sqrt{5} < 3 \times 2.237 \implies 6.708 < 3\sqrt{5} < 6.711$. Subtracting 4 from all parts: $6.708 - 4 < 3\sqrt{5} - 4 < 6.711 - 4 \implies 2.708 < A < 2.711$.

Question 26French reading, grammar and structured written expression

In French grammar, which mood and tense must be used in the subordinate clause of the sentence: 'Je doute fort qu'il [...] à l'heure à l'épreuve du BEPC'?

  1. Subjonctif présent: 'vienne' Correct answer.
  2. Indicatif futur simple: 'viendra'
  3. Indicatif présent: 'vient'
  4. Conditionnel présent: 'viendrait'

Explanation

Verbs expressing doubt, uncertainty, or denial such as 'douter que' require the subordinate clause verb to be in the subjunctive mood. For a present context, the subjonctif présent form of 'venir' is 'qu'il vienne'.

Question 27French reading, grammar and structured written expression

Which of the following sentences exhibits the correct grammatical agreement of the past participle (participe passé)?

  1. Les épreuves que le professeur a préparé étaient très instructives.
  2. Les épreuves que le professeur a préparées étaient très instructives. Correct answer.
  3. Les épreuves que le professeur a préparée étaient très instructives.
  4. Les épreuves que le professeur a préparés étaient très instructives.

Explanation

With the auxiliary verb 'avoir', the past participle agrees in gender and number with the direct object (COD) if the COD is placed before the verb. Here, the COD is the relative pronoun 'que' (representing the feminine plural noun 'les épreuves'), requiring the feminine plural ending '-ées' in 'préparées'.

Question 28French reading, grammar and structured written expression

In the famous line from Pierre Corneille's Le Cid, Chimène tells Rodrigue: 'Va, je ne te hais point.' Which figure of speech (figure de style) is employed to mean 'je t'aime'?

  1. Une hyperbole
  2. Un pléonasme
  3. Une litote Correct answer.
  4. Une antithèse

Explanation

A litote is a figure of speech in which an understatement or negative construction is used to suggest a much stronger positive meaning. Saying 'je ne te hais point' (I do not hate you at all) is a classic litote used to express profound love.

Question 29French reading, grammar and structured written expression

Transforming the direct speech sentence: Le proviseur a annoncé: 'Les candidats composeront demain' into indirect speech (discours indirect) yields:

  1. Le proviseur a annoncé que les candidats composeront demain.
  2. Le proviseur a annoncé que les candidats ont composé le lendemain.
  3. Le proviseur a annoncé que les candidats composent demain.
  4. Le proviseur a annoncé que les candidats composeraient le lendemain. Correct answer.

Explanation

When reporting speech introduced by a past tense verb ('a annoncé'), the future indicative ('composeront') shifts to the conditional present ('composeraient') according to the rules of concordance des temps, and time adverbs shift ('demain' becomes 'le lendemain').

Question 30French reading, grammar and structured written expression

What is the grammatical function and nature of the underlined clause in: 'Comme la pluie tombait abondamment, les élèves sont restés sous le préau'?

  1. Proposition subordonnée circonstancielle de cause Correct answer.
  2. Proposition subordonnée circonstancielle de conséquence
  3. Proposition subordonnée circonstancielle de concession
  4. Proposition subordonnée complétive conjonctive

Explanation

The subordinate clause 'Comme la pluie tombait abondamment' is introduced by the subordinating conjunction 'comme' placed at the beginning of the sentence to express the cause or reason for the main clause action.

Question 31French reading, grammar and structured written expression

A teacher says to a student who just spilled ink on the desk: 'C'est du propre ! Félicitations pour ce chef-d'œuvre !' What figure of speech is being used?

  1. Une métaphore filée
  2. Une antiphrase (ironie) Correct answer.
  3. Une personnification
  4. Un euphémisme

Explanation

An antiphrase is a figure of speech in which one says the exact opposite of what one actually means, typically with an ironic tone. Praising a mess as a 'chef-d'œuvre' is an explicit antiphrase.

Question 32French reading, grammar and structured written expression

What is the correct passive voice transformation of the active sentence: 'Le jury publiera la liste des admis au BEPC'?

  1. La liste des admis au BEPC est publiée par le jury.
  2. La liste des admis au BEPC a été publiée par le jury.
  3. La liste des admis au BEPC sera publiée par le jury. Correct answer.
  4. La liste des admis au BEPC serait publiée par le jury.

Explanation

In passive transformation, the direct object becomes the subject, the original subject becomes the agent complement with 'par', and the auxiliary 'être' is conjugated in the tense of the active verb (futur simple: 'sera') followed by the past participle ('publiée').

Question 33French reading, grammar and structured written expression

In the sentence: 'Pourriez-vous me prêter votre dictionnaire de français, s'il vous plaît ?', what is the semantic value of the conditionnel présent?

  1. L'expression d'un ordre impératif strict
  2. L'expression d'un fait certain dans le passé
  3. L'expression d'une action future certaine
  4. L'expression d'une demande polie (valeur d'atténuation / politesse) Correct answer.

Explanation

The conditional mood can be used as a 'conditionnel de politesse' to soften a request, inquiry, or command, making it polite and courteous rather than brusque.

Question 34French reading, grammar and structured written expression

What is the key structural difference between a 'comparaison' and a 'métaphore' in French stylistic analysis?

  1. A comparaison uses an explicit linking word (comme, pareil à, tel que), whereas a métaphore assimilates two elements without a comparison tool. Correct answer.
  2. A métaphore always compares a person to an animal, while a comparaison only compares inanimate objects.
  3. A comparaison always uses the subjunctive mood, while a métaphore requires the indicative mood.
  4. A métaphore must rhyme, whereas a comparaison is strictly reserved for prose.

Explanation

Both figures establish an analogy between a comparé and a comparant. A comparaison explicitly includes an outil de comparaison ('comme', 'semblable à', 'ainsi que'), whereas a métaphore merges the two concepts directly without any comparison tool.

Question 35French reading, grammar and structured written expression

Which of the following sentences correctly applies the orthographic rules for color adjectives?

  1. Elle portait des robes bleues marines et des chaussures marrons.
  2. Elle portait des robes bleu marine et des chaussures marron. Correct answer.
  3. Elle portait des robes bleues marine et des chaussures marrons.
  4. Elle portait des robes bleu marine et des chaussures marronnes.

Explanation

Compound color adjectives (such as 'bleu marine') are invariable in gender and number. In addition, color adjectives derived from nouns (such as 'marron', derived from the chestnut) are invariable, so both remain uninflected.

Question 36French reading, grammar and structured written expression

Which subordinating conjunction of concession requires the subjunctive mood in the subordinate clause?

  1. Même si
  2. Tandis que
  3. Bien que Correct answer.
  4. Pendant que

Explanation

'Bien que' (and 'quoique') is a concessive subordinating conjunction that systematically requires the subjunctive mood (e.g., 'Bien qu'il fasse chaud...'). In contrast, 'même si' takes the indicative.

Question 37French reading, grammar and structured written expression

In French morphology, which prefix indicates the opposite or negation of the base root in words like 'infaillible', 'illisible', and 'irresponsable'?

  1. The locative prefix trans-
  2. The temporal prefix pré-
  3. The repetitive prefix re-
  4. The privative prefix in- (and its allomorphs il-, ir-, im-) Correct answer.

Explanation

The Latin negative/privative prefix 'in-' assimilates phonetically to 'il-' before 'l', 'ir-' before 'r', and 'im-' before 'm/b/p', meaning 'not' or 'lacking'.

Question 38French reading, grammar and structured written expression

In text analysis, what constitutes a 'champ lexical'?

  1. A set of words (nouns, verbs, adjectives) related to the same central theme or domain within a text Correct answer.
  2. A dictionary entry listing all historical etymologies of a single verb
  3. A single word having multiple distinct definitions depending on context
  4. A group of words that share the exact same grammatical suffix

Explanation

A 'champ lexical' (lexical field) consists of all words in a text-regardless of their grammatical category-that belong to the same topic or semantic field (e.g., doctor, scalpel, disease, healing belong to the lexical field of medicine).

Question 39French reading, grammar and structured written expression

Which of the following pairs distinguishes correctly between the verbal participle (participe présent) and the verbal adjective (adjectif verbal)?

  1. Participe présent: 'fatigant' (invariable verb) / Adjectif verbal: 'fatiguant' (agrees in gender/number)
  2. Participe présent: 'fatiguant' (invariable verb) / Adjectif verbal: 'fatigant' (agrees in gender/number) Correct answer.
  3. Participe présent: 'provoquant' / Adjectif verbal: 'provoquant' (both invariable)
  4. Participe présent: 'adhérant' / Adjectif verbal: 'adhérant' (both variable)

Explanation

Certain verbs change spelling between the invariable participe présent (which retains the verbal stem with 'u', e.g., 'fatiguant', 'naviguant') and the adjectif verbal (which drops the 'u', e.g., 'fatigant', 'navigant' and agrees in gender and number).

Question 40French reading, grammar and structured written expression

In a narrative text in the past (récit au passé), what is the typical functional distinction between the 'passé simple' and the 'imparfait'?

  1. Passé simple is only used for future events, while imparfait is used for past events.
  2. Passé simple expresses indefinite duration, while imparfait expresses instantaneous sudden events.
  3. Passé simple expresses foregrounded, punctual, or sequential completed actions, while imparfait expresses background descriptions, ongoing actions, or habitual repetition. Correct answer.
  4. Passé simple is restricted to dialogue, while imparfait is restricted to stage directions.

Explanation

In French literary narratives, the passé simple advances the plot by presenting discrete, completed, foreground actions in chronological succession. The imparfait provides the scenic backdrop, expressing continuous duration, descriptions, or recurring habitual actions.

Question 41French reading, grammar and structured written expression

In the sentence: 'J'entends les oiseaux chanter dès l'aube', what is the nature of the subordinate clause 'les oiseaux chanter'?

  1. Une proposition subordonnée relative
  2. Une proposition subordonnée complétive conjonctive
  3. Une proposition subordonnée interrogative indirecte
  4. Une proposition subordonnée infinitive Correct answer.

Explanation

A proposition subordonnée infinitive occurs after perception verbs (entendre, voir, sentir, écouter) where the infinitive verb ('chanter') has its own distinct semantic subject ('les oiseaux') which is not the subject of the main verb.

Question 42French reading, grammar and structured written expression

In the sentence: 'Toute la ville de Yaoundé a célébré la victoire des Lions Indomptables', what figure of speech substitutes 'la ville' for 'les habitants de la ville'?

  1. Une métonymie (le contenant pour le contenu) Correct answer.
  2. Un oxymore
  3. Une allitération
  4. Une anaphore

Explanation

A métonymie designates an entity by naming another entity closely linked to it by a logical relationship, such as substituting the container/place ('la ville') for the contents/inhabitants ('les habitants').

Question 43French reading, grammar and structured written expression

A literary text that aims to provoke deep sadness, compassion, and pity in the reader for the suffering of innocent characters belongs to which 'registre' (tonalité)?

  1. Le registre satirique
  2. Le registre pathétique Correct answer.
  3. Le registre épique
  4. Le registre comique

Explanation

The 'registre pathétique' (from Greek pathos, suffering/feeling) uses emotional vocabulary, exclamations, and vivid depictions of distress to evoke empathy, pity, and sorrow in the reader.

Question 44French reading, grammar and structured written expression

Which of the following sentences expresses an intention or purpose (but) rather than a realized result (conséquence)?

  1. Il s'est exprimé si clairement que chacun a compris la leçon.
  2. Il s'exprime tellement vite que personne ne le comprend.
  3. Il s'exprime clairement afin que chacun puisse comprendre la leçon. Correct answer.
  4. Il s'est exprimé de telle manière que tout le monde est parti.

Explanation

'Afin que' followed by the subjunctive ('puisse') introduces a goal, purpose, or aim (circonstancielle de but). The other options express an accomplished result or effect (circonstancielle de conséquence) using 'si... que' or 'de telle manière que' with the indicative.

Question 45French reading, grammar and structured written expression

Which of the following sentences demonstrates the correct agreement of the pronominal verb's past participle?

  1. Elles se sont lavées les mains avant d'entrer dans la salle d'examen.
  2. Elles se sont lavée les mains avant d'entrer dans la salle d'examen.
  3. Elles se sont lavés les mains avant d'entrer dans la salle d'examen.
  4. Elles se sont lavé les mains avant d'entrer dans la salle d'examen. Correct answer.

Explanation

For pronominal verbs where 'se' is an indirect object (COI), the past participle agrees only with a preceding direct object (COD). In 'Elles se sont lavé les mains', the COD is 'les mains' which is placed AFTER the verb; hence 'lavé' remains invariable.

Question 46French reading, grammar and structured written expression

Which stylistic device unites two contradictory terms in a single grammatical unit, as seen in the phrase 'un silence assourdissant'?

  1. Un oxymore Correct answer.
  2. Un pléonasme
  3. Une gradation
  4. Une hyperbole

Explanation

An oxymore (oxymoron) brings together two contradictory or mutually exclusive terms within the same syntactical phrase to create a striking semantic tension (e.g., 'silence assourdissant', 'obscure clarté').

Question 47French reading, grammar and structured written expression

In the sentence: 'Ces candidates étaient [...] émues par la proclamation des résultats', what is the correct spelling and rule for the adverb 'tout'?

  1. 'toutes' (mandatory agreement before any plural adjective)
  2. 'tout' (invariable adverb before a feminine adjective beginning with a vowel sound) Correct answer.
  3. 'toute' (feminine singular agreement)
  4. 'touts' (plural adverbial form)

Explanation

When 'tout' is used as an adverb meaning 'entirely/wholly', it remains invariable before a feminine adjective beginning with a vowel sound (e.g., 'tout émues', 'tout étonnées'). It only inflects before a feminine adjective beginning with a consonant or aspirated 'h' (e.g., 'toutes contentes', 'toutes honteuses').

Question 48French reading, grammar and structured written expression

Which characteristic specifically identifies 'le discours indirect libre' in narrative literature?

  1. The speech is enclosed in quotation marks with explicit introductory tags such as 'dit-il'.
  2. The speech is always introduced by 'que' and placed strictly in the present tense.
  3. The characters' thoughts and words are reported without subordinating conjunctions or introductory reporting verbs, while adopting past tenses and third-person pronouns. Correct answer.
  4. The speech is written as a theatrical script with characters' names preceding dialogue.

Explanation

Free indirect discourse (discours indirect libre) integrates a character's direct voice and emotional cadence into the narrator's flow without quotation marks, dashes, or subordinating verbs, maintaining third-person pronouns and narrative past tenses (imparfait/conditionnel).

Question 49French reading, grammar and structured written expression

Choose the correctly spelled sentence distinguishing the homophones 'leur' and 'leurs':

  1. Les professeurs leurs ont remis leur convocations pour l'examen.
  2. Les professeurs leurs ont remis leurs convocations pour l'examen.
  3. Les professeurs leur ont remis leur convocations pour l'examen.
  4. Les professeurs leur ont remis leurs convocations pour l'examen. Correct answer.

Explanation

When 'leur' is a personal pronoun placed before a verb ('leur ont remis'), it is always invariable (no 's'). When 'leur/leurs' is a possessive determiner modifying a plural noun ('convocations'), it takes an 's' ('leurs convocations').

Question 50Mechanics, fields, thermal behavior, waves and modern models

An electrical resistor has a resistance $R = 40\ \Omega$ and carries a direct current $I = 0.25\text{ A}$. According to Ohm's law, what is the voltage $U$ across its terminals?

  1. $160\text{ V}$
  2. $2.5\text{ V}$
  3. $10\text{ V}$ Correct answer.
  4. $100\text{ V}$

Explanation

According to Ohm's law, $U = R \times I$. Substituting the given values: $U = 40\ \Omega \times 0.25\text{ A} = 10\text{ V}$.