Bac E Bénin common mistakes
Bac E Bénin · Understand the traps and how to avoid them.
When computing a limit of a rational or quotient function at a point or at infinity, the candidate substitutes the value directly, obtains an indeterminate form such as 0/0 or ∞/∞, and then writes that the limit 'does not exist' or equals that indeterminate symbol, instead of factoring or dividing by the dominant term.
In class, limits are often met as 'replace x by a and read the result'. The candidate has memorised the substitution reflex but not the decision tree for indeterminate forms, and under exam pressure the first numeric result is treated as the answer.
What to do instead
Before any substitution, list the forbidden values and check whether the numerator and denominator both vanish or both diverge. If they do, factor the numerator and denominator (or multiply by the conjugate for radicals, or divide by the highest power for infinity), simplify, and only then substitute. Train on a fixed set of five forms until the check is automatic.
For a piecewise-defined function, the candidate checks continuity or differentiability only by evaluating the formula at the joining point, or checks only one side, and concludes the function is continuous (or differentiable) there without comparing the two one-sided limits.
The candidate treats 'the function has a value at a' as equivalent to 'the function is continuous at a', a confusion reinforced by most exercises where the given formula happens to be continuous. The asymmetry of one-sided limits is rarely practised.
What to do instead
Adopt a written three-step protocol for every junction point a: compute the left limit, compute the right limit, compare both with f(a). For differentiability, add the two one-sided difference quotients and compare them. Always write the three lines explicitly, even when the answer seems obvious.
When computing a definite integral, the candidate applies the integration-by-parts formula or a substitution without changing the bounds, or omits the constant of integration in an indefinite integral and then uses it as if it were a definite value.
The mechanics of the formula are learned as a symbolic manipulation, and the bounds are perceived as decoration rather than as part of the variable change. Time pressure encourages skipping the bookkeeping line.
What to do instead
For every substitution, write the new bounds explicitly on the integral sign before integrating, and add a final check that the numerical result is plausible (sign, order of magnitude). For indefinite integrals, write '+ C' as a required final token and lose no marks by habit.
Faced with a first-order differential equation, the candidate separates variables or identifies the solution form without first putting the equation in the standard form y' + a(x)y = b(x), and consequently misreads the coefficient or the second member, or forgets to use the initial condition to determine the constant.
Exercises are often presented already in a convenient form, so the normalisation step is never internalised. The initial condition is treated as optional information rather than as the step that selects one solution among a family.
What to do instead
Always rewrite the equation in standard form first, name a(x) and b(x) explicitly, then solve. End every solution by substituting the initial condition and stating the particular solution; verify by differentiating the proposed solution and substituting back into the original equation.
For a recurrence relation, the candidate verifies the property for the first two or three values of n and then declares the general property proved, or writes the induction hypothesis and never uses it in the hereditary step.
The candidate confuses numerical evidence with proof, a confusion common at this level, and the hereditary step is the most abstract part of the argument, so it is either skipped or reduced to a restatement of what must be shown.
What to do instead
Impose a rigid three-line template: (1) initialisation, stating the exact value checked; (2) hypothesis, 'suppose the property holds for some n ≥ n0'; (3) heredity, beginning with 'we must show...' and explicitly citing the hypothesis at the point where it is used. If the hypothesis is never cited, the proof is incomplete.
When solving a linear system or a matrix problem, the candidate performs row operations on the augmented matrix but forgets that the same operation must be reflected in the right-hand column, or multiplies matrices in the wrong order when the problem involves a product of matrices.
Row reduction is practised mechanically on coefficient matrices, so the augmented column is treated as a separate annotation. Matrix multiplication is non-commutative but is often met first in contexts where the order happens not to matter.
What to do instead
Always write the augmented matrix with a vertical bar and carry the bar through every operation. For products, write the dimensions of each factor above it before multiplying and check that the inner dimensions match; verify order by testing with a simple numerical example.
In probability problems, the candidate computes P(A ∩ B) as P(A) × P(B) without checking independence, or confuses P(A | B) with P(B | A) when reading a conditional-probability question.
The multiplication rule for independent events is the first formula learned and becomes the default, while conditional probability is encountered later and its direction is easy to lose in a word problem.
What to do instead
Before multiplying, write explicitly whether the events are stated or provably independent; if not, use the general rule P(A ∩ B) = P(A) × P(A | B). For conditional questions, rewrite the sentence in the form 'given that ..., what is the probability that ...' and match the given event to the denominator before computing.
In financial mathematics, the candidate applies an annuity formula with the wrong number of periods or the wrong rate per period, for example using an annual rate with a number of months, or counting n payments where the first is made immediately rather than at the end of the first period.
The formulas for present and future values of annuities look alike, and the distinction between payments at the beginning and at the end of the period is a modelling decision that is rarely made explicit in the statement.
What to do instead
Before computing, draw a time line, mark each payment date, and state in writing: the rate per period, the number of periods, and whether payments are at the beginning or the end. Convert the rate to the period of the payments explicitly. Then choose the formula whose description matches the time line.
In accounting and economics questions, the candidate confuses the accounting result with the cash position, or records a transaction without respecting the double-entry balance, for example debiting an expense and also debiting the bank account.
Everyday language treats 'profit' and 'cash' as synonyms, and the debit/credit convention is new vocabulary that is memorised as a label rather than as a system of reciprocal entries.
What to do instead
For every transaction, write the two entries side by side and check that total debits equal total credits before moving on. When a question asks about profit versus cash, restate the distinction in one sentence (revenue recognised versus money received) and answer the question actually asked.
In geometry and coordinate problems, the candidate computes a distance, a midpoint, or a vector norm using the coordinates of a single point, or drops the square root in the distance formula, and does not check the result against the figure described in the text.
The formulas are recalled as patterns of symbols rather than as statements about two distinct points, and the final plausibility check is skipped because the computation already feels finished.
What to do instead
Label the points A(x_A, y_A) and B(x_B, y_B) explicitly, write the difference coordinates before squaring, and keep the square root until the final line. Finish every geometry problem with a one-line sanity check: sign of the vector, order of magnitude of the distance, and consistency with the described configuration.