Bac Mathématiques Algeria common mistakes
Bac Mathématiques Algeria · Understand the traps and how to avoid them.
When computing a limit with an indeterminate form, the candidate substitutes the value, writes "= 0/0", then stops or declares the limit does not exist, instead of factoring, using the conjugate quantity, or comparing growth rates.
The candidate memorised the list of indeterminate forms but never built the reflex that an indeterminate form is a signal to transform the expression, not a result. Classroom drills often give the factorisation away, so the candidate never practises choosing the transformation under exam pressure.
What to do instead
Adopt a fixed decision order printed at the top of the rough sheet: (1) direct substitution; (2) if 0/0, factor by the root or multiply by the conjugate; (3) if ∞/∞, factor out the dominant power; (4) if the expression mixes ln, exp and powers, factor out the fastest-growing term and use the comparison theorems. Train on five limits per session where the transformation is not obvious, and always write the intermediate factored expression before concluding.
The candidate applies the intermediate value theorem or the derivative sign to a function without first checking and stating the required hypotheses (continuity on a closed interval, derivability on an open interval), and concludes existence of a solution or the direction of variation from an incomplete argument.
The theorem statements are learned as formulas to plug numbers into, and the hypothesis line is treated as decoration. Graders in this exam award marks for the hypothesis verification, so the habit is never corrected by feedback on the final answer alone.
What to do instead
Write theorem applications in a rigid three-line template: hypotheses, then theorem, then conclusion, with the interval named explicitly. For variation tables, always start by stating the domain of definition and where the function is derivable. Practise by grading two model solutions, one complete and one missing the hypothesis, and listing the marks lost.
In exercises on the exponential and logarithm functions, the candidate solves an equation or inequality involving ln or exp without restricting to the domain of definition, producing solutions such as ln(x) = a answered by x = e^a even when the original equation also contains ln(x-3), and forgetting to intersect the conditions.
The candidate treats ln and exp as ordinary algebraic operations and focuses on the mechanics of the equation. The domain condition feels like an extra step with no visible payoff, so it is dropped under time pressure.
What to do instead
Before solving any equation with logarithms, write the system of conditions on a separate line and box it, then solve, then intersect the solution set with the box. For inequalities, build the sign table on the restricted domain only. Do ten mixed exercises where at least three have empty solution sets because of the domain, so the check becomes automatic.
The candidate proves a recurrence-defined sequence is convergent by simply computing the first few terms, observing they approach a value, and writing that the limit is that value, without proving monotonicity and boundedness or using an auxiliary geometric sequence.
Numerical exploration is the first tool taught and gives a convincing-looking answer quickly. The candidate confuses the conjecture produced by the calculator with the proof, and the exam's wording rewards the proof, not the conjecture.
What to do instead
Separate the work into two clearly labelled parts: conjecture (compute u1 to u5, state the suspected bound and limit) and proof (show by recurrence that the sequence is increasing and bounded above, or exhibit v_n = u_n - L as geometric). Always end by solving L = f(L) only after convergence is established. Keep a checklist of the three standard proof routes and name the one used.
When computing a definite integral, the candidate integrates a product directly term by term, for example writing the integral of x·e^x as (x^2/2)·e^x, or forgets to change the bounds after a substitution and evaluates the primitive in the new variable between the old bounds.
The linearity of the integral is over-generalised to products, and integration by parts is memorised as a formula without the habit of tracking the variable change through the bounds. Substitution is often practised only with indefinite integrals, where the bounds problem never appears.
What to do instead
For every substitution, write the full chain: u = g(x), du = g'(x)dx, new bounds g(a) and g(b), then evaluate entirely in u. For products, decide explicitly between integration by parts (state u and dv, with u chosen so its derivative simplifies) and expansion. Verify each result by differentiating the primitive, and do this verification in writing at least once per exercise.
In complex-number geometry, the candidate translates a condition such as |z - a| = |z - b| or arg((z - c)/(z - d)) = π/2 into a locus by guessing the figure, or computes a modulus and argument but never connects them to distances and angles, so the geometric interpretation question is answered with an algebraic expression only.
Modulus and argument are practised as computational skills, and the geometric dictionary (modulus = distance, argument = oriented angle) is learned separately and never fused with the algebra. The candidate also confuses the argument of a quotient with the difference of arguments in the wrong order.
What to do instead
Build a one-page translation table and drill it: |z - a| is the distance from M to A, |z - a| = |z - b| is the perpendicular bisector, arg((z - b)/(z - a)) is the oriented angle from vector AM to BM. For each geometry question, first name the points, then write the condition in terms of distances and angles, then identify the locus, then justify with the theorem. Check the order of the quotient by testing one concrete numerical example.
In arithmetic, the candidate uses Bézout or Gauss after verifying only one hypothesis: for instance, concludes that a divides c from a | bc and a | b, or finds a particular solution of au + bv = 1 without first checking gcd(a, b) = 1, and then divides by a in a congruence without justification.
The theorems are recalled by their conclusion rather than by their exact hypotheses, and the gcd computation is seen as a preliminary formality. Simplification by division is imported from ordinary equation solving, where no coprimality condition exists.
What to do instead
Write each theorem as a conditional sentence with its hypotheses in the same line as its use, and compute gcd explicitly with the Euclidean algorithm before invoking Bézout. For congruences, never divide by a coefficient without writing "since gcd(a, n) = 1, we may divide" or handling the multiple solutions when the gcd exceeds 1. Solve three congruence systems per session with an explicit gcd line each time.
In solid geometry, the candidate computes a scalar or cross product and then misreads what it gives: it uses a zero dot product to claim two lines are parallel, or takes the cross product of two direction vectors and calls it the normal to the plane containing them, or forgets that the cross product in space requires an orientation and gives a vector, not a number.
The two products are memorised as procedures with similar-looking notation, and the distinction between a scalar and a vector result is not tied to its geometric meaning. The candidate also works in coordinates without drawing or naming the lines and planes involved.
What to do instead
Anchor each product to one geometric sentence: u·v = 0 means perpendicular, u and v collinear means the cross product is zero, and u × v is normal to both. Before computing, write what object is sought (a normal vector, a distance, an angle) and therefore which product is needed. Finish every problem by checking the result against a rough sketch of the configuration.
In probability, the candidate computes P(A∪B) as P(A) + P(B) for non-disjoint events, confuses P(A|B) with P(B|A) in tree diagrams, or treats sampling without replacement as independent and multiplies probabilities that should be conditioned.
The addition rule for mutually exclusive events is learned first and never updated with the inclusion-exclusion correction. Conditional probability is taught through formulas rather than through the tree, so the direction of conditioning is decided by the order of words in the question rather than by the structure of the experiment.
What to do instead
Draw the tree before any calculation, label each branch with a conditional probability, and multiply along branches and add across them. State explicitly whether the experiment is with or without replacement and whether events are independent, and write the inclusion-exclusion formula whenever the events can overlap. Verify total probability sums to 1 as a systematic check.
When asked to prove a statement, the candidate begins from the desired conclusion and manipulates both sides until something true appears, or verifies the claim on two or three numerical examples and declares it proved, without identifying the hypothesis, the conclusion, and a valid chain of implications.
Algebra practice rewards transforming expressions until they simplify, and that habit is carried into proof, where working backwards from the conclusion is only valid with equivalences and reversibility. Numerical testing is the fastest way to feel confident and is rarely penalised in classwork.
What to do instead
Before writing, separate the page into hypothesis, goal, and available theorems. Use reasoning by contradiction or by contrapositive when direct proof stalls, and write each step as an implication with its justification. Reserve numerical testing strictly for the conjecture phase, labelled as such. Practise on short statements where the correct method is not signalled by the exercise, and have the proof checked line by line for reversibility.