Armenia Mathematics Unified Exam common mistakes
Armenia Mathematics Unified Exam · Understand the traps and how to avoid them.
When solving an equation with a parameter, the student divides both sides by the parameter without considering the case where the parameter equals zero, thereby losing the solution for that value.
The student treats the parameter as a fixed nonzero number and forgets that division by zero is undefined; this often stems from overgeneralizing procedures for linear equations.
What to do instead
Before dividing by any expression containing a parameter, explicitly state the condition that the expression is nonzero, then analyze the zero case separately and include it in the final answer.
In inequalities, the student multiplies or divides by a negative number but fails to reverse the inequality sign.
The student focuses on the arithmetic and forgets the order property of inequalities; this is especially common when the negative factor is hidden in an expression like (1 - x).
What to do instead
Always rewrite the inequality so that the coefficient of the variable is positive before solving, or circle the inequality sign and write 'flip?' above it whenever multiplying or dividing by a negative quantity.
When finding the domain of a function, the student omits restrictions such as denominator not zero, radicand nonnegative, and logarithm argument positive, and gives an answer that includes forbidden x-values.
The student equates 'domain' with 'all real numbers' unless a square root is visible, and does not systematically list all operations that impose restrictions.
What to do instead
For every function, list each operation in order (division, even root, logarithm, tangent) and write the corresponding condition; then intersect all conditions before stating the domain.
In trigonometry, the student gives only the principal solution of an equation like sin x = a and omits the second family of solutions (e.g., π - x) or forgets the period.
The student relies on the inverse sine value alone and does not visualize the unit circle or the symmetry of the sine function.
What to do instead
For each inverse-trig equation, sketch the unit circle, mark both intersection points with the horizontal line y = a, and write both solution families with the period 2πk (or πk for tangent).
In probability, the student adds probabilities of events that can occur together (e.g., P(A∪B) = P(A)+P(B)) without subtracting the intersection.
The student confuses mutually exclusive events with arbitrary events and applies the addition rule outside its conditions.
What to do instead
Before adding, check whether the events can happen simultaneously; if yes, use P(A∪B) = P(A)+P(B)-P(A∩B), or draw a Venn diagram to visualize the overlap.
In calculus, when finding the derivative of a composite function, the student differentiates the outer function but forgets to multiply by the derivative of the inner function.
The student focuses on the outer operation and does not treat the inner expression as a variable requiring its own derivative.
What to do instead
Always write the chain rule explicitly: (f(g(x)))' = f'(g(x))·g'(x). After computing, check by identifying the inner function and verifying its derivative appears as a factor.
In sequences, the student uses the formula for the sum of the first n terms of an arithmetic progression but substitutes n instead of (n-1) in the nth term formula, or confuses a_n with S_n.
The student memorizes formulas without understanding the indexing; the notation a_n and S_n look similar and are used interchangeably under time pressure.
What to do instead
Write the definitions side by side: a_n = a_1 + (n-1)d and S_n = n(a_1+a_n)/2. For each problem, explicitly label what is given (a_1, d, n, a_n, S_n) before substituting.
In plane geometry, the student uses a theorem (e.g., the Pythagorean theorem or the inscribed angle theorem) without verifying that its hypotheses are satisfied, such as assuming a triangle is right-angled when it is not.
The student pattern-matches the diagram to a familiar theorem and skips checking the conditions, especially when the figure looks like a standard configuration.
What to do instead
Before applying any theorem, write down its conditions (e.g., 'right triangle', 'angle subtends diameter') and verify each from the given data; if a condition fails, choose a different theorem.
In solid geometry, the student computes the volume of a pyramid or cone using the full base area times height without the factor 1/3, or uses the slant height instead of the perpendicular height.
The student conflates the volume formulas for prisms/cylinders with those for pyramids/cones, and does not distinguish between slant height and altitude in 3D figures.
What to do instead
Memorize volume formulas with the 1/3 factor for pointed solids. In problems, explicitly identify the perpendicular height (not the slant height) and mark it on a diagram before substituting.
In combinatorics, the student uses permutations when the order of selection does not matter (or combinations when it does), leading to an answer that is off by a factorial factor.
The student does not clearly define whether the task involves arranging or merely choosing, and often defaults to the formula that was used most recently.
What to do instead
For each counting problem, ask: 'Does swapping two selected items produce a different outcome?' If yes, use permutations; if no, use combinations. Write this decision explicitly before computing.