Slovakia Maturita Math common mistakes
Slovakia Maturita Math · Understand the traps and how to avoid them.
When simplifying an expression like (x²−9)/(x−3), the candidate cancels only the x² against x and writes x−9 or x−3 instead of factoring the numerator as (x−3)(x+3) and cancelling the whole binomial.
The candidate treats terms as if they were factors and applies 'cancel the common letter' rules learned on monomials, so they never check whether the numerator is a difference of squares or has a common factor.
What to do instead
Before cancelling anything, force a factorisation step: write numerator and denominator fully factored, then cross out only whole factors. Drill the pattern a²−b²=(a−b)(a+b) and always state the condition x≠3.
The candidate solves an equation with a fraction such as 3/(x−2)=5 by multiplying only the left side by (x−2), or by cross-multiplying but forgetting to state and check the domain restriction x≠2.
Fractional equations are handled as if they were ordinary linear equations; the candidate does not internalise that multiplying by an expression containing the unknown can introduce or lose solutions.
What to do instead
Adopt a fixed routine: write the domain conditions first, multiply the entire equation by the common denominator, solve, then test each root against the conditions and reject any that make a denominator zero. Practise with equations that deliberately produce an extraneous root.
The candidate computes with powers and roots by distributing over sums, e.g. writing √(a+b)=√a+√b or (a+b)²=a²+b², and applies a^m·a^n=a^(m+n) to (a^m)^n incorrectly.
The visual similarity of the symbols invites pattern-matching from the distributive law of multiplication over addition; the candidate never verifies with a numerical substitution.
What to do instead
Make a habit of a quick numerical sanity check with simple numbers (e.g. a=9, b=16) whenever a formula is applied. Memorise the correct identities (a+b)²=a²+2ab+b² and (a^m)^n=a^(mn) and write them out before substituting.
The candidate reads a function's domain from the graph or formula by looking only at where the curve is drawn, missing that a denominator cannot be zero or that an even root needs a non-negative argument, and gives the range instead of the domain.
Domain and range are confused as vocabulary, and the candidate relies on the sketch rather than on the algebraic conditions that define the domain.
What to do instead
For every function, list the algebraic restrictions explicitly (denominator ≠ 0, radicand ≥ 0, logarithm argument > 0) before sketching, then read the range separately off the graph. Practise paired questions that ask for both and label each answer.
When solving an inequality such as −2x+5>1, the candidate divides by −2 and keeps the inequality sign, or solves the related equation and reports a single value instead of an interval.
The rule that multiplying or dividing by a negative number reverses the inequality is easily forgotten because most practice is with equations, where the operation is harmless.
What to do instead
Always isolate the variable with a positive coefficient where possible, or explicitly write 'divide by −2, flip the sign' as a step. Finish by testing one number from the proposed interval in the original inequality.
The candidate sketches or interprets a graph without accounting for transformations, e.g. plotting y=(x−2)²+3 with the vertex at (2, −3) or shifting the parabola the wrong way, and misreads the effect of a negative leading coefficient on the direction of opening.
The candidate memorises 'minus means left' loosely and does not connect the sign inside the bracket to the horizontal shift, nor the sign of a to the reflection.
What to do instead
Anchor each family in its parent graph and apply transformations in a fixed order (horizontal shift, stretch, vertical shift), checking the vertex or key point numerically. Verify by substituting the vertex coordinates into the equation.
The candidate uses the wrong trigonometric ratio or the wrong side in a right triangle, for example using sine when the two given sides are the legs, or computing an angle with the tangent ratio but entering the sides inverted.
SOHCAHTOA is recalled as a string without being linked to which sides are opposite, adjacent and hypotenuse relative to the marked angle.
What to do instead
Before choosing a ratio, label the three sides relative to the angle in question on the diagram, then select the ratio that contains exactly the two known or wanted quantities. Solve for the unknown symbolically first, substitute numbers last.
The candidate mixes units or uses the wrong area/perimeter formula for composite figures, e.g. adding a triangle's area using base × height without halving, or combining lengths in centimetres with areas in metres squared without converting.
Formulas are recalled as a jumble and unit conversion is treated as an afterthought, so the candidate works in whatever units the problem states and reports them unchanged.
What to do instead
Write the formula with its meaning (area of triangle = ½·base·height), convert all lengths to one unit before computing, and carry units through the calculation so the final answer's unit is forced to be correct. Split composite figures into named simple parts and sum them explicitly.
The candidate computes permutations when the selection order does not matter, or combinations when it does, e.g. counting the number of ways to choose 3 students from 30 as 30·29·28 instead of C(30,3).
The candidate focuses on the numbers in the problem and not on whether rearranging the chosen items produces a different outcome, so the combinatorial structure is never identified.
What to do instead
Ask one diagnostic question first: 'If I swap two chosen items, is it a different result?' Yes means ordered (permutation/variation), no means unordered (combination). Write the answer as a formula with symbols before evaluating.
The candidate adds probabilities of non-mutually-exclusive events without subtracting the overlap, or multiplies probabilities of dependent events as if they were independent, and reports a probability greater than 1 without noticing.
The addition and multiplication rules are memorised in their simplest form and the conditions (mutually exclusive, independent) are not checked against the problem wording.
What to do instead
Before computing, classify the events: write P(A∪B)=P(A)+P(B)−P(A∩B) and use the conditional form P(A∩B)=P(A)·P(B|A) unless independence is stated. Always check that the final probability lies between 0 and 1.