UNSA ETF Math Entrance Exam common mistakes
UNSA ETF Math Entrance Exam · Understand the traps and how to avoid them.
When simplifying a fraction or radical, the candidate cancels a term across a sum, for example rewriting (x+6)/6 as x+1 or (a+b)/b as a/b+1.
Fraction rules are memorized as 'cancel the same thing on top and bottom', and the candidate treats the fraction bar as applying to each term separately rather than to the whole numerator. The habit forms because pure-product fractions like 6x/6 do simplify this way.
What to do instead
Before cancelling, factor the numerator and denominator completely and check that each is a single product. Test with numbers: set x=6 in (x+6)/6 to get 2, versus x+1=7, showing the rewrite fails. Practise rewriting sums as products first, then cancel only common factors.
The candidate solves an equation by dividing both sides by an expression containing the unknown, then reports only the remaining roots, silently dropping the solution where that expression equals zero.
Dividing feels like the cleanest way to simplify, and the candidate does not register that division by a variable quantity is only valid when that quantity is nonzero. Checking each case feels like extra work with no visible payoff.
What to do instead
Adopt a fixed routine: move everything to one side, factor, and set each factor to zero. Never divide by a variable expression; instead bring it out as a separate factor. As a check, substitute the discarded value back into the original equation to confirm it is a genuine solution.
The candidate applies a transformation to a graph in the wrong direction or order, for example shifting y=f(x) left when the formula says f(x-3), or applying a stretch before a shift when the order matters.
Horizontal changes act opposite to intuition because they modify the input before the function is evaluated, so a minus sign produces a rightward shift. When several transformations combine, the candidate applies them in reading order rather than in the order that preserves the input structure.
What to do instead
Track a single test point through each transformation and verify it against the formula. For combined transformations, rewrite the expression in the form a*f(b(x-h))+k and read the parameters from that form, then confirm with two or three sample points.
The candidate uses the sine rule or cosine rule without checking which triangle configuration the given data produce, and reports the acute angle when the obtuse one is also consistent (the ambiguous case).
Textbook problems often supply data with a unique solution, so the candidate never develops the habit of testing whether two triangles fit. The inverse sine function returns only the principal value, hiding the supplementary angle.
What to do instead
Whenever two sides and a non-included angle are given, explicitly compute both candidate angles (theta and 180-theta) and check whether each leaves a valid third angle summing with the given one to 180. Confirm the side-angle correspondence before substituting into any rule.
The candidate computes a limit by substituting the value directly, obtains an indeterminate form such as 0/0, and then treats that result as the answer or gives up rather than resolving it.
Direct substitution works for most continuous functions, so the candidate generalizes it to every case. The indeterminate form looks like a number rather than a signal that algebraic work is required.
What to do instead
Treat 0/0 or infinity/infinity as a prompt, not a result. Systematically try factoring and cancelling, rationalizing, or dividing by the highest power, and only then substitute. State the form explicitly in working so the required next step is obvious.
The candidate adds probabilities of overlapping events, or multiplies probabilities of events that are not independent, without checking the relationship between the events.
The addition and multiplication rules are learned as formulas to apply on sight, and the conditions attached to each (mutually exclusive versus independent) are treated as footnotes. Everyday language of 'or' and 'and' reinforces the wrong mapping.
What to do instead
Before computing, write down whether the events can occur together and whether one changes the chance of the other. Use P(A or B)=P(A)+P(B)-P(A and B) as the default and subtract the overlap; for dependent events use conditional probability. Test with a small sample space or a probability table.
The candidate computes the modulus of a complex number correctly but reports the argument in the wrong quadrant, for example giving arctan(b/a) as the argument when a is negative.
The formula arctan(b/a) is memorized without the quadrant adjustment, and the inverse tangent function cannot distinguish opposite directions. The candidate also forgets that the argument is defined up to multiples of 2*pi.
What to do instead
Always plot the point (a,b) first and determine the quadrant visually. Use arctan(b/a) only as a reference angle, then add pi when a is negative. State the argument in a chosen range such as (-pi, pi] and check the answer against the plot.
The candidate confuses the terms of an arithmetic or geometric sequence with the partial sums, for example using the sum formula when asked for a single term, or applying the arithmetic mean relationship to a geometric sequence.
The formulas look similar and are often memorized as a block without the conditions attached to each. The distinction between the nth term and the sum of the first n terms blurs under time pressure.
What to do instead
Write the definitions side by side before starting: a_n = a_1+(n-1)d versus S_n = n(a_1+a_n)/2, and a_n = a_1*r^(n-1) versus S_n = a_1(1-r^n)/(1-r). Underline what the question asks for, and verify with a short sequence written out by hand.
The candidate computes a vector dot product or cross product and then uses the result as if it were a vector, or uses the dot product to find a perpendicular vector.
The two products share notation and both appear in angle and perpendicularity problems, so their outputs get conflated. The geometric meaning of each product is not linked to its formula.
What to do instead
Anchor each product to its output type and use: the dot product yields a scalar and tests perpendicularity (zero means perpendicular) and gives angles; the cross product yields a vector perpendicular to both inputs. Write the output type next to each calculation as a check.
The candidate finds the equation of a line or circle but ignores domain restrictions, such as dividing by a quantity that could be zero, taking a square root of a negative expression, or accepting extraneous roots introduced by squaring.
Algebraic manipulation is treated as reversible, so every result is assumed valid. Squaring, multiplying by a variable expression, and clearing denominators all can introduce solutions or hide excluded values that the candidate does not track.
What to do instead
Record the domain or excluded values before manipulating, and after solving substitute every candidate back into the original equation. Flag any step that squares both sides or multiplies by a variable expression, and check those candidates with extra care.