Scio NSZ Math common mistakes
Scio NSZ Math · Understand the traps and how to avoid them.
When a word problem gives a rate or ratio (e.g., two workers, mixture concentrations, speed with a current), the candidate picks the operation that 'looks right' from keywords like 'total' or 'times' instead of writing an equation with a clearly defined variable for the unknown quantity.
Under time pressure the brain pattern-matches on familiar words. Rate and ratio problems look like arithmetic but require setting up a relationship; without a written variable, the candidate silently assumes the wrong base for the percentage or the wrong direction for the current.
What to do instead
Before computing, write one line: 'Let x = ___' naming the exact unknown, then write the relationship as an equation (e.g., work rate = 1/t, combined rate = sum of individual rates). Check the answer by substituting back into the original sentence, not into your equation.
The candidate applies a percent change to the wrong base: adds a markup then a discount to the original price instead of compounding, or computes 'percent of' against the new value rather than the original.
Successive percentage changes are intuitively treated as additive (a 20% increase then a 20% decrease 'cancels out'), because the candidate never writes the multiplier form. The base silently shifts between steps.
What to do instead
Convert every percent change to a multiplier (increase 20% -> x1.20, decrease 20% -> x0.80) and multiply in sequence. For 'A is what percent of B', always divide by B. Verify with a concrete number (start at 100) when the algebra feels ambiguous.
The candidate solves an equation by dividing or multiplying both sides by an expression containing the variable and drops the case where that expression equals zero, losing a valid solution (or keeps an extraneous one).
Cancellation feels like simplification, and the candidate is trained to 'get x alone' rather than to track when an operation is undefined or non-reversible. Rational and radical equations punish this most.
What to do instead
Before dividing by anything containing x, ask 'could this be zero?' and record that case separately. After solving, substitute each root into the original equation (not a simplified form) to discard extraneous roots from squaring or cross-multiplying.
The candidate misreads inequality direction and interval notation: flips the sign when adding a negative instead of when multiplying/dividing by a negative, or writes a solution set with the wrong bracket type for an excluded endpoint.
The flip rule is memorized as 'negative numbers flip it', which is imprecise. Endpoint inclusion is treated as cosmetic, so open vs. closed brackets are chosen by habit rather than from whether the inequality is strict.
What to do instead
State the rule precisely: multiplying or dividing both sides by a negative number reverses the inequality. Test the solution with one value inside and one outside the interval. Match strict (<, >) to parentheses and non-strict (<=, >=) to square brackets, and check whether the domain itself excludes an endpoint.
The candidate computes a mean, median, or standard deviation from raw data without checking whether the question asks about a sample or a population, or reports the mean when the question asks which measure is most robust to an outlier.
Descriptive statistics questions are read as 'compute the average'. The distinction between n and n-1, and between center and spread, is glossed over because the candidate answers the number they can calculate fastest.
What to do instead
Underline the statistic requested and the population/sample wording. Use n for a population variance and n-1 for a sample variance. When asked about robustness or skew, reason qualitatively first: the median resists outliers, the mean does not, and the mean is pulled toward the tail.
The candidate confuses independent and conditional probability: multiplies P(A) x P(B) for events that are not independent, or computes P(A and B) when the question asks for P(A given B).
The multiplication rule is over-learned as 'and means multiply', and the conditional symbol is skimmed. Without checking independence, the candidate applies the simple product rule to dependent draws.
What to do instead
Write the general rule first: P(A and B) = P(A) x P(B|A), which collapses to the product only when independent. For 'given', restrict the sample space to B and divide by P(B). For without-replacement draws, adjust the denominator after each draw.
The candidate substitutes a value into a function or composite incorrectly: evaluates f(g(x)) as f(x) x g(x), or plugs the number into the inner function and stops, reporting the intermediate value as the answer.
Function notation is read as multiplication, and composite expressions are processed left to right without tracking which output feeds which input. The candidate stops at the first computed number.
What to do instead
Read f(g(x)) inside-out: compute g(x) first, then feed that result into f. Keep the intermediate labeled. For inverse functions, swap x and y and solve, then verify with f(f^-1(x)) = x on one test value.
The candidate answers a geometry question using a formula that assumes the wrong figure: uses the circumference formula for area, applies the Pythagorean theorem to a non-right triangle, or uses the slant height as the perpendicular height in a cone or pyramid volume.
Formulas are recalled by shape of the symbol rather than by what the quantity measures. Diagrams in the candidate's head supply a right angle or a height that the problem never stated.
What to do instead
Before substituting, name each quantity and its role (radius vs. diameter, slant vs. perpendicular height). Confirm a right angle exists before using Pythagoras or basic trig; otherwise use the law of sines/cosines. Sanity-check units: area in square units, volume in cubic units.
The candidate leaves answers in the wrong form or at the wrong precision: an exact radical or fraction is rounded too early, or the requested form (simplified fraction, decimal places, significant figures) is ignored.
The candidate computes in a calculator and transcribes the display, carrying rounded intermediates forward. The final instruction line about form is read after the work is done, if at all.
What to do instead
Carry exact values (fractions, radicals) through the work and round only at the final step. Read the answer-format instruction before starting and note it. If a decimal is required, keep at least one extra digit in intermediates and round once at the end.
The candidate runs out of time because they spend too long on one hard item, then rush the remaining questions and make avoidable arithmetic slips on items they could have solved.
Sunk-cost thinking on a single problem, combined with no pacing plan. Hard items early in a section consume the budget meant for easier points later, and fatigue increases slip rate on the rushed remainder.
What to do instead
Set a per-item time budget from the section length and question count. If an item exceeds roughly 1.5x the budget, mark it, write down the approach in one line, and move on. Return to marked items with remaining time, and reserve the last few minutes for checking arithmetic on completed answers rather than starting new problems.