AEPA Mathematics (NT304) common mistakes
AEPA Mathematics (NT304) · Understand the traps and how to avoid them.
When simplifying a radical or rational expression, the candidate cancels a term across a plus or minus sign, e.g. writing (x+3)/x as 3 or (x²+9)/(x+3) as x+3.
The candidate has over-generalized the cancellation rule from multiplication of factors to addition of terms, because the visual pattern of matching symbols feels like it should cancel.
What to do instead
Before cancelling, force the candidate to factor the numerator and denominator completely and then circle only factors connected by multiplication; drill a set of 'cancellation traps' where a term looks cancellable but is not, and require a numeric check by substituting x = 2 into original and simplified forms.
The candidate converts a word problem into an equation with the wrong relationship, e.g. writing 3x + 5 = 20 for 'five less than three times a number is twenty' instead of 3x − 5 = 20.
The candidate translates phrase-by-phrase in the order the words appear rather than mapping the structure of the sentence onto operations, and 'less than' reverses operand order.
What to do instead
Practice a translation protocol: identify the unknown, identify the operation words with their reversal rules ('less than', 'divided by'), then verify by substituting a concrete value back into the English sentence; keep a personal glossary of reversal phrases.
The candidate solves an inequality and reports the solution without flipping the inequality sign when multiplying or dividing by a negative number, e.g. −2x > 6 answered as x > −3.
The candidate treats inequalities as equations and applies the same manipulation routine, since the sign flip is a rule with no analogue in equation solving and is easily dropped under time pressure.
What to do instead
Adopt a habit of testing one value from the proposed solution set in the original inequality; also require writing the flip explicitly as a separate step ('divide by −2, reverse sign') so it becomes a visible action rather than a silent one.
The candidate confuses the slope and intercept of a linear function or misreads slope from a graph, e.g. computing slope as run/rise or taking the y-intercept as the x-value where the line crosses the x-axis.
The candidate memorized 'rise over run' as a phrase without anchoring it to the definition (change in y over change in x) and does not consistently identify which axis is which under diagram pressure.
What to do instead
Rebuild slope from the definition using two labeled points and the formula (y₂ − y₁)/(x₂ − x₁); practice reading intercepts by naming the axis crossed, and check by plugging a point into y = mx + b.
The candidate computes the mean, median, or standard deviation of a data set and then answers a question about a different statistic, or reports the mean of grouped data without weighting by frequency.
The candidate pattern-matches 'average' to the most familiar procedure (add and divide) and skips the step of identifying exactly which statistic the question asks for and whether the data are grouped.
What to do instead
Require underlining the requested statistic in the prompt before computing; for grouped data, build a frequency table and use Σ(f·x)/Σf; verify reasonableness by checking whether the answer lies between the min and max and near the visual center.
The candidate computes the probability of a compound event by adding probabilities of overlapping events, or treats dependent events as independent, e.g. P(A or B) = P(A) + P(B) when A and B can co-occur.
The candidate memorized 'or means add, and means multiply' without the conditions attached, and does not check whether events overlap or whether sampling is with or without replacement.
What to do instead
Train a decision checklist: for 'or', test for overlap and subtract the intersection; for 'and', test for independence and adjust for the changed denominator in without-replacement draws; verify with a small sample space or Venn diagram.
The candidate applies a perimeter formula when area is requested, or uses the diameter in place of the radius, e.g. computing circle area as πd² or circumference as 2πd.
The candidate relies on formula recall without checking what each symbol represents, and perimeter and area formulas are stored together and retrieved interchangeably.
What to do instead
Annotate every formula with units (linear vs square) and label the given measurement as radius or diameter before substituting; sanity-check by dimensional analysis and by comparing against a rough estimate (area of a circle slightly larger than a square on the radius).
The candidate reasons about a geometric figure using a diagram that is not drawn to scale, assuming lines are parallel, angles are right, or segments are equal because they look that way.
The candidate treats the illustration as given information rather than as a sketch, and visual impressions override stated givens under time pressure.
What to do instead
Institute a rule that only stated or marked information may be used; require writing a 'givens' list from the text before looking at the figure, and redraw or add marks so that assumptions become explicit claims that must be justified.
The candidate mishandles place value and unit conversion in multi-step problems, e.g. converting square units linearly (1 m² = 100 cm²) or misaligning decimals when adding.
The candidate applies the linear conversion factor to area and volume without accounting for the exponent, and decimal alignment errors stem from treating numerals as whole numbers rather than place-value quantities.
What to do instead
Drill conversions with the exponent applied explicitly (m² to cm² multiplies by 100²); for decimals, pad with trailing zeros and align on the decimal point; check magnitude by estimating with round numbers first.
The candidate solves a system of equations or a quadratic and reports a partial or extraneous answer, e.g. giving only the positive root when both are valid, or accepting a root that makes a denominator zero.
The candidate stops at the first solution found and does not build in a verification step, and extraneous roots arise from squaring or clearing denominators without checking the domain.
What to do instead
Adopt a completion routine: after solving, ask 'how many solutions should this have?' (degree of polynomial, two lines), then substitute every candidate back into the original equation and discard those that violate the domain.