OAE Mathematics common mistakes
OAE Mathematics · Understand the traps and how to avoid them.
Solving a word problem by grabbing the numbers and applying the first operation that seems to fit, without first writing what quantity is asked for and what units it should carry.
Under time pressure, candidates pattern-match on keywords ('total' means add, 'left' means subtract) instead of modeling the relationship, so multi-step problems collapse into a single wrong operation.
What to do instead
Before computing, write a one-line 'want' statement with units (e.g., 'want: cost per student, dollars/student') and list the given quantities with their units. Then choose operations that make the units cancel toward the wanted unit. Practice with problems where the keyword misleads (e.g., 'how many more groups' requires division, not addition).
Treating rational and irrational numbers as interchangeable in classification and simplification tasks, e.g., writing √2 ≈ 1.414 and then using 1.414 as if it were exact, or claiming 0.333... is irrational because the decimal repeats.
Candidates memorize decimal approximations early and never revisit the definitions; the distinction between terminating, repeating, and non-repeating non-terminating decimals is rarely tested in prior coursework.
What to do instead
Rebuild the classification from definitions: rational = ratio of two integers, so repeating and terminating decimals are rational; irrational decimals never repeat and never terminate. Do drills sorting numbers like 22/7, √9, √10, π, 0.121221222... into rational/irrational and justify each in one sentence. Never substitute an approximation when an exact form is required.
Applying exponent and radical rules as if all bases were positive, e.g., writing √(x²) = x, (x²)^(1/2) = x, or √(a+b) = √a + √b.
Rules are learned as symbol manipulations without domain conditions, and the absolute-value subtlety of √(x²) is a classic trap that feels like an exception rather than the rule.
What to do instead
State each rule with its conditions aloud: √(x²) = |x|; √(ab) = √a·√b only for a,b ≥ 0; √(a+b) cannot be split. Test every simplification by plugging in a negative and a positive value (e.g., x = −3) to catch sign errors before moving on.
Confusing the sequence's index with its value: computing a_10 by adding the common difference nine times but labeling the first term a_1, or assuming a recursive rule and an explicit rule produce the same starting index.
Textbook formulas differ on whether sequences start at n = 0 or n = 1, and candidates carry over a memorized formula without checking which convention the problem uses.
What to do instead
Always write the first three terms explicitly from the given rule before generalizing. For arithmetic sequences, derive a_n = a_1 + (n−1)d by counting the gaps, and verify by substituting n = 1, 2, 3. For geometric sequences, check r by dividing consecutive terms rather than assuming it.
Solving an equation by performing an operation on one side only, or dividing by an expression that could be zero without noting the excluded value.
Procedural fluency is practiced on one-step equations, so multi-step manipulation loses the balance metaphor; the zero-division case is invisible unless explicitly checked.
What to do instead
Adopt a two-column format: operation applied on the left, same operation on the right, every line. Before dividing by any variable expression, write 'assume ≠ 0' and check that case separately. After solving, substitute the answer back into the original equation, not the simplified one.
Treating a function's domain and range as afterthoughts, e.g., reporting the range of f(x) = x² as all reals, or giving the domain of 1/(x−2) as all reals.
Candidates graph by plotting points and reading the visible window, so the behavior outside the window and the algebraic restrictions (division by zero, even roots of negatives) never enter the analysis.
What to do instead
For every function, run a checklist: denominators ≠ 0, radicands ≥ 0 for even roots, and log arguments > 0. Then find the range by solving y = f(x) for x and asking which y values permit a real x. Confirm with a quick sketch showing asymptotes and endpoints.
Mixing up perimeter, area, and volume formulas for the same figure, e.g., using 2πr for the area of a circle or confusing the slant height and perpendicular height of a cone or pyramid.
Formulas are memorized as strings of symbols without attaching each to a geometric quantity, and slant versus perpendicular height is a distinction diagrams usually hide.
What to do instead
Attach units to every formula: perimeter in linear units, area in square units, volume in cubic units. For cones and pyramids, draw the right triangle relating slant height, perpendicular height, and radius/apothem, and label which one the problem gives. Derive the circle area once by cutting and rearranging sectors so the formula is not just a string.
Applying a scale factor to area or volume as if it were linear, e.g., doubling the sides of a rectangle and expecting the area to double, or tripling a cube's edge and expecting volume to triple.
Similarity ratios are taught as linear proportions, and the squaring and cubing of the ratio are easy to forget when the problem is phrased in everyday terms.
What to do instead
Memorize the similarity law: lengths scale by k, areas by k², volumes by k³. On every similar-figures problem, write the three ratios side by side before substituting. Sanity-check with a concrete example (a 1×1 square doubled to 2×2 has four times the area).
Reading a mean, median, or standard deviation from a histogram or box plot by eyeballing the tallest bar or the middle of the axis rather than computing from the grouped data or the five-number summary.
Graphs invite visual shortcuts, and the median of grouped data requires cumulative frequencies that are tedious to build, so candidates guess instead.
What to do instead
For histograms, build a cumulative-frequency column and locate the median class before estimating. For box plots, explicitly identify minimum, Q1, median, Q3, maximum, and remember the mean is not marked. When comparing distributions, describe center, spread, and shape in that order, citing the specific statistic that supports each claim.
Miscounting outcomes in probability problems by treating ordered and unordered selections as the same, e.g., using combinations when order matters, or forgetting that without-replacement changes the denominator on the second draw.
The formulas for permutations and combinations look similar, and the phrase 'at random' does not signal whether order is being tracked, so candidates default to whichever formula they remember.
What to do instead
Before choosing a formula, ask two questions: does order change the outcome, and is replacement allowed? Write the sample space for a small version of the problem (e.g., two draws from three items) and count by hand to confirm which formula matches. For without-replacement probabilities, write the denominator as n, then n−1, explicitly.