ORELA Mathematics (NT304) common mistakes
ORELA Mathematics (NT304) · Understand the traps and how to avoid them.
Attempting to solve every problem in strict order, so the 60-minute, 45-question limit is exhausted by item 35 and the final constructed-response or multi-step items are left blank.
Candidates treat the test like a classroom test where every item counts equally, not realizing that unanswered items cost the same as wrong ones and that later items are not harder on average.
What to do instead
Do two passes. On pass one, spend at most 60-70 seconds per item, flag anything requiring more than two setup steps, and answer every item with at least an elimination guess. Use the remaining time for flagged items. Practice with a timer on full 45-item sets until the pace is automatic.
Reading a word problem, immediately grabbing the numbers, and applying the operation that appears last in the sentence rather than defining the unknown and writing an equation.
Under time pressure, surface cues ('total', 'left', 'times as many') trigger a reflex operation; candidates skip the translation step that turns prose into algebra.
What to do instead
Force a written translation before computing: 'Let x = ___', then one equation with units attached. Check by substituting the answer back into the original sentence. Drill 20 mixed word problems where the required operation is deliberately not the one the keyword suggests.
Confusing perimeter and area formulas, or applying area formulas to composite figures without decomposing them into rectangles, triangles, and semicircles first.
Formulas are memorized as strings rather than derived from meaning; composite figures require spatial decomposition, a separate skill from formula recall.
What to do instead
For every figure, label dimensions with units and ask 'am I covering (area) or outlining (perimeter)?' For composites, sketch the decomposition and label each sub-region before computing. Rebuild the formulas from a labeled diagram once so they are not rote.
Mishandling operations with negative numbers and absolute value, e.g. computing -3^2 as 9, or treating |x - 5| < 3 as x - 5 < 3 only.
Order-of-operations and the two-case nature of absolute value inequalities are common gaps; the minus sign gets absorbed into the base instead of applying after exponentiation.
What to do instead
Write exponentiation with explicit parentheses: -(3^2) versus (-3)^2. For every absolute value equation or inequality, write both cases and solve each, then test one point from each interval on the number line. Do ten such items until the two-case reflex is automatic.
Solving a linear equation or inequality and forgetting that multiplying or dividing by a negative number reverses the inequality symbol, or dropping the inequality direction entirely.
The reversal rule is procedural and easy to skip when the algebra is otherwise fluent; candidates focus on isolating x and stop watching the symbol.
What to do instead
Circle any negative multiplier or divisor before applying it, and flip the symbol at that moment. Verify by testing a value from the proposed solution set in the original inequality. Include at least one coefficient-reversal item in every practice set.
Misapplying exponent and radical rules, such as writing (x^2)^3 as x^5, or simplifying sqrt(a + b) as sqrt(a) + sqrt(b).
Rules for multiplying powers, raising a power to a power, and distributing over sums look similar; the distributive error is reinforced by confusing exponentiation with multiplication.
What to do instead
Keep a one-page rule sheet with a counterexample beside each rule (e.g. sqrt(9 + 16) = 5, not 7). When simplifying, expand small cases by hand to confirm: (x^2)^3 = x^2·x^2·x^2 = x^6.
Setting up a proportion or percent problem with the parts in the wrong positions, e.g. computing a percent increase as (new - old)/new instead of (new - old)/old.
The base of the percent is chosen by habit rather than by asking 'percent of what?'; ratio tables are skipped in favor of cross-multiplying whatever is adjacent.
What to do instead
Before computing, write the sentence 'The change is ___ percent of the original ___' and fill both blanks. Use a labeled ratio table (part / whole) for every proportion. Practice distinguishing markup, discount, and percent-change items in the same set.
Treating a function's domain and range as interchangeable, or assuming the domain of a rational or radical function is all real numbers.
Domain restrictions come from two specific sources (division by zero, even roots of negatives) that are easy to forget once the algebra of the expression looks routine.
What to do instead
Run a two-question checklist on every function: 'Where is the denominator zero?' and 'Where is the radicand negative?' Exclude those values explicitly and state the domain in interval notation. Graph the function to confirm the range visually.
Computing a mean, median, or standard deviation without checking whether the data set is skewed or contains an outlier, then reporting the mean as the best measure of center.
Mean is the default because it is the most practiced; the choice-of-measure reasoning that the exam tests is a separate conceptual skill.
What to do instead
For every data set, compute mean and median and note the gap. If they differ substantially or an outlier is present, select the median and justify it in one sentence. Practice writing that justification, since the exam rewards the reasoning, not just the number.
Answering a probability question with the count of favorable outcomes instead of the ratio, or failing to adjust the denominator for sampling without replacement.
Counting feels like the whole task, and the 'without replacement' condition is buried in the wording rather than stated as a formula cue.
What to do instead
Always write P = favorable / total before computing, and state whether the denominator changes between draws. For two-stage problems, draw a tree diagram with the updated denominator on each branch, then multiply along the path.