BQA Grade 12 common mistakes
BQA Grade 12 · Understand the traps and how to avoid them.
Adding or subtracting the denominators of fractions with unlike denominators (e.g., writing 1/2 + 1/3 = 2/5) instead of rewriting both fractions over a common denominator.
The visual symmetry of the two fractions invites component-wise addition, and the student has never consolidated the meaning of a fraction as a single number rather than a pair of numbers.
What to do instead
Before computing, have the student restate the problem in words ('one half plus one third of the same whole'), then convert to a shared denominator using a visual area model, and finally check the answer's size against each addend (the sum must exceed 1/2).
Distributing a negative sign or exponent across a binomial incorrectly, for instance writing -(x + 3) = -x + 3 or (x + 3)^2 = x^2 + 9.
The student applies a shortcut pattern from multiplication (a(b + c) = ab + ac) to operations that are not distributive, and reads the minus sign as attached to the first term only.
What to do instead
Require the student to rewrite subtraction as adding the opposite and to expand squares by writing the binomial twice; then verify with a numerical substitution such as x = 2 in both the original and the simplified expression.
Confusing the slope and the intercept when translating a verbal description into a linear model, so the starting value is used as the rate of change (or vice versa).
Students match numbers to the equation y = mx + b by position rather than by meaning, and word problems rarely label which quantity is the rate.
What to do instead
Have the student build a small table of values (input 0, 1, 2) from the description first, identify the change per step as the slope and the value at step zero as the intercept, and only then write the equation.
Determining a function's domain or range from a formula without excluding values that make a denominator zero or a radicand negative.
Students treat domain as a property of the variable's letter or of the graph's visible extent, and algebraic restrictions are checked only when a problem explicitly says 'find the domain'.
What to do instead
Establish a routine: before graphing or evaluating, list the operations present, flag division and even roots, solve the resulting inequalities, and state the domain in interval notation as part of the answer.
Applying a scale factor to only one dimension when enlarging a figure, or assuming that doubling the side length doubles the area.
Linear intuition is applied to two- and three-dimensional quantities, and the exponent in the area formula is not connected to the number of dimensions being scaled.
What to do instead
Have the student compute the area before and after a dilation with concrete numbers (a 3-by-4 rectangle doubled to 6-by-8) and record the ratio, then generalize that area scales by the square of the factor and volume by the cube.
Treating conditional probability as the reverse conditional, reporting P(A given B) when the question asks for P(B given A).
The two quantities look interchangeable in everyday language, and students substitute the more easily computed conditional without checking which event is the given condition.
What to do instead
Circle the phrase after 'given' or 'among those who' before computing, restate the question as a fraction of a restricted group, and confirm with a two-way table by dividing the correct cell by the correct row or column total.
Reporting a correlation between two variables as evidence that one causes the other, without considering confounding variables or the direction of the relationship.
Observational data is presented in the same format as experimental data, and students have not been trained to ask how the data were generated.
What to do instead
Require a written sentence identifying the study type (experiment with random assignment versus observational), naming at least one plausible confounding variable, and stating the conclusion only as an association unless random assignment is present.
Reading a value off a graph or table at the wrong scale, such as taking a point's height using the gridline spacing rather than the labeled axis increment.
Students count grid squares instead of reading axis labels, and time pressure discourages the check of the scale before extracting a value.
What to do instead
Make 'state the axis increments and units' the first written step for any data-display item, and have the student estimate the answer's order of magnitude before selecting an option so an off-by-a-factor error is caught.
Setting up a proportion or unit conversion with the matching quantities in inconsistent positions, producing a reciprocal answer.
Students memorize 'cross multiply' without tracking which units occupy numerator and denominator, so the setup is never dimensionally checked.
What to do instead
Teach dimensional analysis as the primary method: write the given quantity with units, multiply by conversion factors written as fractions, and cancel units explicitly until only the target unit remains; if the units do not cancel, the setup is wrong.
Answering an open-response item with only a numerical result, omitting the justification or the interpretation of the result in context that the rubric rewards.
Students equate mathematical work with computation and have practiced mostly multiple-choice items where only the final value is scored.
What to do instead
Practice a fixed three-part response frame (state the result with units, show the key step that justifies it, and write one sentence interpreting it in the problem's context), and self-score against the rubric before moving on.