MB Essential Math 40S common mistakes
MB Essential Math 40S · Understand the traps and how to avoid them.
When converting between units in a measurement problem, the candidate multiplies where division is needed (or vice versa) because they match the unit names instead of tracking whether the answer should get larger or smaller.
Unit conversion is often memorised as a list of factors without a reasoning check about direction. Under time pressure the candidate grabs the first factor they recall and applies it in whichever operation feels natural, so a length in metres converted to centimetres can come out smaller than it started.
What to do instead
Before computing, write a one-line estimate: 'The answer should be bigger/smaller than the given value, because centimetres are smaller units than metres.' Then set up the conversion as a fraction with the unwanted unit on the bottom so it cancels, and check the result against the estimate. Practise five conversions per session with the estimate written first.
The candidate reads a table or graph, pulls the number that appears next to the row label, and never checks whether the row and column headings indicate the value is cumulative, per-unit, or already a total.
Tables in practical math contexts frequently present running totals or rates that must be combined with a second figure. Candidates scan for the label they recognise and stop reading, treating the first matching number as the final answer.
What to do instead
Adopt a fixed reading routine: read the table title, then the column headings, then the units, then the row of interest, and only then the cell. Write down in words what the cell represents before using it. If the cell is a rate, explicitly write the multiplication that converts it to the quantity the question asks for.
In a multi-step word problem, the candidate produces a numerically correct intermediate value and then submits it as the final answer, ignoring the last sentence that asks for a different quantity.
Working memory is consumed by the arithmetic, and the last sentence is read before the calculation but not re-read after it. The intermediate result feels like an accomplishment, so the candidate stops.
What to do instead
Before calculating, underline the actual question and restate it in the margin as a short phrase, for example 'find total cost, not cost per person'. After computing, compare the answer's units and magnitude against that restated question. Make re-reading the question a mandatory step in a checklist used on every practice problem.
The candidate sets up a proportion or ratio with the terms in inconsistent order, so the two sides of the equation compare different things, and the cross-multiplication produces a plausible but wrong number.
Proportions are often written by copying the order of numbers from the problem text rather than by labelling each position. Without labels, any arrangement looks equally valid, and the arithmetic still works out cleanly enough to escape suspicion.
What to do instead
Always write units next to each term in the proportion and confirm that the units on the top of both fractions match and the units on the bottom of both fractions match. If they do not, rearrange before solving. Solve by scaling to a unit rate as a cross-check on the cross-multiplied result.
When a problem involves a loan, investment, or deduction, the candidate applies a single percentage to the original amount and stops, rather than recognising that a second percentage applies to the new amount.
Successive percentage changes are treated as additive. The candidate reasons that a 10 percent increase followed by a 10 percent decrease cancels out, which is intuitive but false, and the error is invisible because the answer is close to the original.
What to do instead
Convert each percentage change into a multiplier (1.10, 0.90) and multiply the multipliers in sequence, never adding or subtracting the percentages. Build a habit of testing the claim on a round number such as 100 before trusting an intuition about cancellation. Include at least one chained-percentage problem in every practice set.
The candidate computes a mean, median, or range from raw data but reports it without checking whether the question asked for a measure of centre or of spread, or whether an outlier should be described rather than included in a summary statistic.
All summary statistics are taught together, and the candidate defaults to whichever one they practised most recently. Outliers are often treated as errors to be removed rather than as data to be interpreted.
What to do instead
Classify the question first: does it ask where the data sits (centre) or how spread out it is (spread)? Name the statistic aloud before computing. When an outlier appears, state its effect on the mean versus the median explicitly, and answer the interpretation question in a sentence rather than only giving a number.
When reading or drawing a graph, the candidate misreads the scale because gridlines represent increments other than one, and reports a value that is off by a constant factor.
The axes are scanned for labels but the interval between gridlines is assumed rather than checked. This is especially likely when only every second or fifth gridline is labelled.
What to do instead
Compute the gridline interval explicitly: subtract two adjacent labelled values and divide by the number of squares between them, writing the result on the graph. Do this for both axes before reading any point. When sketching, label the interval on each axis as part of the drawing.
The candidate substitutes values into a formula without first rewriting the formula to isolate the unknown, producing an equation they then solve by guesswork or abandon.
Formula rearrangement is a distinct algebra skill, and candidates who are shaky on it try to substitute first and untangle later. The resulting equation mixes the unknown into several terms and becomes intractable.
What to do instead
Practise rearrangement as a standalone drill: isolate each variable in turn for the formulas used in the course, without substituting any numbers. When solving, rearrange symbolically first, then substitute as the final step. Verify by substituting a simple set of numbers into both the original and rearranged forms.
The candidate rounds at every intermediate step, so the final answer drifts away from the correct value and can miss an acceptable range or a multiple-choice option entirely.
Each rounding feels harmless, but errors accumulate across a multi-step calculation. Candidates also round too early because they are copying intermediate values from a calculator display.
What to do instead
Keep full precision in the calculator's memory or answer register and round only the final result, to the precision the question specifies. Where a question gives a tolerance, state the unrounded value alongside the rounded one. Practise a problem twice, once with early rounding, to see how far the answer moves.
The candidate gives a bare number as the answer to a contextual problem, omitting the unit, the direction or sign, and any required statement of what the number means.
The candidate treats the task as arithmetic and stops when the calculation is done, not recognising that communication of the result is part of the mark scheme. Negative signs in particular are dropped because they seem like a formatting detail.
What to do instead
Use a fixed answer template: value, unit, and one sentence of interpretation, for example 'the balance is negative, meaning the account is overdrawn'. Check the sign against the context before writing. In practice, mark your own answers against the template and count missing units as errors.