Calculation mistakes in ESAT Chemistry and Biology

Where the marks go

Chemistry and Biology can feel as if they need more content than Mathematics 1. Even so, the quickest gains often come from the small calculations: concentrations, ratios, percentages, reading graphs, converting units and working out proportional change.

These mistakes are frustrating because you often understand the science perfectly well. The mark goes because the last step was rushed, or because you read a scale wrongly.

Start with the unit you want

Before you calculate anything, decide what unit the answer should be in. Then check each quantity in the question against it. The unit often tells you what to do. mol dm⁻³ means moles divided by a volume in dm³, and a rate per minute means something divided by a time.

This matters most when the wrong options are near misses. Look out for an answer that's ten or a thousand times too big, a ratio turned upside down, a percentage change worked out from the wrong starting value, and a percentage written as a decimal.

A concentration calculation

Suppose a question asks how many moles of sodium hydroxide are in 25.0 cm³ of a 0.200 mol dm⁻³ solution.

The concentration is per dm³, so convert the volume first: 25.0 cm³ is 0.0250 dm³. Then multiply: 0.0250 × 0.200 = 0.00500 mol, or 5.00 × 10⁻³ mol.

If you multiply 25.0 by 0.200 without converting, you get 5.00 mol, which is a thousand times too big, and it could well be one of the options. Writing 'moles = volume in dm³ × concentration' before you start makes the conversion much harder to miss.

Dilution works the same way, and often needs no moles at all. If 10 cm³ of a 1.0 mol dm⁻³ solution is made up to 250 cm³, the volume is 25 times bigger, so the concentration is 1.0 ÷ 25 = 0.040 mol dm⁻³.

A percentage change calculation

Say a sample of hydrated copper sulfate is heated and its mass falls from 2.50 g to 1.60 g. The question asks for the percentage decrease in mass.

The change is 0.90 g, and a percentage change is always the change divided by the starting value: 0.90 ÷ 2.50 = 0.36, so the answer is 36%.

Two wrong answers are easy to reach. Dividing by the final mass gives 0.90 ÷ 1.60, which is about 56%. Stopping at 0.36 and choosing an option that says 0.36% is the other. When you check a percentage change, ask yourself what you divided by. If it wasn't the starting value, do it again.

Reading a Biology data table

Biology data questions often give you a table and ask which result is biggest or which changed most. Read the column headings and units before you look at the numbers.

Here's an example. A table shows the rate of oxygen production, in bubbles per minute, for two pondweed plants. Plant A produces 20 bubbles a minute in low light and 30 in bright light. Plant B produces 8 and 16. The question asks which plant's rate increased by the larger percentage.

Plant A can look like the answer, because its rate went up by 10 and Plant B's only went up by 8. But A's increase is 50% of its starting rate and B's is 100%, so the answer is B.

Other things worth checking: whether you're comparing values when the question asks about change, whether you've read the right column or axis, whether there's a control you should compare against, and whether the question wants the biggest total or the biggest rate. A plant with the greatest mass after 20 days hasn't necessarily grown fastest if it started off bigger.

Keeping a log of your mistakes

After each timed set, write one line for every calculation you got wrong, saying what happened. For example: 'used cm³ in a mol dm⁻³ calculation', 'divided by the final mass' or 'compared totals when the question asked about change'.

When the same line appears twice, practise five short questions of that type. Then put the same idea back into a mixed timed set, where you have to spot it without being told what the topic is. Data questions in particular need timed practice, because reading a table carefully feels easy until the clock is going.