When a calculator finds the answer, the examiner still needs to see your reasoning. A copied picture of the screen or the words “from calculator” do not show what you set up, what you read or why the result makes sense.
Good documentation is short but complete. It is the last step of graphic display calculator interpretation.
What should your working contain?
Five short items are enough.
- The equation or function you entered, written in algebra, not calculator notation.
- The window or table range, so the reader knows what you looked at.
- The feature you used: for example, the intersection of two graphs or the root of one.
- The values read, with the rounding you used.
- A check and a sentence answer, including units.
A quick sketch with labelled axes and the key points is often worth adding. It shows understanding, but it does not replace the written line of reasoning.
Worked example
A ball’s height in metres after t seconds is h = 20t − 5t². When is the height 15 m?
Equation: solve 20t − 5t² = 15.
Set-up: plot y = 20x − 5x² and y = 15 with 0 ≤ x ≤ 4 and 0 ≤ y ≤ 25. The first graph has its turning point at t = 2, h = 40 − 20 = 20, which is inside the window.
Feature and reading: the intersection tool gives x = 1 and x = 3.
Check: at t = 1, h = 20 − 5 = 15. At t = 3, h = 60 − 45 = 15. Both agree.
Answer: the height is 15 m at t = 1 second (rising) and t = 3 seconds (falling).
Algebra confirms it: 5t² − 20t + 15 = 0 becomes t² − 4t + 3 = 0, so (t − 1)(t − 3) = 0.
The mistake to watch for
Weak working: “Used calculator. t = 1, 3.” with a screenshot pasted beside it.
There is no equation, no window and no check, so the examiner cannot tell whether the method was valid. If the reading were wrong, there would be nothing to credit.
The correction is to write the five items above. A single clear line for each is enough, and the screenshot becomes unnecessary because the written working carries the information.
Check yourself
1. For the ball above, find when h = 20, and explain what the result shows.
Show answer
20t − 5t² = 20 gives t² − 4t + 4 = 0, so (t − 2)² = 0 and t = 2 only. The horizontal line h = 20 touches the graph at its maximum point, so the ball reaches 20 m exactly once, at its highest point.
2. Find when h = 10, giving answers to 3 significant figures, and show a check.
Show answer
20t − 5t² = 10 gives t² − 4t + 2 = 0, so t = 2 ± √2. With √2 = 1.41421, t = 0.58579 or 3.41421. To 3 significant figures: t = 0.586 s and t = 3.41 s. Check: at t = 3.41421, t² = 11.65685 and 20t − 5t² = 68.2842 − 58.2843 = 10.0.
3. A student writes “Answer: x = 2.6 (graph)” for a quadratic equation. List two things missing.
Show answer
Any two of these: the equation that was solved, the window or range used, the feature read from the graph, a substitution check, and a stated accuracy or units. The examiner needs the method as well as the number.
Where this leads next
Try writing the five items for each question in the mixed practice set. The mistake log and retest queue helps you track which item you forget most. Back to the module overview when you are ready to revise the whole route.
Clear written working is a habit that improves with feedback. A teacher in online one-to-one Mathematics tuition can give that feedback on your own solutions.