A long solution is a chain, and a wrong first link spoils the rest. You can find the broken link quickly, repair only what depends on it, and catch the next one sooner.
This page belongs to the SPM Additional Mathematics guide. The slips here are close cousins of those in when a correct method still loses accuracy.
What does the student usually say?
“I was nearly at the end, then the answer came out strange and I had no idea where it went wrong.” Or: “I did everything right except one line at the start.”
An expansion slip, found by substitution
The question, invented for this page: solve (x + 3)² = 2x + 11.
The slip. The student expands (x + 3)² as x² + 9. Then x² + 9 = 2x + 11 gives x² − 2x − 2 = 0, and the quadratic formula gives x = 1 ± √3, so x ≈ 2.73 or x ≈ −0.73.
The check. Put x ≈ 2.73 back in. The left side is (5.73)² ≈ 32.8, and the right side is 2(2.73) + 11 ≈ 16.5. They are far apart, so something is wrong.
The repair. Look at the lines above the answer, starting from the top. The first wrong line is the expansion: (x + 3)² = x² + 6x + 9, with the middle term 6x.
The redo. x² + 6x + 9 = 2x + 11 gives x² + 4x − 2 = 0. So x = (−4 ± √24) ÷ 2 = −2 ± √6, which is x ≈ 0.449 or x ≈ −4.449.
Check x ≈ 0.449: the left side is (3.449)² ≈ 11.90, and the right side is 2(0.449) + 11 ≈ 11.90. They agree.
What goes into a restart routine?
- Do not start again from the top. Start from the first line that does not match the question.
- Cross out with a single line so the method stays visible.
- Recompute only the lines that depend on the wrong one.
- Check the new answer by substitution.
What can I do myself?
- Check every expansion with a number: put x = 1 into both sides and confirm they match.
- Substitute every final answer back into the original question, even when time is short.
- Keep a list of your early slips in the mistake log and paper-error review, and read it before each practice session.
- Try a second method on at least one long question a week. Using multiple methods to check explains how.
When might one-to-one tuition help?
When the same kind of first-line slip returns across chapters, it is a habit, not a knowledge gap. A teacher can watch you write the first three lines of several questions and see when your attention drops.
The one-hour trial class (from RM50) suits this well if you bring two long solutions with the error marked. Learn more at online one-to-one Additional Mathematics tuition.