# Notes

- Learner: 16, Grade 10 FSM (South Africa). Set up by her father, Anton. Missed many classes. Test Sat 31 Oct 2026.
- Main difficulty (from Anton): recognising WHICH factorising rule applies to a problem, not the rules themselves. So lesson 3 asks for the rule first, then shows the factorisation.
- Use the notes' words: "salient point" (not vertex), "restriction", "common factor", "trinomial", "grouping", "factor theorem", "synthetic division". Coordinates are written with a semicolon: (p; q).
- Source scans: abs.pdf has a text layer. term1.pdf and term2.pdf are image-only; I OCR'd them (RapidOCR) and checked the factorising pages by eye.
- abs.pdf has NO absolute value inequalities. Lesson 1 §4 covers them briefly from Paul's Online Notes and flags them as not in the notes. Check with her whether the teacher covered them.
- Some handwritten worked answers in the notes are incomplete or wrong (e.g. term1 p.3 Ex 3 groups a² − a − b² − b as a(a−1) − b(b+1), which leads nowhere). The lessons use the verified answers.
- Quiz design: in the rule-picking drill all options are the same fixed list of 6 rules in the same order every time, so order gives no clue. In the MCQs the correct option is placed in varied positions by quiz.js.
- Every answer checked with sympy (factorisations expanded back; equations solved).
- No learning records yet: nothing has been demonstrated. Write 0001 after she does the practice test (score + missed rule types).
- Lesson 5 is built from past exams, using ONLY questions on the notes' topics (Anton: the exams covered extra material that is not on this test). Excluded: algebraic fractions, completing the square, quadratic formula, nature of roots, polynomial inequalities, complex numbers (including factorising in ℂ), matrices, partial fractions, area estimation, probability and statistics. Also 2018 Q9c y = |x² − 4| (|quadratic| graphs are not in abs.pdf).
- Memo issues: 2021 Q10a restriction written with > and < instead of ≥ and ≤ (same answer); 2018 memo has no Q9; 2024 graph question is numbered 5.3 in the paper and 6.3 in the memo. No wrong final answers found.