Term 1 Week 7 · Inequalities in two variables and the region of solutions · CG Quarter 1, competencies 9–10
| # | The misconception | Where it shows | What to do |
|---|---|---|---|
| 1 | "> means shade above, < means shade below" | Fails on x² − y < 4 | The §B pair. Both are true at (0, 0), and one says < |
| 2 | The origin always works as a test point | Fails on y > −x | Day 2. Do not pre-empt it today — the surprise is the teaching |
| 3 | Broken and solid are decorative | Item 2 of the exit ticket | Ask which points a broken curve leaves out. Answer: exactly the ones on it |
| 4 | "Inside the parabola" is the answer | Fails on a downward parabola | Day 3, y < −x² + 4 |
| 5 | A region can be written as a list of points | Learners try to name four or five solutions and stop | Ask for the next one. And the next. The point lands quickly |
| 6 | Testing one point is not a proof | Raised by strong learners | It is a real question — see §IV.C. Answer it properly, do not brush it off |
| 7 | The boundary must be re-derived for each form | Learners graph x² − y = 4 as a new curve | Rearranging to y = x² − 4 is the same curve, and showing that is half of §C.3 |