Matric past papers · DBE (CAPS) · Paper 2
DBE Grade 12 Analytical geometry
Every analytical geometry question from the DBE NSC Paper 2 papers of November 2021–2024 and May/June 2021, 2022, 2024, 2025, in one booklet — 16 questions, 319 marks, with the official marking guideline for every one of them. Free to download, in English and Afrikaans.
Download
- Questions (English) 24 pages, 0.7 MB
- Solutions (English) 48 pages, 2.4 MB
- Vrae (Afrikaans) 23 pages, 0.6 MB
- Oplossings (Afrikaans) 48 pages, 2.4 MB
Each question is a clip of the original DBE page: the wording, the mark allocations and the diagrams are exactly as they were printed. Only the blank answer space has been removed, so work in a separate book. The solutions booklet is the board’s own marking guideline, not a rewritten one.
What is in it
16 questions in 2 chapters, ordered so you can work through one skill at a time.
| # | Question | Skills | Marks | From |
|---|---|---|---|---|
| 1 | A right angle at Q, and a line drawn parallel to LQ | Parallel and perpendicular lines, The equation of a straight line, Gradient | 19 | May/June 2021 Q3 |
| 2 | The gradient of DC, then a point that has to lie on it | Gradient, The equation of a straight line, Proving what a figure is | 19 | November 2024 Q3 |
| 3 | A midpoint, an angle of inclination, and a parallel triangle | The midpoint of a line segment, The angle of inclination, Parallel and perpendicular lines | 20 | November 2022 Q3 |
| 4 | A right angle at L, and where LN crosses the x-axis | The distance between two points, Parallel and perpendicular lines, The equation of a straight line | 20 | November 2023 Q3 |
| 5 | A trapezium with one pair of sides parallel | Gradient, Parallel and perpendicular lines, Proving what a figure is, The equation of a straight line | 21 | May/June 2022 Q3 |
| 6 | A whole triangle built from one line's equation | The equation of a straight line, Gradient, Areas on the Cartesian plane | 21 | May/June 2025 Q3 |
| 7 | A midpoint, an angle of inclination, and the point S beyond B | The midpoint of a line segment, The angle of inclination, The equation of a straight line, Gradient | 22 | May/June 2024 Q3 |
| 8 | Find k, then three lines all cutting the x-axis | Gradient, The angle of inclination, The equation of a straight line, Areas on the Cartesian plane | 24 | November 2021 Q3 |
| 9 | A circle inside a parallelogram, with CD as its tangent | Centre and radius from the equation, Tangents to a circle, Proving what a figure is | 15 | November 2021 Q4 |
| 10 | p from two points on the circle, using the midpoint of AB | Centre and radius from the equation, The midpoint of a line segment, The equation of a circle | 18 | May/June 2024 Q4 |
| 11 | A diameter, a cyclic quadrilateral, and where CV leads | Centre and radius from the equation, The equation of a circle, Tangents to a circle | 20 | May/June 2021 Q4 |
| 12 | The centre recovered from a tangent and an intercept | Centre and radius from the equation, Tangents to a circle, The equation of a circle | 20 | May/June 2022 Q4 |
| 13 | PN as a diameter, and the tangent at N | Centre and radius from the equation, Tangents to a circle, The equation of a circle | 20 | November 2022 Q4 |
| 14 | Two circles, and the tangent common to both | The equation of a circle, Tangents to a circle, Two circles together | 20 | November 2023 Q4 |
| 15 | A tangent at P, then the other points that lie on the circle | Centre and radius from the equation, Tangents to a circle, The equation of a circle | 20 | November 2024 Q4 |
| 16 | A tangent at E, and fifteen units along MT | The equation of a circle, Tangents to a circle, The distance between two points | 20 | May/June 2025 Q4 |