Matric past papers · DBE (CAPS) · Paper 2
DBE Grade 12 Euclidean geometry
Every euclidean geometry question from the DBE NSC Paper 2 papers of November 2021–2024 and May/June 2021, 2022, 2024, 2025, in one booklet — 22 questions, 333 marks, with the official marking guideline for every one of them. Free to download, in English and Afrikaans.
Download
- Questions (English) 37 pages, 0.9 MB
- Solutions (English) 52 pages, 2.1 MB
- Vrae (Afrikaans) 36 pages, 1.0 MB
- Oplossings (Afrikaans) 52 pages, 2.1 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
22 questions in 3 chapters, ordered so you can work through one skill at a time.
| # | Question | Skills | Marks | From |
|---|---|---|---|---|
| 1 | Why ST = TR, then two angles in a cyclic quadrilateral | Tangents, and tangents from a point outside, Cyclic quadrilaterals, Angles in the same segment | 5 | November 2021 Q9 |
| 2 | An exterior angle of a cyclic quadrilateral, then AD = DC | Cyclic quadrilaterals, Angles in the same segment | 6 | November 2024 Q9 |
| 3 | A diameter and a bisected angle: find three more | The angle in a semi-circle, and diameters, Chords, and the line from the centre, The angle at the centre | 12 | May/June 2024 Q9 |
| 4 | Two diameters, a perpendicular chord, everything in terms of x | Chords, and the line from the centre, The angle in a semi-circle, and diameters, The angle at the centre | 13 | November 2021 Q10 |
| 5 | A diameter drawn through a cyclic quadrilateral | Cyclic quadrilaterals, The angle in a semi-circle, and diameters, The angle at the centre | 13 | November 2022 Q8 |
| 6 | A tangent, a parallel line, and a cyclic quadrilateral to prove | The tangent-chord theorem, Proving a quadrilateral is cyclic, Cyclic quadrilaterals | 13 | November 2022 Q10 |
| 7 | Two circles with a tangent common to both at Q | Tangents, and tangents from a point outside, The tangent-chord theorem, The angle in a semi-circle, and diameters | 15 | May/June 2021 Q10 |
| 8 | Two tangents meeting a chord that has been produced | Tangents, and tangents from a point outside, Cyclic quadrilaterals, Proving a quadrilateral is cyclic | 15 | November 2023 Q10 |
| 9 | A diameter cutting a chord, and the angles around it | The angle in a semi-circle, and diameters, Chords, and the line from the centre, The angle at the centre | 16 | May/June 2021 Q8 |
| 10 | A cyclic quadrilateral with one pair of sides parallel | Cyclic quadrilaterals, Angles in the same segment, The tangent-chord theorem | 16 | May/June 2022 Q9 |
| 11 | A diameter produced until it meets a tangent | Tangents, and tangents from a point outside, The angle in a semi-circle, and diameters, Proving a quadrilateral is cyclic | 19 | May/June 2024 Q10 |
| 12 | Two circles touching internally, and a tangent common to both | Tangents, and tangents from a point outside, The tangent-chord theorem, Cyclic quadrilaterals | 20 | November 2024 Q11 |
| 13 | A parallelogram cut by a line, and the length of FB | The proportion theorem, Products and ratios of lengths | 9 | November 2023 Q9 |
| 14 | A line drawn across a triangle, and the ratios it creates | The proportion theorem, Similar triangles, Products and ratios of lengths | 20 | May/June 2025 Q9 |
| 15 | The tangent-chord theorem, proved and then used | Proving the theorem itself, not using it, The tangent-chord theorem, Tangents, and tangents from a point outside | 11 | May/June 2024 Q8 |
| 16 | The line from the centre that bisects a chord | Proving the theorem itself, not using it, Chords, and the line from the centre | 14 | November 2022 Q9 |
| 17 | A line parallel to one side of a triangle, proved | Proving the theorem itself, not using it, The proportion theorem | 15 | November 2024 Q10 |
| 18 | The angle at the centre is twice the angle at the circumference | Proving the theorem itself, not using it, The angle at the centre | 16 | November 2023 Q8 |
| 19 | The proportion theorem, then the rider that follows it | Proving the theorem itself, not using it, The proportion theorem, Similar triangles | 17 | May/June 2021 Q9 |
| 20 | Equiangular triangles have their sides in proportion | Proving the theorem itself, not using it, Similar triangles, The proportion theorem | 20 | May/June 2025 Q10 |
| 21 | The tangent-chord theorem again, and a long rider after it | Proving the theorem itself, not using it, The tangent-chord theorem, Tangents, and tangents from a point outside | 23 | November 2021 Q11 |
| 22 | Equiangular triangles, then the longest rider in the book | Proving the theorem itself, not using it, Similar triangles, Products and ratios of lengths | 25 | May/June 2022 Q10 |