Matric past papers · DBE (CAPS) · Paper 2
DBE Grade 12 Trigonometry
Every trigonometry question from the DBE NSC Paper 2 papers of November 2021–2024 and May/June 2021, 2022, 2024, 2025, in one booklet — 28 questions, 385 marks, with the official marking guideline for every one of them. Free to download, in English and Afrikaans.
Download
- Questions (English) 33 pages, 1.0 MB
- Solutions (English) 52 pages, 2.1 MB
- Vrae (Afrikaans) 34 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
28 questions in 3 chapters, ordered so you can work through one skill at a time.
| # | Question | Skills | Marks | From |
|---|---|---|---|---|
| 1 | Simplify to one ratio, then a sum of two sines | Reduction formulae, Compound angles, Proving an identity | 12 | May/June 2022 Q6 |
| 2 | cos A from a point, then the double and compound angles | Ratios from a point, and the quadrants, Double angles, Compound angles | 12 | November 2024 Q5 |
| 3 | Two identities to prove, one of them a difference of sines | Proving an identity, Compound angles, Double angles | 13 | May/June 2025 Q6 |
| 4 | Derive cos(alpha + beta), then use it to simplify | Compound angles, Proving an identity, General solutions | 15 | November 2021 Q6 |
| 5 | Reduce to a single ratio, then prove an identity | Reduction formulae, Proving an identity, General solutions | 17 | November 2021 Q5 |
| 6 | Simplify, then everything in terms of cos 35 = m | Reduction formulae, Ratios from a point, and the quadrants, Compound angles | 18 | May/June 2021 Q5 |
| 7 | A point in the second quadrant, and the ratios it fixes | Ratios from a point, and the quadrants, Reduction formulae, Double angles | 18 | May/June 2022 Q5 |
| 8 | Derive cos(x + y) from the identity given, then apply it | Compound angles, Proving an identity, General solutions | 18 | November 2024 Q6 |
| 9 | cos theta = 5/13 with the quadrant given, then a simplification | Ratios from a point, and the quadrants, Reduction formulae, Compound angles | 19 | May/June 2025 Q5 |
| 10 | Everything in terms of sin 40 = p, then an identity to prove | Ratios from a point, and the quadrants, Reduction formulae, Proving an identity | 26 | May/June 2024 Q5 |
| 11 | 13 sin x + 3 = 0, and the whole chain that follows from it | Ratios from a point, and the quadrants, Reduction formulae, Proving an identity, General solutions | 30 | November 2022 Q5 |
| 12 | sin beta given with its quadrant - the longest question in the book | Ratios from a point, and the quadrants, Double angles, Proving an identity, General solutions | 31 | November 2023 Q5 |
| 13 | Draw a cosine onto a sine that is already sketched | The graphs of sin, cos and tan, Period, amplitude and asymptotes | 8 | November 2021 Q7 |
| 14 | A cosine and a shifted sine on one set of axes | The graphs of sin, cos and tan, Where two trig graphs meet | 10 | May/June 2022 Q7 |
| 15 | tan x against 2 sin 2x, and where the two cross | The graphs of sin, cos and tan, Where two trig graphs meet | 10 | November 2022 Q6 |
| 16 | Find a from where cos(x + a) meets sin 2x | The graphs of sin, cos and tan, Where two trig graphs meet, Period, amplitude and asymptotes | 10 | May/June 2024 Q6 |
| 17 | Range, period, and where 2 cos x + 1 meets sin 2x | The graphs of sin, cos and tan, Period, amplitude and asymptotes, Where two trig graphs meet | 10 | May/June 2025 Q7 |
| 18 | The asymptote of tan x, and reading the graph around it | The graphs of sin, cos and tan, Period, amplitude and asymptotes | 11 | November 2024 Q7 |
| 19 | Period, amplitude, and a point that lies on f | The graphs of sin, cos and tan, Period, amplitude and asymptotes, Where two trig graphs meet | 12 | November 2023 Q6 |
| 20 | cos 2x against minus sin x, without a calculator | The graphs of sin, cos and tan, Where two trig graphs meet, Ratios from a point, and the quadrants | 13 | May/June 2021 Q6 |
| 21 | A vertical tower, an angle of depression, and an area q | Three-dimensional problems, The area rule, Angles of elevation and depression | 7 | November 2023 Q7 |
| 22 | A ramp into a building: its height, its angle and its length | Angles of elevation and depression, The sine rule | 8 | May/June 2022 Q8 |
| 23 | A point directly above a triangle, with 2AD = BC | Three-dimensional problems, The cosine rule, The sine rule | 8 | May/June 2025 Q8 |
| 24 | Two boards meeting at right angles | Three-dimensional problems, The cosine rule | 9 | May/June 2021 Q7 |
| 25 | Two observers 19 m apart, and a building 16 m high | Three-dimensional problems, Angles of elevation and depression, The cosine rule | 9 | November 2024 Q8 |
| 26 | A hook on a gallery ceiling, seen from three points | Three-dimensional problems, Angles of elevation and depression, The sine rule | 10 | November 2021 Q8 |
| 27 | A flagpole and the two cables anchoring it | Three-dimensional problems, The sine rule, The cosine rule | 10 | November 2022 Q7 |
| 28 | Derive the area rule, then put it to work | The area rule, The sine rule | 11 | May/June 2024 Q7 |