Matric past papers · DBE (CAPS) · Paper 1
DBE Grade 12 Patterns, sequences and series
Every patterns, sequences and series question from the DBE NSC Paper 1 papers of November 2021–2024 and May/June 2021, 2022, 2024, 2025, in one booklet — 17 questions, 205 marks, with the official marking guideline for every one of them. Free to download, in English and Afrikaans.
Download
- Questions (English) 18 pages, 0.5 MB
- Solutions (English) 25 pages, 1.9 MB
- Vrae (Afrikaans) 18 pages, 0.5 MB
- Oplossings (Afrikaans) 25 pages, 1.9 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
17 questions in 3 chapters, ordered so you can work through one skill at a time.
| # | Question | Skills | Marks | From |
|---|---|---|---|---|
| 1 | A quadratic pattern, a difference of 33, then adding m to every term | Quadratic patterns and second differences, Finding the general term Tn | 9 | May/June 2025 Q3 |
| 2 | Find b from the first difference, then the 60th term | Quadratic patterns and second differences, Finding the general term Tn | 10 | November 2022 Q3 |
| 3 | A pattern that turns, and where its terms start to fall | Quadratic patterns and second differences, Finding the general term Tn | 11 | November 2021 Q3 |
| 4 | 3 ; 7 ; 12 ..., then what must be added to reach 13 527 | Quadratic patterns and second differences, Finding the general term Tn, Arithmetic sequences and series | 15 | May/June 2024 Q3 |
| 5 | When a term of the pattern equals a term of its own differences | Quadratic patterns and second differences, Finding the general term Tn | 17 | May/June 2021 Q2 |
| 6 | A linear pattern, its sum, and a sigma expansion | Arithmetic sequences and series, Summing the first n terms, Sigma notation | 10 | November 2021 Q4 |
| 7 | Twenty terms, then seventy-five, and the term that had to change | Arithmetic sequences and series, Summing the first n terms, Solving for n | 14 | November 2024 Q2 |
| 8 | From the 7th term to the number of terms, then the first forty | Arithmetic sequences and series, Solving for n, Summing the first n terms | 16 | May/June 2022 Q2 |
| 9 | T91 and S91, then a quadratic pattern from three differences | Arithmetic sequences and series, Summing the first n terms, Solving for n, Quadratic patterns and second differences | 16 | November 2023 Q2 |
| 10 | An athlete's weekly kilometres as an arithmetic series | Arithmetic sequences and series, Summing the first n terms, A sequence modelling something real | 18 | May/June 2025 Q2 |
| 11 | Find x, show the sum formula, then the sum to infinity | Geometric sequences and series, Summing the first n terms, Convergence and the sum to infinity | 6 | November 2021 Q2 |
| 12 | The general term, then which term of the series equals 15 625 | Geometric sequences and series, Finding the general term Tn, Solving for n | 9 | May/June 2021 Q3 |
| 13 | Does it converge? Then k from a sigma that comes to 29 520 | Convergence and the sum to infinity, Geometric sequences and series, Sigma notation | 9 | May/June 2024 Q2 |
| 14 | k from a sum of 98 301, then a geometric and an arithmetic together | Geometric sequences and series, Sigma notation, Arithmetic sequences and series | 10 | November 2023 Q3 |
| 15 | Circles inside circles, and the series their radii make | Geometric sequences and series, Convergence and the sum to infinity, A sequence modelling something real | 10 | November 2024 Q3 |
| 16 | The 10th term, then the values of t that let it converge | Geometric sequences and series, Sigma notation, Convergence and the sum to infinity | 11 | May/June 2022 Q3 |
| 17 | r from the 6th term, then how many terms reach 114 674 | Geometric sequences and series, Summing the first n terms, Solving for n | 14 | November 2022 Q2 |