Matric past papers · DBE (CAPS) · Paper 1
DBE Grade 12 Algebra and equations
Every algebra and equations question from the DBE NSC Paper 1 papers of November 2021–2024 and May/June 2021, 2022, 2024, 2025, in one booklet — 8 questions, 201 marks, with the official marking guideline for every one of them. Free to download, in English and Afrikaans.
Download
- Questions (English) 12 pages, 0.3 MB
- Solutions (English) 21 pages, 2.1 MB
- Vrae (Afrikaans) 12 pages, 0.3 MB
- Oplossings (Afrikaans) 21 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
8 questions in 1 chapters, ordered so you can work through one skill at a time.
| # | Question | Skills | Marks | From |
|---|---|---|---|---|
| 1 | Four equations, a simultaneous pair, then 2^x times 3^y = 24 | Solving a quadratic by factorising, The quadratic formula, to two decimal places, Quadratic inequalities, Equations containing a surd, Simultaneous equations, Exponential equations | 24 | May/June 2021 Q1 |
| 2 | A simultaneous pair, then proving a root cannot be real | Solving a quadratic by factorising, The quadratic formula, to two decimal places, Quadratic inequalities, Equations containing a surd, Simultaneous equations, The nature of the roots | 24 | November 2021 Q1 |
| 3 | Reciprocals in a simultaneous pair, then m + n from powers of 2 and 3 | Solving a quadratic by factorising, The quadratic formula, to two decimal places, Quadratic inequalities, Equations containing a surd, Simultaneous equations, Exponential equations | 24 | November 2023 Q1 |
| 4 | Show an expression is always even, then two exponential unknowns | Solving a quadratic by factorising, The quadratic formula, to two decimal places, Quadratic inequalities, Equations containing a surd, Simultaneous equations, Exponential equations, Proving a numerical property | 25 | November 2022 Q1 |
| 5 | A rectangle from its perimeter and area, then a divisibility proof | Solving a quadratic by factorising, The quadratic formula, to two decimal places, Quadratic inequalities, Equations containing a surd, A word problem that becomes an equation, Proving a numerical property | 25 | May/June 2025 Q1 |
| 6 | A substitution into an exponential equation, then a ratio of powers of 2 | Solving a quadratic by factorising, The quadratic formula, to two decimal places, Quadratic inequalities, Exponential equations, Simultaneous equations | 26 | May/June 2022 Q1 |
| 7 | An exponential equation, then a telescoping product P x T | Solving a quadratic by factorising, The quadratic formula, to two decimal places, Quadratic inequalities, Equations containing a surd, Exponential equations, Simultaneous equations | 26 | May/June 2024 Q1 |
| 8 | A simultaneous pair, then when an endless product stays an integer | Solving a quadratic by factorising, The quadratic formula, to two decimal places, Quadratic inequalities, Equations containing a surd, Simultaneous equations, Proving a numerical property | 27 | November 2024 Q1 |