Grade 12 Mathematics · NSC past papers · free

Maths Predictor

Practise real NSC exam questions. The first is of medium difficulty; the next ones get harder after a right answer and easier after a wrong one until the level is found, then keep practising there, in the sections losing the most marks. The predicted exam mark narrows with every question.

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Practice

Section

Predicted exam mark

No marks yet

Mark a first question to see a prediction.

Each question marked narrows the range.

Goal mark

Sections to work on

Where the most exam marks are expected to be lost, from the marks so far.

All sections

Section	In the exam	Marked	Expected

In the exam: the section's marks out of 300 (both papers). Expected: the predicted share of them. A section with few marks marked leans on the overall level.

Wrote a whole paper? Enter its marks

Write a whole past paper from the Department of Basic Education's PDFs in 3 hours, as in the exam, mark it strictly with the memo, then tap each sub-question's marks (0 for one not reached). These marks count in the prediction too.

Marks are kept in this browser only.

How the prediction works

Every question has a difficulty: the share of its marks the candidates earned in that November exam, from the Department of Basic Education's diagnostic report for the year. A right answer to a hard question raises the estimated level more than a right answer to an easy one, and a wrong answer to an easy question lowers it more than a wrong answer to a hard one. Each exam section (Algebra, Calculus, Euclidean geometry and the others) can sit a little above or below the overall level.

The questions: the first is of medium difficulty. While the level is being found, each next question is one with about an even chance of half its marks, so they get harder after a right answer and easier after a wrong one, taking the sections in turn by their exam marks. Once the range is narrow enough (after 8 to 14 questions), the questions stay at the level found, where about 60% of the marks are expected, from the sections losing the most exam marks.

The predicted exam mark is each section's expected share of its marks, weighted by its marks in the exam (both papers, 300 marks), plus how much one learner's mark varies between papers and days. The range is set to hold the exam mark 8 times in 10 if the exam goes like the practice. It narrows with every question marked but never closes completely.

It is an estimate, not a promise of a final mark. Practice marked kindly, or written with the memo open, predicts too high. The difficulties come from samples of candidates' scripts, and the final NSC Mathematics mark also includes school-based assessment, which this does not predict.

Questions, memos and sources

Questions and memos: images from the National Senior Certificate Mathematics Paper 1 and Paper 2 question papers and marking guidelines (memos), November 2021 to 2025, © Department of Basic Education, shown for practice with credit to the DBE. The PDFs are on the DBE's past papers page.

Difficulty: the DBE's National Senior Certificate Diagnostic Reports, Part 1, 2021 to 2025, "Average performance per subquestion" in Paper 1 and Paper 2. The DBE notes that these come from a random sample of candidates' scripts and "might not accurately reflect national averages", but are "useful in assessing the relative degrees of challenge of each question".

Section weights: the DBE's Mathematics Examination Guidelines, Grade 12 (2021). The spread of candidates' marks: the 2024 Diagnostic Report's performance distribution curves in Mathematics.