IEB Grade 12 Mathematics: The Complete Guide

The final exam has two papers:

• Paper 1 (3 hours, 150 marks): algebra, number patterns, functions, finance, calculus and probability.
• Paper 2 (3 hours, 150 marks): statistics, analytical geometry, trigonometry and Euclidean geometry.

Your final Mathematics mark combines the exam with your school-based assessment (SBA) from Grade 12 tests, tasks and the preliminary exam. The IEB's Subject Assessment Guidelines for 2026 set the SBA at 25% of the total assessment; your school confirms the details for your year.

Questions run in a generally progressive order of difficulty, and they are not grouped strictly by topic: an easier trigonometry question can appear early in Paper 2 and a harder one near the end. About 20% of the marks test knowledge, 30% routine procedures, 35% complex procedures and 15% problem solving.

The IEB examines the CAPS Mathematics content, but its papers have a style of their own: more unfamiliar contexts, more questions that combine topics, and fewer marks for routine procedures on their own.

Marks per section, from the IEB Subject Assessment Guidelines (each can vary by about 3 marks):

• Algebra, equations and inequalities: about 25
• Number patterns, sequences and series: about 25
• Functions and graphs: about 35
• Finance, growth and decay: about 15
• Differential calculus: about 35
• Probability: about 15

Functions and calculus together are almost half of Paper 1, and they overlap: cubic graphs, tangents and the graph of $f^{\prime }(x)$ use both. If time is short, secure these first.

• Statistics: about 20
• Analytical geometry: about 40
• Trigonometry: about 50
• Euclidean geometry and measurement: about 40

Trigonometry is the largest single section on either paper. Euclidean geometry rewards practice more than any other section, because the same theorems and reasons come up every year.

• Method, not just answers. Marks are given for each step. A correct answer with no working may not earn full marks.
• Reasons in geometry. Every statement needs an accepted reason. Marks in geometry are usually split between the statement and the reason, so an angle with no reason loses marks.
• Unfamiliar contexts. Questions often put a familiar method into a new setting: a drone's height, a water tank, comparing two loan offers to decide which costs less. Read slowly, write down what is given, and match it to a method you know.
• Bookwork proofs. Some theorem proofs and derivations are examinable word for word, such as the sum of an arithmetic series and the tan-chord theorem. Bookwork is capped at 5 marks in Paper 1 and 6 marks in Paper 2. The derivations of the compound angle and annuity formulae are not examined.
• Notation. Limits on every line in first principles, $k\in \mathbb{Z}$ in general solutions, and units in answers.

• You may use an approved scientific calculator that is not programmable or graphical. Some questions say "without using a calculator": there you must show every step of the exact working, because an answer read off a calculator earns little or no credit.
• Check your calculator is in degree mode before every Paper 2.
• An information sheet with the main formulas is provided (quadratic formula, sequences and series, finance, analytical geometry, trigonometric identities and rules, statistics and the probability addition rule). Formulas for right prisms and cylinders, the conversion between nominal and effective interest rates, special angle values and all geometry theorems are not on it, so learn them.

Weeks 1 to 4: close the biggest gaps. Work through the topic pages for calculus, functions and trigonometry. Do the four practice questions on each page without looking at the solutions first.

Weeks 5 to 7: geometry and finance. Learn every geometry reason and the examinable proofs. Practise finance until you can choose between the future value and present value formulas without hesitating.

Weeks 8 to 9: the smaller sections. Algebra, sequences, probability and statistics. These are reliable marks.

Weeks 10 to 12: full papers under time. Write our practice papers in 3 hours, mark them with the memo, and redo every question you lost marks on. Keep the cheat sheets next to you for quick revision.

If you are behind, a few sessions with a tutor who knows the IEB papers can cut weeks off this plan. Find an IEB maths tutor.

• Results come out after the November exams, usually in January. If a mark is lower than expected, ask your school about the IEB re-mark process early, because the deadlines are short.
• University offers. Many universities make provisional offers on Grade 11 final marks or Grade 12 mid-year marks, then confirm them on final results. Each university sets its own rules. Your Maths mark often decides entry to engineering, commerce, health sciences and science degrees.
• The NBT (National Benchmark Tests). Some universities and programmes ask for the NBT, and some of those also want the Mathematics (MAT) test. Check what your chosen programme needs and book early, because sessions fill up.
• AP Mathematics. Strong learners can take IEB Advanced Programme Mathematics alongside Mathematics. It does not replace Mathematics.

Admission rules differ between universities and change from year to year, so always check the current prospectus.