How to pass A/L Combined Maths in Sri Lanka
Written by Idasara Academy (drafted by AI agents from the cited sources).
To pass G.C.E. A/L Combined Mathematics in Sri Lanka, work through the National Institute of Education (NIE) syllabus term by term, and both of its parts together. Combined Mathematics I has 27 competencies, from real numbers and functions through calculus to complex numbers and matrices. Combined Mathematics II has 5: vectors, forces, motion, probability and statistics (NIE syllabus, pp. x–xii). The NIE schedules topics from both parts in every term of Grades 12 and 13 (NIE syllabus, pp. 3–6). Practise each topic's questions as soon as you finish it, check what you got wrong, and fix it before you move on. This is the Sri Lankan G.C.E. (A/L), not Cambridge or Edexcel A-Level Mathematics.
"Practise, check, fix" is Idasara's method, not an NIE statement. Every fact on this page names the page of the NIE A/L Combined Mathematics syllabus it comes from.
How do I pass A/L Combined Maths, step by step?
1. What do I actually have to learn for A/L Combined Maths?
The NIE syllabus, effective from 2017, taught over Grades 12 and 13. It comes in two parts. Combined Mathematics I has 27 competencies: algebra, trigonometry, calculus, coordinate geometry, series, complex numbers, counting and matrices. Combined Mathematics II has 5: vectors, systems of coplanar forces, the Newtonian model of motion, probability, and statistics (NIE syllabus, p. i, pp. x–xii). Learn the competency list first, so you always know where a lesson or a question belongs.
→ Free: the A/L Combined Maths hub: every topic and its teaching time
2. Is there anything to do before Grade 12 starts?
Yes. The NIE sets out a basic course for students starting Combined Mathematics, covering basic algebra and plane geometry. Its periods are not part of the syllabus's own periods, and it is meant to be taught before the course begins (NIE syllabus, p. 1). Idasara's suggestion: if your O/L algebra is not secure, work through the basic course first. Indices and logarithms come back almost at once in the first term (competency 6, NIE syllabus, p. 3).
→ Free: Indices and logarithms notes
3. Do I study Pure and Applied one after the other?
No. The NIE runs both parts side by side. In the first term of Grade 12, Combined Mathematics I's topics include real numbers, functions, trigonometry, polynomials and inequalities. Combined Mathematics II covers vectors and systems of coplanar forces acting at a point in the same term (NIE syllabus, p. 3). If your class teaches one part first, the table below shows what the NIE places alongside it.
→ Free: Systems of coplanar forces notes
4. In what order does calculus come?
Over three terms: limits in the second term of Grade 12, then derivatives and their applications in the third term, then integration in the first term of Grade 13 (NIE syllabus, pp. 4–5). Idasara's suggestion: each term builds on the one before it, so practise limits until they are routine before you start differentiating.
→ Free: a Limits model question with "Check my answer"
5. Why do forces and motion come back every term?
Because the NIE spreads them out. Competency 2 of Combined Mathematics II (systems of coplanar forces, through to centre of mass) and competency 3 (the Newtonian model, through to simple harmonic motion) each run across four or five terms, from Grade 12 into the second term of Grade 13 (NIE syllabus, pp. 3–6). Idasara's suggestion: keep one running set of worked mechanics methods and add to it each term, rather than starting again.
→ Free: Newtonian model of motion notes
6. How do I know my answers would earn the marks?
Attempt a question before you read the solution, then compare your working line by line. The NIE expects students to explain their solutions, using diagrams as well as numerical, symbolic and word statements (NIE syllabus, p. 66, on teaching strategy). Idasara's suggestion: write out every step, not just the answer, and keep a list of the steps you missed and re-try those questions a week later.
→ Free: A/L Combined Maths model questions, by lesson
7. How do I revise when I am sitting the examination again?
Topic by topic, starting with the ones you lost marks on. Read the topic's revision notes, then do its practice questions before you move to the next one (Idasara's suggestion).
→ Free: A/L Combined Maths revision notes
How the exam works
G.C.E. A/L Combined Mathematics is set by the Department of Examinations in two papers (the structure for the examination from 2019 onwards). Each paper takes 3 hours, plus 10 minutes' reading time, and has two parts: Part A, 10 compulsory questions at 25 marks each (250); Part B, answer 5 of 7 questions at 150 marks each (750) — 1,000 marks a paper. The final mark is the two papers' total divided by 20, out of 100. (Department of Examinations structure booklet, p. 115.)
Where is my competency?
The NIE numbers this syllabus by competency, not by unit: 27 in Combined Mathematics I and 5 in Combined Mathematics II. Your school's term may cut a competency in a different place (step 3). Teaching time per topic is on the A/L Combined Maths hub, not repeated here.
| Grade · term (NIE) | Part · No. | NIE competency | Free pages |
|---|---|---|---|
| Grade 12 · Term 1 | I · 1 | Analyses the system of real numbers | No free page yet |
| Grade 12 · Term 1 | I · 2 | Analyses single variable functions | No free page yet |
| Grade 12 · Term 1 | I · 4 | Manipulates polynomial functions | Notes · Practice |
| Grade 12 · Term 1 | I · 5 | Resolves rational functions into partial fractions | Notes · Practice |
| Grade 12 · Term 1 | I · 6 | Manipulates index laws and logarithmic laws | Notes · Practice |
| Grade 12 · Term 1 | I · 7 | Solves inequalities involving real numbers | Notes · Practice |
| Grade 12 · Term 1 | I · 8 | Uses relations involving angular measures | No free page yet |
| Grade 12 · Term 1 | I · 9 | Interprets trigonometric functions | Notes · Practice |
| Grade 12 · Term 1 | I · 10 | Manipulates trigonometric identities | No free page yet |
| Grade 12 · Term 1 | I · 17 | Uses the rectangular system of Cartesian axes | Notes · Practice |
| Grade 12 · Term 1 | II · 1 | Manipulates vectors | No free page yet |
| Grade 12 · Terms 1–2 | I · 11 | Applies sine rule and cosine rule | Notes · Practice |
| Grade 12 · Term 1 → Grade 13 · Term 2 | II · 2 | Uses systems of coplanar forces (to centre of mass) | Notes · Practice |
| Grade 12 · Term 2 | I · 3 | Analyses quadratic functions | Notes · Practice |
| Grade 12 · Term 2 | I · 12 | Solves problems involving inverse trigonometric functions | No free page yet |
| Grade 12 · Term 2 | I · 13 | Determines the limit of a function | Notes · Practice |
| Grade 12 · Term 2 → Grade 13 · Term 2 | II · 3 | Applies the Newtonian model to motion in a plane (to simple harmonic motion) | Notes · Practice |
| Grade 12 · Term 3 | I · 14 | Differentiates functions using suitable methods | Notes · Practice |
| Grade 12 · Term 3 | I · 15 | Analyses the behaviour of a function using derivatives | No free page yet |
| Grade 13 · Term 1 | I · 16 | Finds indefinite and definite integrals of functions | Notes · Practice |
| Grade 13 · Term 1 | I · 18 | Interprets the straight line in terms of Cartesian coordinates | Notes · Practice |
| Grade 13 · Term 2 | I · 19 | Applies the principle of mathematical induction | Notes · Practice |
| Grade 13 · Term 2 | I · 20 | Finds sums of finite series | Notes · Practice |
| Grade 13 · Term 2 | I · 21 | Investigates infinite series | Notes · Practice |
| Grade 13 · Term 2 | I · 24 | Uses permutations and combinations for counting | Notes · Practice |
| Grade 13 · Term 2 | I · 26 | Interprets the Cartesian equation of a circle | Notes · Practice |
| Grade 13 · Term 2 | I · 27 | Explores properties of circles | Notes · Practice |
| Grade 13 · Terms 2–3 | II · 4 | Applies mathematical models to analyse random events (probability) | Notes · Practice |
| Grade 13 · Term 3 | I · 22 | Explores the binomial expansion for positive integral indices | Notes · Practice |
| Grade 13 · Term 3 | I · 23 | Interprets the system of complex numbers | Notes · Practice |
| Grade 13 · Term 3 | I · 25 | Manipulates matrices | Notes · Practice |
| Grade 13 · Term 3 | II · 5 | Applies statistical tools to develop decision-making skills | Notes · Practice |
Names come from the competency lists on pp. x–xii of the NIE syllabus and the headings of its detailed syllabus (pp. 8–65), with the NIE's spelling normalised. The terms come from the term-wise breakdown on pp. 3–6: a competency sits in every term that lists one of its competency levels, and rows are ordered by the first of those terms. Each link opens the first free lesson on the site whose title matches that competency; most competencies have several lessons, so a link does not mean the competency is fully covered. Seven competencies have no matching lesson yet, and none is linked. Where the site has two lessons on one topic (the sine and cosine rule; systems of coplanar forces), one of each is linked.
Which path fits you?
- Starting Grade 12 — the basic course, then both parts of the first term (steps 2–3). → Indices and logarithms notes
- In Grade 13 — integration and the straight line in the first term, while mechanics continues (steps 4–5). → Definite integral notes
- Sitting the examination again — topic by topic, weakest first (step 7). → Revision notes
- Studying in Sinhala → සිංහල
- Studying in Tamil → தமிழ்
- A parent — what your child gets, and what it costs. → Pricing · For parents