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H2 Mathematics combines pure mathematics with probability and statistics. For JC students and parents, the useful questions are what the examination covers, which earlier skills it assumes, and how to turn that coverage into a workable learning plan.
This curriculum guide uses SEAB syllabus 9758 for the 2026 and 2027 examinations, checked on 18 September 2026. The topic coverage and paper format summarised here agree across those two documents. Use the syllabus for your examination year, rather than the year you enter JC1.
Start with the paper format, use the checklist to identify gaps, then try the short modelling example. The suggested teaching sequence is illustrative: confirm actual topic order and school assessment coverage with your teachers.
Both examination papers last three hours and carry 100 marks each. Paper 2 includes pure mathematics as well as statistics.
Use the topic checklist with an attempted question beside each rating; recognising a chapter title is not evidence of readiness.
Repair algebra, logarithms, trigonometry and basic calculus while learning new H2 topics.
MF27 is shared across mathematics syllabuses. A formula appearing in it does not by itself make that topic examinable in H2.
School teaching order varies. Choose revision priorities from your mistakes and upcoming assessment scope.
Which syllabus and examination year should you use?
The primary references are SEAB’s 2026 H2 Mathematics syllabus and SEAB’s 2027 H2 Mathematics syllabus. In both, the examination scheme is on page 5, the content outline on pages 6–13, and assumed Additional Mathematics knowledge on pages 14–15. Pages 3–4 explain the assessment objectives and calculator expectations.
This page is a planning guide, not a replacement for the detailed inclusions and exclusions in those PDFs. It retains one curriculum URL so you can return to the same reference as your course progresses.
H2 Math paper format: what each paper tests
According to the examination scheme on page 5 of the 2026 syllabus and 2027 syllabus:
- Paper 1: three hours, 100 marks, 50% of the total; 10–12 pure mathematics questions.
- Paper 2: three hours, 100 marks, 50% of the total. Section A has 4–5 pure mathematics questions worth 40 marks. Section B has 6–8 probability and statistics questions worth 60 marks.
- Answer every question in both papers. Paper 1 and Paper 2 Section B each contain a real-world application question worth at least 12 marks.
Together, this gives 140 pure mathematics marks and 60 probability/statistics marks out of 200: a 70:30 split. It does not specify a guaranteed allocation for individual chapters. Do not prepare for Paper 2 as though it were statistics only.
An approved graphing calculator without a computer algebra system is expected. Follow each question’s instructions: when unsupported calculator answers are disallowed, show mathematical steps, not a list of calculator commands. Sketch graphs used to obtain a solution. See page 4 of the syllabus.
For practice, write the model or equation before reaching for the calculator, and explain what the result means afterwards. This makes mistakes in setup easier to diagnose.
A topic checklist you can actually use
The groups below follow the content outline, pages 6–13, also checked against the 2027 outline. The self-check prompts are suggested practice tasks, not a complete list of examination requirements.
Mark each group not yet taught, needs repair, or can apply independently. Beside each rating, record a question you attempted and the step where you needed help. Revisit the rating after a different question, rather than immediately after copying a solution.
For the hypothesis-testing topic, practise connecting p-values, critical regions and conclusions in one complete population-mean test.
Functions, graphs, equations and inequalities
Can you explain domain and range, decide whether an inverse or composite exists, sketch transformations and parametric graphs, and solve equations or inequalities?
Check: Explain why a denominator cannot be zero before stating an inequality solution. If an inverse fails, identify the repeated output rather than just saying “not one-to-one”.
Sequences and series
Can you move between terms and sums, work with AP/GP and recurrence relations, and check convergence?
Check: Write out the first few terms of a recurrence before using a calculator. For an infinite geometric series, verify ${|r|\lt 1}$ before using its sum.
Vectors
Can you use vector operations, dot and cross products, and line/plane geometry to find angles, intersections and point-to-line or point-to-plane distances?
Check: Draw the relationship and identify a direction or normal vector before choosing a formula. The current syllabus excludes the shortest distance and common perpendicular between two skew lines. Use the Vectors core-concepts guide for the underlying tools, keeping this scope boundary in mind.
Complex numbers
Can you calculate in Cartesian form, interpret modulus, argument and conjugates, use conjugate roots, and represent operations on an Argand diagram?
Check: Multiply a number by ${i}$ and explain the change in its position. Do not add polar/exponential-form methods or De Moivre’s theorem to your H2 revision checklist; they are outside the listed current content.
Calculus and Maclaurin series
Can you connect derivatives to graphs, handle implicit and parametric differentiation, solve optimisation/rate problems, use Maclaurin approximations with their conditions, integrate using the required techniques, calculate areas/volumes, and formulate and solve separable differential equations?
Check: In an optimisation problem, state the feasible domain and justify the maximum or minimum. In a differential equation, use the given condition to determine the constant and interpret the solution.
Probability and statistics
Can you organise counting cases, distinguish independence from mutual exclusivity, and use conditional probability? Can you work with discrete random variables, binomial and normal models, sampling, tests for a population mean, and correlation/linear regression? For population-mean tests, the syllabus specifies a normal population with known variance or a large sample from any population.
Check: State why a model fits before calculating. For a test, identify the population mean being tested and interpret the decision. For regression, explain whether a prediction is interpolation or extrapolation and whether it is sensible.
Poisson distributions and normal approximation to the binomial are not part of the current H2 content outline; do not import them from older notes or the shared formula booklet.
Prerequisites: repair the tools that keep interrupting you
SEAB assumes O-Level Mathematics and lists specific Additional Mathematics foundations on pages 14–15, also present in the 2027 document. These are assumed mathematical skills, not a statement of school admission grades. Check subject-entry criteria with the school.
Use these short diagnostic tasks to locate a gap:
Try these A Math-to-H2 worked examples to see how familiar algebra and differentiation develop into new H2 decisions.
Algebra, surds and logarithms
Simplify ${\frac{x^2-9}{x-3}}$ and state its restriction. The result is ${x+3}$, with ${x\ne3}$; cancelling a factor does not restore the missing input. Solve ${\ln(x-1)=\ln 4}$: the answer is ${x=5}$, consistent with ${x>1}$.
Also check completing the square, quadratic root conditions, polynomial division, partial fractions and surd manipulation. If you lose time on these inside a calculus question, practise that exact operation before retrying the longer problem.
Give trigonometry extra attention
In our teaching experience, trigonometry is often the weakest prerequisite. Algebra, surds and logarithms can become more manageable with sustained practice, but trigonometry deserves its own foundation check rather than being treated as one more algebra exercise.
Check whether you can explain radians, recognise trigonometric graphs, use identities and the R-formula, and find every solution within a stated interval. Separate these skills: knowing an identity does not necessarily mean you can choose when to use it.
For example, ${\sin x=1/2}$ on ${0\le x\le2\pi}$ gives ${x=\pi/6}$ or ${5\pi/6}$. The calculator's inverse sine gives the principal value ${\pi/6}$. Sine is also positive in the second quadrant, giving ${\pi-\pi/6=5\pi/6}$. Check both against the interval. One calculator inverse value is not the full solution set.
If this step is unclear, revisit the sine graph or unit circle, then try another equation over a stated interval. Keep coordinate geometry on your checklist too: can you find the centre and radius of a circle from its equation?
Basic calculus
Differentiate ${e^{2x}}$ and integrate ${e^{2x}}$. The answers are ${2e^{2x}}$ and ${\frac12 e^{2x}+C}$. Explain why the factor changes instead of memorising both as unrelated rules.
Check product, quotient and chain rules, gradients, rates of change and basic antiderivatives. Repair these alongside your current chapter; you do not need to postpone every H2 question until all secondary work feels perfect.
An illustrative JC1 and JC2 learning sequence
A typical planning pattern is to build core pure mathematics in JC1, then complete remaining content and develop statistics and mixed-paper practice in JC2. This is an illustration, not a SEAB-prescribed teaching order or a promise about any school’s timetable. Some schools start statistics earlier or introduce pure topics later.
- Early JC1: revisit algebra and trigonometry alongside graphs, functions and inequalities. Practise explaining domain restrictions and graphical reasoning.
- As JC1 progresses: connect sequences and series, develop calculus, and give vectors repeated practice once taught. Introduce complex numbers wherever your school places them.
- Across JC2: complete remaining pure topics; connect counting and probability to distributions, then sampling and hypothesis testing. Include correlation and regression.
- Before each school examination: confirm the tested chapters, repair specific gaps and practise mixed questions within that scope. Move towards full three-hour papers when the full syllabus has been taught.
Learning order and revision order are different. If you already know the foundations, calculus may be your next priority; if algebra keeps breaking your solutions, start with that bottleneck. Use the H2 Math revision-order guide for the fuller decision process. School mid-year, promotional and preliminary examinations are local milestones, not extra SEAB papers.
Keep vectors practice regular. Students often tell us they understood a concept, left it for a while, and then forgot how to use it. Needing a review is not a reason to panic or decide you cannot do vectors. Revisit the specific idea, attempt a question, and return to it regularly. For example, rotate a short block on dot products, projections or line-and-plane relationships alongside your current topic. Focus on recognising the idea again, rather than expecting to remember every method after one round of practice.
Worked example: turning an unfamiliar situation into mathematics
Original practice question. A rectangular outdoor display uses a wall as one side. There are 24 metres of edging for the other three sides. The display can extend at most 5 metres out from the wall. What dimensions give the largest area?
Let ${x}$ metres be the distance out from the wall and ${y}$ metres the length along it. Two sides extend out from the wall, so together they use ${2x}$ metres of edging. Only the opposite side needs the remaining ${y}$ metres; the wall side needs none. The edging constraint gives
$$2x+y=24,\qquad y=24-2x.$$
The area is therefore
$$A(x)=x(24-2x)=24x-2x^2.$$
Before differentiating, translate “at most 5 metres” into the feasible domain ${0\lt x\le5}$. Zero is excluded because the display must have a positive width; 5 is included because it is allowed. The corresponding length ${y=24-2x}$ stays positive throughout this interval. Differentiate:
$$A\prime(x)=24-4x.$$
Setting the derivative to zero gives ${x=6}$, but that lies outside the allowed domain. On ${0\lt x\le5}$, the derivative is positive, so the area increases throughout the feasible interval. The maximum occurs at ${x=5}$, giving ${y=14}$ and
$$A_{\max}=5\times14=70\text{ m}^2.$$
Independent check: completing the square gives ${A(x)=72-2(x-6)^2}$. Among allowed values, ${x=5}$ is closest to 6, again giving 70 square metres.
Plausible wrong turn: reporting ${x=6}$, ${y=12}$, and 72 square metres after solving ${A\prime(x)=0}$. The differentiation is correct, but the proposed display extends too far from the wall. Setting the derivative to zero identifies a stationary point of the unrestricted quadratic; it does not check whether that point is allowed. Here the maximum is at the permitted boundary, where the derivative need not be zero.
A useful checking routine: state the domain, find any stationary points within it, examine the permitted boundaries, and give your answer in the original units. In this example, the positive derivative already shows that the largest allowed width gives the largest area.
The useful H2 habit is to connect the context, equation, domain and conclusion. A familiar quadratic becomes a modelling question when you must decide what the variables represent and which answers are feasible. This short example illustrates that habit; it is not a full-length examination application question.
MF27: a reference booklet, not a syllabus checklist
SEAB supplies a formula/results list in the examination. Its current MF27 booklet is shared across multiple mathematics syllabuses, as shown on SEAB’s 2026 syllabus page. For example, MF27 page 5 lists Poisson and geometric distributions, but their presence does not add them to H2 syllabus 9758.
Use the MF27 resource and download beside the syllabus. Practise finding a relevant result, identifying its conditions and substituting correctly. Keep a separate note of methods you need to construct yourself, such as translating a situation into an equation or deciding whether an answer is physically possible.
When older worksheets contain unfamiliar content, check the current syllabus’s inclusions and exclusions before spending revision time on it.
What to revise next
Choose one checklist item marked “needs repair” that affects your current school work. Attempt a question with notes closed, identify the first step you cannot justify, review that specific idea, then try a different question. Keep a brief record: topic → missing step → repair → retest result.
Use the H2 revision toolkit to choose an appropriate resource rather than collecting several sets of notes. Keep taught vectors skills in regular rotation and revisit calculus as your algebra becomes more fluent.
If you need help identifying prerequisite gaps or organising practice around your school’s pace, see Tim Gan Math’s H2 Math tuition programme. The course page is the place to check current class arrangements and fees; this guide focuses on the syllabus and learning decisions.
Conclusion
Use the syllabus to define the scope, and your attempted questions to decide the next step. A topic is useful to you when you can choose a method, explain its conditions and interpret the answer.
Action Steps:
Confirm your examination year and school assessment scope.
Rate the topic groups using a recent attempted question as evidence.
Repair one prerequisite gap, then retry it inside an H2 question.
Use MF27 during practice and check unfamiliar material against the syllabus.
Your next revision session should have a specific question to answer, not just a chapter title to reread.