H3 Mathematics Tuition in Singapore

H3 Mathematics Tuition

At SG Maths Tuition, I teach H3 Mathematics (Syllabus 9820), also commonly called H3 Maths or H3 Math, strictly one-to-one in Singapore. With proof-writing, that individual attention is where the marks are won.

H3 Mathematics is taken in addition to H2 Mathematics by students with strong ability and genuine interest in the subject. It is a different kind of course. Instead of piling on techniques, the syllabus turns on proof and rigour: methods of proof, numbers and modular arithmetic, functions, sequences and limits, classical inequalities, and counting.

The assessment is unusual too. One 3-hour paper of 80 marks sets just six questions: five worth 10 to 14 marks each, and a final question worth 16 to 20 marks that asks students to read a short mathematical text and respond to it. The right answer alone earns little. Marks go to a complete, watertight argument.

Almost no student arrives able to write proofs. That is exactly what I teach: building arguments, finding the idea that opens a problem, and writing it up to the standard the examiners demand.

H3 Mathematics sits on top of H2 Mathematics, so a secure H2 foundation comes first, and I teach both. See my JC Maths overview for how H1 Math, H2 Math, H2 Further Mathematics, and H3 Mathematics compare, or my H2 Further Mathematics page for the double-maths route.

Why Choose SG Maths Tuition for H3 Mathematics Tutoring?

Small group of students reviewing maths together on a tablet

One-to-one lessons that critique every proof

H3 work is discussed, not lectured, so I teach it strictly one-to-one. I workshop proofs with you: compare attempts, hunt for gaps, trace more than one route to the same result, and critique every line of a written argument until it is watertight.

Portrait of Dr. Ng explaining a maths concept

A Tutor Who Knows the Subject Well

I hold a Ph.D. in Mathematics and a B.Sc. First Class Honours in Mathematics from the National University of Singapore, with over 15 years of tutoring experience. H3 Mathematics is the one A-Level subject where research training pays off directly. Building and judging proofs is the daily work of a mathematics Ph.D., and I teach that craft firsthand, in line with the H3 syllabus.

Student working through maths practice beside graphed results

Steady Progress, One Foundation at a Time

Over their time with me, many JC students go on to gain two to three grades. With H3 students the progress shows up on the page: arguments that started as scattered calculations harden into structured proofs with every claim justified. That is exactly what the H3 paper rewards.

Reference books and notes tabbed by maths topic

Meeting the Demands of H3 Mathematics

The H3 paper sets only six questions in three hours, so there is nowhere to hide. Each question is a sustained piece of reasoning worth 10 to 20 marks, and the final one means reading an unfamiliar mathematical text and working with it on the spot. All of this runs alongside the full H2 syllabus. I train the mathematics and the stamina together.

Calculator and stationery laid out for exam practice

My Teaching Methodology

I teach proof as a craft. First the standard methods (induction, contradiction, counting arguments), then the habits of rigour: state what is assumed, justify every step, check the edge cases. Students rebuild their own flawed proofs until they hold, because at H3 Mathematics the write-up is the answer.

Calculator and notebook ready for timed maths practice

Comprehensive and Customised Learning Materials

H3 practice material is scarce, so I write my own: summary notes on each content area, problem sets in number theory, inequalities, and counting graded from approachable to past-paper standard, and short mathematical texts with questions to rehearse the reading-based format of the final exam question.

Intensive Examination Preparation

My mock papers follow the H3 format, six long questions in three hours, so students learn to judge when an approach is working and when to drop it. Timed practice covers the text-based final question, and I time the intensive revision to line up with each student's H2 exam prep.

Consistent Feedback and Monitoring

Every written proof gets detailed feedback: whether the argument is truly complete, where the rigour slipped, and how an examiner would mark it. Parents get regular updates on progress in both H3 Mathematics and the underlying H2 work, since the two move together.

Step-by-Step Teaching Methodology

Review the student's recent H3 attempts and school assignments to gauge proof-writing maturity and pin down content gaps in number theory, inequalities, and counting. Pin down the dates that count (weighted assessments and the H3 paper itself), and build the schedule around them.

Build a study plan: the methods of proof first, then the content areas, all kept in step with the student's parallel H2 workload. Set goals and give honest guidance on the work required.

Work through problems and drill full proof write-ups, including reading short mathematical texts and answering questions on them, as the final exam question requires. Reinforce with timed attempts at long-form questions.

Give consistent feedback on each written proof, covering completeness, rigour, and presentation, and steer students and parents on priorities ahead of assessments and the A-Level paper.

Topics covered for H3 Mathematics (Syllabus 9820)

Proof and Reasoning

Mathematical statements: conditionals, quantifiers, and the converse, inverse, contrapositive, and negation of a statement
Methods of proof: direct proof, disproof by counterexample, proof by contradiction, and proof by cases
Mathematical induction
Reasoning principles: the pigeonhole principle, the symmetry principle, and combinatorial arguments
Problem-solving heuristics: working backwards, considering cases, and solving a simpler or related problem
Mathematical investigation: forming and testing a conjecture, generalising or finding special cases, and completing or critiquing a given solution
Reading and responding to a short mathematical text, the skill tested by the final question of the paper
Constructing and writing complete, rigorous arguments

Content Areas

Functions, sequences and series, including summation by the method of differences
Introduction to limits: comparing growth rates and operations on limits
Complex numbers
Calculus: reduction formulae and improper integrals
Counting: the bijection principle and the inclusion-exclusion principle
Inequalities: AM–GM, Cauchy–Schwarz, and the triangle inequality
Congruence and modular arithmetic

Assessed in a single 3-hour paper of 80 marks with six questions: five worth 10 to 14 marks each, and a final question worth 16 to 20 marks based on a short mathematical text.

H3 Mathematics One-to-One Booking

H3 Maths one-to-one classes: 2 hours per class

Weekdays (Tue-Fri)

7:00 pm

Saturday

4:00 pm
6:00 pm
8:00 pm

Sunday

4:00 pm
6:00 pm
8:00 pm

Slots subject to availability; contact to confirm.

Frequently Asked Questions (FAQ) - H3 Mathematics Tuition

Who should take H3 Mathematics, and how is it assessed?

H3 Mathematics is taken in addition to H2 Mathematics by students with strong ability and interest in the subject. The emphasis throughout is on proof and rigorous reasoning.

It is assessed in a single 3-hour paper of 80 marks with six questions: five worth 10 to 14 marks each, and a final question worth 16 to 20 marks that asks students to read a short mathematical text and respond to it.

When are lessons held, and how long is each one?

For H3 Maths one-to-one lessons, these are the usual timeslots:

Tue-Fri: 7:00 pm.

Sat: 4:00 pm, 6:00 pm, 8:00 pm.

Sun: 4:00 pm, 6:00 pm, 8:00 pm.

Each lesson runs 2 hours. WhatsApp me to confirm a slot.

Are H3 Maths lessons one-to-one?

Yes. I teach H3 Maths strictly one-to-one.

Reason: H3 Mathematics turns on proof and rigour, and almost no student arrives able to write proofs to the standard the examiners demand.

One-to-one lets me critique every line of a written argument, work through more than one route to a result, and build proof-writing from where each student actually is.

It also means no question goes unasked, and we can dwell on a single proof for as long as it takes.

Do you offer trial lessons?

Yes, I offer trial lessons for new students.

Please WhatsApp me or Contact me to arrange for a trial lesson.

How much are the fees?

H3 Maths is taught one-to-one. Please WhatsApp me or Contact me for one-to-one rates, available timeslots, and payment due dates.

Where can I find your payment, refund, holiday, and cancellation policies?

These policies are the same for all levels and are listed in full in the FAQ on my homepage, covering payment methods (PayNow / bank transfer), the refund policy for new students, public holidays and school vacation periods, and class cancellations and make-ups.

Is the syllabus aligned with MOE requirements?

Yes. My teaching follows the latest MOE syllabus for H3 Mathematics, and I monitor the questions set in the Cambridge GCE A-Level examinations as well as in promo and prelim papers set by individual JCs.

What materials do students receive?

Summary notes of each content area, topical worksheets and problem sets, mock quizzes, and full length practice papers, including short mathematical texts with questions, to rehearse the format of the final exam question.

Do you provide exam preparation?

Yes, I provide June holiday intensive revision bootcamps, mock tests and timed quizzes, and intensive revision before major exams. For H3 students this means timed practice on full six-question papers and repeated, marked proof write-ups.

A Message from Dr Ng

Mathematics has been my full time work as a private tutor ever since I completed my Ph.D. in Mathematics at the National University of Singapore (NUS) in 2011, following the Bachelor of Science (B.Sc.) First Class Honours degree I read at NUS in 2002. Of all the A-Level subjects, H3 is the one that feels nearest to the research mathematics I once lived in: proof, rigour, and ideas drawn out from first principles. What keeps me at it full time is the quiet pleasure of sitting beside one student and tracing, line by line, the argument that finally holds.

Individualised Lessons, Lasting Understanding

For H3 Mathematics, I work through each topic in a steady, settled order so the ideas have room to land. We take time to familiarise ourselves with the kinds of questions that come up in weighted assessments and examinations. Wherever a student starts, my aim is simply to help their understanding grow and their confidence with proof steady. When a shaky idea surfaces, we slow down and sort it out together, then return to it in fresh problems until the reasoning sits firmly. I keep the timing in step with each student's wider H2 preparation, so neither course gets crowded out.

My Academic Credentials

These credentials say I have spent a long time close to research mathematics, the kind of thinking H3 rewards. What they cannot show is the steady, one-to-one work of helping you write a proof that holds.

Ph.D. in Mathematics, National University of Singapore (NUS)

B.Sc. First Class Honours in Mathematics, NUS

GPA: 4.9 / 5.0 (Placed on Dean's List for 4 Semesters)

Associate Faculty, Singapore University of Social Sciences (SUSS)

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