Free Practice Questions for HKDSE Maths M1
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Key Facts: HKDSE Maths M1 Exam
HKDSE Mathematics Module 1 is examined by a single paper of 2 hours 30 minutes carrying 100 marks (HKEAA).
The M1 paper is divided into Section A (50 marks, 8-12 short questions) and Section B (50 marks, 3-5 long questions).
M1 is assessed 100% by conventional long-answer questions, with no multiple-choice component (HKEAA assessment framework).
HKDSE results are graded 5**, 5*, 5, 4, 3, 2, 1, with U for performance below Level 1.
The 2026 HKDSE subject fee for M1 is HK$519 for school and permanent-HKID candidates and HK$1,119 for non-permanent-resident private candidates.
The M1 syllabus has three areas: Foundation Knowledge, Calculus, and Statistics (Curriculum and Assessment Guide, EDB/HKEAA).
Students may take at most one Extended Part module, either M1 (Calculus and Statistics) or M2 (Algebra and Calculus).
Level 5** in HKDSE Mathematics carries 56 UCAS tariff points for international university applications.
HKDSE M1 is a single 2.5-hour, 100-mark conventional paper split into Section A (50 marks) and Section B (50 marks), covering calculus and statistics and graded on the 5**-to-U HKDSE level scale.
Sample HKDSE Maths M1 Practice Questions
Try these sample questions to review concepts for the HKDSE Maths M1 exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1In the expansion of (1 + 2x)^5, what is the coefficient of x^3?
2What is the constant term in the expansion of (1 + x)^4?
3Using the exponential series, the expansion of e^x in ascending powers of x begins with which terms?
4Which series correctly gives the expansion of ln(1 + x) for |x| < 1?
5Solve for x: e^(2x) = 7. Give the value to 4 decimal places.
6A population grows according to N = 200 e^(0.05t), where t is in years. What is the population when t = 10? (4 d.p.)
7The term independent of x in the expansion of (2x + 3/x)^4 contains which power of x as its core? What is that constant term?
8If ln a = 2 and ln b = 3, what is the value of ln(a^2 / b)?
9Using the first two terms of the series for e^x, the approximation e^0.02 is closest to which value?
10What is the coefficient of x^2 in the expansion of e^(3x) using the exponential series?
About the HKDSE Maths M1 Exam
Mathematics Extended Part Module 1 (Calculus and Statistics) is an optional extension to the HKDSE Mathematics Compulsory Part, taken by students who need more mathematics for science, engineering, business and social-science pathways. It is assessed by a single public examination paper of 2 hours 30 minutes carrying 100 marks, made up entirely of conventional questions. The paper is split into Section A (50 marks, 8-12 short questions) and Section B (50 marks, 3-5 long questions), with all questions attempted. The syllabus covers a Foundation Knowledge area (binomial expansion, exponential and logarithmic functions), a Calculus area (differentiation, integration and their applications, plus the trapezoidal rule), and a Statistics area (binomial, geometric, Poisson and normal distributions, sampling and estimation). Results are reported on the HKDSE level scale and are used for university admission through JUPAS and, internationally, via UCAS tariff points.
Exam sponsor: Hong Kong Examinations and Assessment Authority (HKEAA). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.
Questions
100 questions
Time Limit
2 hours 30 minutes
Passing Score
Graded on the HKDSE levels 5**, 5*, 5, 4, 3, 2, 1 and U; the Extended Part level is reported separately from the Compulsory Part.
Exam / Certification Fees
2026 HKDSE: HK$519 per subject (school candidates and permanent-HKID private candidates); HK$1,119 per subject for non-permanent-resident private candidates.
Exam sponsor websiteFees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.
Our practice resources: topics covered
We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.
Foundation Knowledge
Binomial expansion of (a+b)^n, the number e and the exponential/logarithmic series, natural logarithms, and exponential growth and decay models.
Calculus
Limits and the derivative, differentiation rules (chain, product, quotient, implicit), second derivatives, applications to rate of change, maxima/minima and curve sketching, indefinite and definite integration, area, and the trapezoidal rule.
Statistics
Conditional probability and Bayes' theorem, discrete random variables and expectation, binomial, geometric and Poisson distributions, the normal distribution and its applications, sampling, point and interval estimation, and basic hypothesis-testing and correlation/regression ideas.
Preparing for the HKDSE Maths M1 Exam
What You Need to Know
- Passing score: Graded on the HKDSE levels 5**, 5*, 5, 4, 3, 2, 1 and U; the Extended Part level is reported separately from the Compulsory Part.
- Exam length: 100 questions
- Time limit: 2 hours 30 minutes
- Exam / certification fees: 2026 HKDSE: HK$519 per subject (school candidates and permanent-HKID private candidates); HK$1,119 per subject for non-permanent-resident private candidates. Official sources
Using Our Practice Resources
- Work through all 100 available questions
- Review every answer and explanation
- Track weak areas and revisit them
- Use our AI tutor for tough concepts
HKDSE Maths M1: Suggested Study Strategy
Frequently Asked Questions
What is HKDSE Mathematics Module 1?
Module 1 (Calculus and Statistics) is one of two optional Extended Part modules of HKDSE Mathematics, taken in addition to the Compulsory Part. It emphasises applied calculus and probability/statistics and is popular with students heading into business, social sciences and life sciences.
How long is the M1 examination and how is it structured?
M1 consists of a single paper lasting 2 hours 30 minutes and carrying 100 marks. Section A has 50 marks (8-12 short questions) and Section B has 50 marks (3-5 long questions); candidates must attempt all questions, which are all conventional (long-answer), with no multiple-choice section.
How is M1 graded?
M1 is reported on the HKDSE seven-level scale with distinction sublevels: 5**, 5*, 5, 4, 3, 2, 1, and U (Unclassified) below Level 1. The Extended Part result is reported separately from the Compulsory Part level.
What is the difference between M1 and M2?
Module 1 (Calculus and Statistics) focuses on applied calculus and statistics (distributions, estimation), while Module 2 (Algebra and Calculus) focuses on pure algebra (mathematical induction, matrices, vectors) and more rigorous calculus. Students may take at most one of the two modules.
Are calculators allowed in the M1 exam?
Yes. Approved electronic calculators and mathematical drawing instruments may be used. Unless otherwise specified, numerical answers should be given exactly or correct to 4 decimal places.
How much does it cost to sit HKDSE M1 in 2026?
For the 2026 HKDSE, school candidates and permanent-HKID private candidates pay HK$519 per non-language subject such as M1; non-permanent-resident private candidates pay HK$1,119 per subject, plus a HK$595 initial fee for private candidates.