- The true grading mechanism for 5** (and why there’s no cutoff)
- The actual structure of Papers 1 and 2
- Three-year preparation plan for Form 4 to Form 6
- Distribution of topics in each part of the test paper
- Past Paper Practice Strategies
- Time allocation and test-taking skills
- The five most common scoring patterns
- Three common improvement paths
DSE Mathematics is a weak area for many students, but it is also one of the subjects that is easiest to make progress through systematic preparation - because its assessment content is stable, its scoring mechanism is transparent, and its previous examination papers are sufficient. Want to get in DSE Mathematics 5**, it depends not on talent, but on three things: correctly understanding the grading mechanism, allocating time according to the structure of the test paper, and reducing avoidable loss of points to close to zero.
1. The true rating mechanism of 5**
Let me first correct a widely spread misunderstanding: there is no official cut-off score for DSE. Hong Kong Examinations and Assessment Authority (HKEAA) never announced The raw marks or percentages corresponding to each level of any subject. DSE Category A subjects adopt Level reference performance reporting (Standards-referenced Reporting) - Levels 1 to 5 are evaluated based on whether the candidate's performance meets the established level description of the level, and the original cutoff points required to reach each level will fluctuate with the difficulty of the test paper each year. Therefore, figures such as "90% required for 5** in a certain year" circulated on the Internet are all estimates derived from tuition centers or candidates' self-reported scores, and the difference between different sources can be about 5 percentage points.
How 5** and 5* actually come about
Subdivisions above Level 5 adopt norm reference Method: Among the candidates who have reached Level 5 or above, about 10% of the best performers will get 5**, and about 30% of the following will get 5*. This means two things:
- 5** is a relative ranking, not an absolute score. The same score can be at different levels in different years - if the overall candidate performance is better that year, the threshold will naturally rise.
- Your competitors are all Level 5 and above candidates. In this group, everyone basically knows how to do most of the questions, and the score difference almost all comes from avoidable points loss: review questions, units, rounding timing, completeness of steps, and time allocation.
So what should be used as review goals?
Since there is no reliable score line, it is not practical to use "I want to get 90%" as a goal. We recommend using three controllable indicators instead:
| index | Target | how to measure |
|---|---|---|
| Avoidable loss rate | close to zero | After each time-limited paper, the points lost are divided into "don't know how to do it" and "know how to do it but make mistakes". The latter should be reduced month by month. |
| Repeat error rate | No more than one error of the same type | Whether errors in the same category appear repeatedly in the wrong question book |
| time limit completion rate | Paper 1 is to be completed in 135 minutes with time for examination; Paper 2 is not left blank | Each timed paper records the actual time taken and the number of unfinished questions |
Also note:DSE Mathematics Core does not have school-based assessment (SBA), the overall subject score consists of only two papers, Paper 1 and Paper 2, and there is no third component to "remediate" it. This is why test-taking training pays particularly high dividends.
2. The actual structure of Volumes 1 and 2
Many students study in the wrong direction because they don't understand where the scores come from. The following is the actual structure of the HKEAA assessment syllabus and sample papers.
| test paper | question type | time | Full marks | account for subjects |
|---|---|---|---|---|
| Paper 1 | For traditional questions, all calculation steps must be presented | 2 hours 15 minutes | 105 points | 65% |
| Paper 2 | Multiple choice questions, 45 questions in total | 1 hour 15 minutes | 45 points | 35% |
Paper 1: Three parts, each worth 35 points
This is the item that is most likely to be written incorrectly. Paper 1 is not simply divided into two parts: "short questions" and "long questions";Three Parts: Part A (1), Part A (2) and Part B, each worth 35 points, a total of 105 points.
| part | Fraction | Number of questions | difficulty | Question scope |
|---|---|---|---|---|
| Part A(1) | 35 points | Questions 8 to 11 | simpler | Core and the basic part of the Form 1 to Form 3 courses |
| Part A(2) | 35 points | Questions 4 to 7 | more difficult | Core and the basic part of the Form 1 to Form 3 courses |
| Part B | 35 points | Questions 4 to 7 | deepest | Basic and non-basic parts of Core and Form 1 to Form 3 courses |
This structure has two direct strategic implications:
- Part A (1) is the 35 points that must be scored in full. The questions are relatively simple and have a fixed format. Almost all points lost are avoidable careless mistakes. For students with a goal of 5**, losing points in this part is equivalent to giving up directly.
- Part B is the position that separates 5** and 5*. Part B covers the non-fundamentals, is the most difficult, and also carries 35 points - the same weight as Part A (1). Many students spend most of their review time on moderately difficult questions, and as a result, Part B only gets half the marks for a long time.
For a topic-by-topic breakdown of each part, see DSE Mathematics Paper 1 Strategy.
Paper 2: 45 questions, no negative marks
Paper 2 has a total of 45 multiple-choice questions, each question is worth 1 point.No points will be deducted for wrong answers. The scope is divided into two parts: Part A accounts for about two-thirds of the entire volume, and the topic range covers the basic topics of the Core and the basic parts of the Form 1 to Form 3 courses; Part B accounts for about one-third, and covers the Core and the entire Form 1 to Form 3 courses.
Two key corollaries:
- Junior secondary subjects can be taken directly. Factoring, percentages and interest, similarity and congruence, Pythagorean theorem, quadrature, basic statistics and probability are never out of scope. Students with unstable foundation should read first Top-up courses.
- There is no negative score, so never leave it blank. When time is insufficient, the expected value of filling in a quick estimate must be higher than leaving it blank.
For detailed tips, see DSE Mathematics Paper 2 Guide.
3. Three-year preparation plan for Form 4 to Form 6
5** Very few are from Form 6 in one year. Below is an executable plan broken down into phases.
Form 4: Lay the foundation
- Target: Ensure a solid foundation in the three learning areas of junior secondary and master the introductory topics of senior secondary.
- Key topics: Quadratic equations, functions and their graphs, exponential functions and logarithmic functions, continued polynomials, variations.
- practice: Complete the textbook exercises and supplementary exercises immediately after each topic, do not accumulate them.
- Weekly investment: Approximately 3 to 4 hours outside of class.
- key decisions: Also evaluate whether to take Extended Modules, see M1 M2 comparison.
Form 5: Deepening and Beginning Practice
- Target: Master most of the required topics and start to develop problem-solving strategies rather than single-question skills.
- Key topics: Continuous trigonometry (trigonometric functions, sine and cosine formulas, three-dimensional problems), equations of straight lines and circles, basic properties of circles, permutations and combinations, continuation probability, and measurement of dispersion.
- practice: Start By Topic to practice previous test questions. Each time you complete a topic, you will practice the related questions of the topic.
- Weekly investment: Approximately 5 to 6 hours outside of class.
- Must do: Create a wrong question book. The wrong question book created this year will become the most valuable asset in Form 6.
Form 6 First Semester (September to January): From learning to practice
- September to October: Complete the remaining topics and start systematic By Topic practice. Our Form 6 course is completed in October, and then we will work hard on the papers. See DSE course schedule.
- November to December: Complete all By Topic exercises and start By Year to complete the complete test paper and strictly time it.
- January: On-campus mock test (Mock). The focus is not on scores, but on identifying problems that arise under real pressure—such as a breakdown in time allocation, or getting stuck on a certain type of question as soon as you encounter it.
Form 6 next semester (February to before exams): narrowing and consolidation
- February: Intensive time-limited practice, complete at least 2 to 3 complete papers (Paper 1 plus Paper 2) every week to maintain the rhythm.
- March: The focus turns to reviewing the wrong question book. The marginal return on making new rolls has declined at this stage, and the return on ensuring that similar mistakes are not repeated is higher.
- final stage before exam: Make reservations for the last 2 to 3 years of test papers to keep your hands on them, and review the formulas and common pitfalls list. It’s not a good idea to try to learn new skills.
| stage | time | Key tasks | Weekly maths time (outside of classroom) |
|---|---|---|---|
| Form 4 | annual | Consolidate the foundation of junior secondary, master senior secondary introductory topics, and evaluate elective M1/M2 | 3 to 4 hours |
| Form 5 | annual | Learn core topics, practice By Topic, and create a wrong question book | 5 to 6 hours |
| On Form 6 | September to January | Complete courses, system operation papers, and Mock diagnosis | 6 to 8 hours |
| Form 6 under | February to exam | Intensive time-limited practice, closed loop of wrong questions, and final sprint | 10+ hours |
For more detailed monthly schedule, see Rush 5** Roadmap.
4. Distribution of topics in each part of the test paper
According to the official classification, Core has a total of 17 learning units, which belong to three learning areas, and there are also "advanced learning units".
| Learning scope | unit of study |
|---|---|
| Numbers and Algebra (9 pieces) | Quadratic equations, functions and their graphs, exponential functions and logarithmic functions, continued polynomials, continued equations, variations, arithmetic and geometric sequences and their summation methods, inequalities and linear programming, graphs of continued functions |
| Measurement, Figures and Space (4 pieces) | Basic properties of circles, trajectories, equations of straight lines and circles, continued triangles |
| Data processing (4 pieces) | Permutations and combinations, continuous probability, measurement of dispersion, applications of statistics |
| Advanced Learning Unit | Comprehensively apply knowledge and skills from three areas to solve cross-topic problems |
Typical topics in each part (observed based on previous test papers)
The following are our observations after sorting out previous examination papers, which are summarized from experience.Allotment ratios not announced by the HKEAA-Official documents do not list how many points each subject carries. Any claim that a certain topic is worth a fixed 10% should be viewed with suspicion.
| part | Appears almost every year | Appear occasionally |
|---|---|---|
| Paper 1 Part A(1) | Exponential operations, factoring, basic equations, percentages and error estimation | Polar coordinates and rectangular coordinates, azimuth angles, sequence |
| Paper 1 Part A(2) | Variation, measurement and quadrature, continuous polynomials, coordinate geometry and locus, statistical measurement, plane geometry (properties of circles) | linear programming |
| Paper 1, Part B | Short questions: statistics, probability, sequence, logarithms, quadratic equations and formulas, circles and straight lines Long questions: standard fractions, linear programming, three-dimensional triangles, properties of circles and four centers, and cocircular problems |
Comprehensive cross-topic problem solving |
| Paper 2 | Part A: Junior secondary basics and compulsory basic topics (factorization, percentages, similarity, Pythagorean theorem, quadrature method) | Part B: Core and the entire junior secondary course, including deeper functions and statistics questions |
Based on this, the review priority is: first ensure zero points for the fixed question types in Part A (1), then attack the middle topics of Part A (2), and finally devote yourself to the long question types of Part B. See the question-by-question breakdown Paper 1 Strategy and How to use Past Paper.
5. Past Paper practice strategies
HKDSE was first held in 2012. As of 2026, it has accumulated 15 previous examination papers, as well as sample examination papers and practice papers from the HKEAA. Quantity is never an issue, the issue is how to use it.
Three levels of manipulation
- Simulate actual combat: Strictly time it, finish it in one go, don’t check the book, don’t pause in the middle. Any exercise that relaxes conditions will not reflect true performance.
- in-depth review: Analyze the causes of errors one by one and record them in categories. The time investment in this step should be no less than making the paper itself.
- learn by analogy: Summarize the rules of question types - for example, "Whenever finding angles in a three-dimensional figure appears, the first step is to find a right triangle in a certain plane." This level is the real ability improvement.
Division of labor between By Topic and By Year
| Strategy | Applicable time | practice | effect |
|---|---|---|---|
| By Topic | Form 5 to Form 6 last semester | After each topic, focus on previous questions on that topic | Quickly build question type identification skills with strong pertinence |
| By Year | Form 6 next semester (2 to 3 months before exams) | Do the entire year's test papers and strictly follow the exam time | Training time management, cross-topic switching and examination rhythm |
Sequence is important: doing the entire paper too early will give you a distorted score because you haven’t learned all the topics yet, which is both undiagnostic and a confidence-destroying test.
Four categories of review
Every wrong question should ask "Why am I wrong?" and be divided into the following four categories - because the four categories of errors require four completely different methods of handling:
| error type | Typical performance | Treatment method |
|---|---|---|
| Wrong concept | Wrong use of theorem and unclear application conditions of formulas | Stop reading the paper, go back to the concept and deduce it again, and understand the source and conditions of the formula. |
| programme error | The method is correct but the order of steps is confusing and steps are skipped | Copy the standard solution three times to establish a fixed writing format |
| Wrong review | Missing the conditions, answering the wrong questions, and wrong units | Develop the habit of circling what you want and what you want first |
| Wrong calculation | Positive and negative signs, rounding timing, computer input | Establish calculation habits and computer operation specifications |
Quantity recommendations and most important reminders
- By Topic: Complete at least 30 to 50 past questions in each unit of study.
- By Year: Complete all previous test papers from 2012 to present, and keep the last 2 to 3 years to one month before the exam.
- Quality is far more important than quantity: Finishing 30 papers without reviewing them is not as effective as taking 10 papers and analyzing each wrong question in depth.
6. Time allocation and test-taking skills
Paper 1: 135 minutes, 105 points
The average session takes about 1.3 minutes. Since each of the three parts is worth 35 points but increases in difficulty, time should not be divided evenly. Here are our recommended allocations (and allow time for inspections):
| part | Fraction | Recommended time | Remark |
|---|---|---|---|
| Part A(1) | 35 points | about 25 minutes | The goal is to lose zero points, and the calculation will be done quickly after completion. |
| Part A(2) | 35 points | about 33 minutes | Mark the questions you are stuck on first, and then go back after completing the questions. |
| Part B | 35 points | about 70 minutes | Long questions are divided into small questions, and the steps are written down for each small question. |
| examine | — | about 7 minutes | Prioritize Part A (1) and all marked questions |
Paper 2: 75 minutes, 45 questions
- Each question lasts approximately 1 minute and 40 seconds on average.
- Simple questions should be completed within 1 minute, and the time saved can be saved for later stages.
- Allow 2 to 3 minutes for complex questions. If time expires, the questions will be marked as skipped.
- Reserve about 5 minutes at the end to check and make sure all questions have been answered - no points will be deducted for incorrect answers.
Four Practical Tips for Multiple Choice Questions
- substitution method: If the direct calculation of an algebra question is complex, it is usually faster to substitute the options back into the question for verification, especially for solving equations and inequalities.
- elimination method: When it is difficult to find a direct answer, it is often easy to eliminate obviously unreasonable options - for example, when finding area or length, negative values can be eliminated immediately.
- special value method: For identity or relationship problems involving unknown numbers, substitute simple values (such as 0, 1, 2) for quick testing.
- computer aided: Be proficient in using equation solving, table function verification functions, and statistical functions to quickly find averages and standard deviations. For permitted models and specific operations, see DSE mathematics computer usage skills.
For complete time management and question abandonment rules, see DSE maths Time Allocation.
7. The five most common scoring patterns
In the Level 5 and above group, almost all of the score difference comes from the following five items - and they can all be eliminated through training.
1. Know what to do but make mistakes (to avoid losing points)
questionI have a good foundation and can do most of the questions, but I always lose a few points on each paper due to signs, units, rounding or copying wrong numbers. Since 5** ranks among the top 10% of candidates who are Level 5 or above, these few points are often a level difference.
deal with- After completing each question, take 10 to 15 seconds to quickly check the calculations, especially checking back to the original form.
- Develop the habit of circling the question and the unit it asks for first.
- Mentally repeat the numbers you enter when using the computer to reduce input errors.
- In Paper 1, every step is written clearly, without skipping a step.
2. No review after finishing the Past Paper
questionThe process stops at "do the paper → correct the answer → check the score". As a result, the same questions will still be wrong next time. This is the biggest investment of time with the lowest return.
deal with- Each wrong question is analyzed and recorded according to four categories: conceptual error, procedural error, review error, and calculation error.
- Repeat wrong questions regularly until such mistakes no longer occur.
- The review time should be no less than the examination time.
3. If you don’t understand the concept, continue to write the paper.
questionYou keep making mistakes on a certain topic, but choose "you will understand if you do more". In fact, conceptual gaps will not be automatically repaired by repeated practice, but will only make the wrong patterns more entrenched.
deal with- If you make more than three mistakes on the same topic, you will stop taking the paper.
- Go back to the conceptual level and deduce the formula again to understand its origin and conditions.
- Complete the basic questions first to confirm your understanding before re-entering the practice.
- If you can't handle it on your own, ask your instructor to handle it as soon as possible. See DSE courses.
4. Blind pursuit of the number of papers
question"I have completed 30 papers" sounds very hard, but if there is no pertinence and review, the impact on the performance may be close to zero.
deal with- Each paper has a clear purpose: is it to practice time, practice a certain type of questions, or provide a comprehensive diagnosis?
- It is better to do less and reflect more deeply.
- Measure progress by the rate of repeated mistakes rather than the number of papers completed.
5. Ignore the steps in Paper 1
questionPaper 1 is scored according to the reasoning steps. If you skip too many steps, even if the final answer is correct, points will be deducted. On the contrary, if you don't understand the answer at all and leave it blank, you will give up even part of the points you deserve.
deal with- When using a formula, write the formula first and then substitute the values.
- For geometry and proof questions, reasons must be written, not just conclusions.
- Answers include units (if applicable).
- Even if you don’t know how to do it, write down relevant formulas, set variables, or list known conditions—never leave them blank.
For a more complete list of points lost, see Common missing points and miscalculated numbers in DSE mathematics.
8. Three common improvement paths
The following are three situations we encounter repeatedly in teaching and their corresponding treatments. This is a generalization of case types and not a claim of performance for a specific student.
| Condition | real bottleneck | Processing order |
|---|---|---|
| My grades in school are average, but I get stuck on comprehensive questions. | Conceptual understanding remains on the surface, and only recognizes standard question types, and has no way of starting when conditions are restructured. | Go back to the conceptual level and deduce it again → focus on practicing different question types → then enter the time-limited test paper |
| Good foundation in mathematics but not familiar with DSE question types (For example, transferring from an international course) | Unfamiliar with DSE’s question format, step writing requirements and time structure | Read the scoring requirements and step format first → By Topic to familiarize yourself with the question types → Intensive By Year limited time practice |
| Chronically low scores and lack of confidence | The basic gap in junior secondary spans multiple grades, and the current topic is just a symptom | Do gap diagnosis first → The concept of bottoming out and rebuilding → Gradually merge into regular schedule |
Practical sharing from graduates
The following are shared by named graduates, who list the subjects they studied, the secondary schools they attended, and their studies at university:
- Hayden Kwan (DSE maths Core, M2 | DBS → University of Oxford): Systematic methods and examination-taking skills are mentioned to fully prepare for DSE.
- Ian Chiu (DSE maths Core, M1 | DBS → Actuarial Science, University of Hong Kong): It is mentioned that the tutor explains the thinking process behind each question instead of just giving the answer.
- Anderson Ng (DSE maths Core, M2 | Mong Kok Chamber of Commerce Secondary School → Department of Mathematics, The Chinese University of Hong Kong): Starting from Form 1, I received guidance and my grades gradually entered the forefront of the school.
See the full version Testimonials and Results.
What the three paths have in common
- start early: Students who have just started in Form 6 often have to use the time they should have practiced to catch up on the basics.
- Diagnose first before taking action: Starting to manipulate the paper without knowing where the gap is is equivalent to pouring water into a leaky bucket.
- Track with quantifiable metrics: It can avoid the score loss rate, wrong question re-commission rate, and time-limited completion rate.
Math Insight’s DSE maths Course
our DSE maths tuition courses Taught by instructors who have personally taken the exam as self-taught students and obtained 5** in Core, M1, and M2. Form 4 and Form 5 follow the school's progress and are taught 1 to 2 lessons in advance; Form 6 completes the entire course in October, and then distributes mock paper in each class and reviews it in the next class, forming a closed loop of "practice → correction → explanation → redo".
- Small class teaching: The teacher-student ratio is no more than 1:7, and each class has about 12 to 14 people, taught by two instructors at the same time.
- Three levels of difficulty exercises: Basic concepts, strengthening and deepening, plus Past Paper from famous schools.
- Wrong question closed loop: Assist in establishing a wrong question book and track the re-occurrence rate of each type of error.
- exam training: Multiple-choice question techniques, paper 1 step-by-step writing method, time allocation and question abandonment rules.
- TOLL: Core has 4 classes per month (1.5 hours each) at HK$1,360; compulsory M1 or M2 (2 hours each) costs HK$1,600. See details Charge page.
DSE Mathematics 5** Frequently Asked Questions
How many points does DSE Mathematics 5** cost?
There are no official cutoffs. DSE adopts level-referenced score reporting, and the HKEAA never publishes the original scores or percentages corresponding to each level; Level 5 and above are further subdivided by norm-reference. Among the candidates who reached Level 5 or above, up to about 10% obtained 5**, and then about 30% obtained 5*. The percentages circulated online are all estimates and may vary by approximately 5 percentage points between sources.
How many parts is the volume divided into?
Three parts: Part A (1) (35 points, questions 8 to 11 are easier), Part A (2) (35 points, questions 4 to 7 are more difficult), Part B (35 points, questions 4 to 7 are the most difficult), a total of 105 points, and the exam time is 2 hours and 15 minutes.
Is there any chance to win 5** even if my foundation is not good?
Yes, but it takes time and the right strategy. There is still enough time to review the gap in Form 4 or Form 5; if you have reached Form 6, you should make a diagnosis first and focus on high-frequency high-scoring topics instead of rereading from the beginning.
When should I start making Past Paper?
Form 5 starts with By Topic, and Form 6 starts with By Year in the next semester. Complete the entire paper and strictly time it, and keep the last 2 to 3 years until one month before the exam. See details How to use Past Paper.
MC should click allocate time?
45 questions, 75 minutes, average about 1 minute and 40 seconds per question. Simple questions should be completed within 1 minute, complex questions should be completed within 2 to 3 minutes, and the last 5 minutes should be left to check and ensure all answers are completed.
Don't know how to do some maths on the long question in Paper 1?
Never leave anything blank. Paper 1 is scored step-by-step. There is a chance to get partial points for writing relevant formulas, setting variables or completing the first step of derivation.
Is there school-based assessment (SBA) for DSE mathematics?
No. The Core overall score consists only of Paper 1 (65%) and Paper 2 (35%), without the third component.
How many sessions of Past Paper can be done?
DSE was first held in 2012 and has accumulated 15 sessions as of 2026. It also has HKEAA sample papers and practice papers. The quantity is sufficient, the key is the depth of review.
Will taking M1 or M2 lower my core?
The two share a lot of Algebra and Calculus foundations and will support each other if handled well; but the time allocation must be clearly divided. Please see the subject selection considerations M1 M2 comparison.