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Free DSE Mathematics Resources: Official Documents and Practical Study Tools

The most useful free resources are all from the HKEAA and the Education Bureau. The problem is not that they can’t be found, but that most students don’t know what each document is used for.

official source Hong Kong Examinations and Assessment Authority (HKEAA), Education Bureau
Previous examination papers The first session in 2012 and a total of 15 sessions until 2026
The most neglected one"Examination Reports and Questions Album"
Ready-to-use tools on this page 6 items, can be copied and used directly
Not available Ready-made formula sheet download (see reasons below)
It is recommended to check every year Assessment Outline and List of Approved Computers

1. Official resources of the HKEAA and their respective uses

The resources of the HKEAA are not just “exam questions”. The following seven types of documents each have different uses, and most students only use the Form 1 type.

HKEAA official resources and when to use them
resourcecontentPractical useUse stage
Assessment outline Course scope, examination paper structure and assessment mode Check the scope; determine whether old questions or informal materials are beyond the scope of the course Read it once before practicing and check it every year
sample test paper (Sample Paper) Sample test paper format and structure of each section Understand the official explanation of Part A(1), Part A(2) and Part B Form 5
practice paper (Practice Paper) Complete practice paper Additional full volume of limited-time material Form 6
Previous examination papers Paper 1 and Paper 2 of 15 sessions since 2012 Main training materials Full journey starting from Form 5
Marking reference Question-by-question scoring rules and score distribution Mark your own Paper 1 and check whether the steps are complete After each roll
Exam reports and test questions album Markers’ comments on candidates’ performance this year and analysis of common mistakes Understand "where most candidates lose points" and prevent similar mistakes Form 6, matching the year it has been done
List of approved computer models Computer models that can be brought into the exam room Check full model number before purchasing; updated annually Before purchasing and taking the test
Score statistics Percentage distribution of candidates in each subject and level Understand the actual competition (for example, Mathematics Core 5** is about 1.3% to 1.5% in recent years) When setting goals

Official website entrance

Both documents must be rechecked every year and do not use previous years' versions:

Assessment outline— The curriculum and assessment model have been revised. Reviewing with the old version may cover the wrong scope.

List of approved computer models— The list is published every year. Computers must be printed with the label "H.K.E.A.A. APPROVED" or "H.K.E.A. APPROVED", otherwise points may be deducted; bringing in an unauthorized computer that can gain an unfair advantage by retrieving data may result in disqualification from the entire exam. See details Computer strategy.

The most ignored one: "Examination Reports and Questions Album"

Why it's worth watching

It contains the markers' comments on the performance of the candidates for that year, directly pointing out which questions the candidates generally made mistakes or misunderstood. This is the only official information that can help you avoid "the pit where most people fall."

Correct usage
  1. First complete the exam papers for that year by yourself (strictly timed).
  2. Use the marking reference to mark and classify the missing points into four categories.
  3. Then I checked the exam report for that year to see if my mistakes were common mistakes among candidates that year.
Why in this order?

Reading the report first will affect your judgment when writing the paper and distort the diagnosis. The value of the report lies in verify Your error pattern, not advance warning.

The complete method of practice and correction can be found in Past Paper practice method.

2. Education Bureau curriculum documents

The HKEAA defines "how to test" and the Education Bureau defines "what to teach". The following documents are the final basis for judging the scope of the course.

Education Bureau Mathematics Curriculum Documents
documentcontentuse
Mathematics Curriculum and Assessment Guide (Form 4 to Form 6) The overall structure of the senior secondary mathematics curriculum, including the three learning areas of the Core and the advanced learning units Confirm the scope of the Core and the purpose of the course
High School Mathematics Curriculum Explained: Core Detailed content descriptions and notes for each unit of study Check the depth requirements of a certain topic; judge whether the informal materials are out of scope
High School Mathematics Curriculum Explanation: Unit 1 (Calculus and Statistics) M1 Detailed content of 23 learning units in three learning areas Confirm M1 scope - e.g. mathematical induction, derivation of trigonometric functions, integration by parts, hypothesis testing None in M1
High School Mathematics Curriculum Explanation: Unit 2 (Algebra and Calculus) M2 Details of three areas and one advanced unit of study Confirm M2 ranges - e.g. complex numbers, L'Hôpital's rule, arc lengths, matrix diagonalization None in M2
Mathematics Education Key Learning Area Curriculum Guide Overall curriculum framework from Primary 1 to Form 6 Understand how the three learning areas of junior secondary are extended to senior secondary

Official website entrance

The most practical function of course explanation is "exclusion". A large number of so-called guides for M1 and M2 on the Internet mix in each other's content or college-level content - for example, mathematical induction is written as an M1 topic (actually it belongs to M2), and complex numbers or L'Hôpital's Law is written as an M2 topic (actually it belongs to the old system or university level). Use the course explanations to check item by item, and you can eliminate content that you will not test before reviewing. For detailed analysis, see M1 complete guide and M2 complete guide.

3. Why use official resources first?

There are a large number of integrated websites that provide formula tables, answers and detailed explanations. They are convenient, but there are three risks, and the risks are all in the direction of "making you think you are ready."

Three risks of unofficial materials
riskspecific situationas a result of
Range is inaccurate The course has been revised and the materials may not be updated; or the content of M1 and M2 may be confused. Spend time reviewing the content you won’t be tested on and miss out on current units
The answer may be wrong There is no review mechanism for unofficial answers and detailed explanations A wrong answer hurts more than no answer - it confirms you are doing something wrong
Can't see the grading criteria Only official marking references show how marks are distributed across steps I don’t know whether I lost points for “not knowing how to do it” or for “not writing”, and the latter is the easiest to correct.

The third item deserves the most emphasis. Paper 1 is scored based on reasoning steps, so "whether the answer is correct or not" is only half of the information. In the marking reference, it is common to mark method points with M and answer points with A, and in some cases, forward calculation is allowed - meaning that if the answer is wrong but the derivation is correct, a considerable number of points can still be obtained. If there are too many steps skipped, points will be deducted even if the answer is correct. This level of practice will never be seen if you only focus on the answers.

This page does not list the reasons for integrating links in the market

Frankly speaking: many websites that provide free formula sheets integrated with past papers are themselves admissions pages of tuition institutions. We do not refer such links—both because of the three accuracy risks mentioned above and because it is disingenuous to send readers to a competitor’s admissions page.

If what you need is Organized teaching materials, our course itself includes instructor-written notes, three-level difficulty exercises and Mock Paper (see below). If you choose to self-study, it is enough to use official resources and the tools on this page - this is also the actual practice of our chief tutor to obtain 5** in three subjects as a self-taught student.

4. Ready-to-use review tools (6 items)

The following six items can be copied and used directly without downloading any files. They are the formats we actually use in our classrooms.

Tool 1: Four-column format of wrong question book

Question book format and filling examples
Question sourceWhere did I go wrong?MisclassificationRepeat offender record
2019 Paper 1 Part A (2) Question 12When expanding −(2x − 5) only the negative sign is assigned to the first termCalculation error (minus sign assigned)3/2 Repeat offender; 3/16 Not committed; 4/1 Not committed
2021 Paper 2 Question 33The question requires π to be expressed, so I changed it to a decimalWrong review (answer format)3/9 Repeated offense once; did not commit subsequent offenses
On-campus exam: Proof of the properties of a circleI wrote that the angles are equal but did not write the reason.programme error (lack of reason)If you commit two consecutive offenses, you will need to copy the standard format again.

Four rules of use: Do not copy the full text of the question (just write the source); write "How did I originally do it" instead of the correct answer; do it again once a week without looking at the answer; repeat the same category twice in a row and you will be upgraded. The fourth column is where the value of the entire book lies—it shows which types of errors were actually eliminated. See the complete method Common points lost and errors counted.

Tool 2: Four types of error classification card

Four types of errors and corresponding processing
typefeatureHandle it correctly
Wrong conceptDo not understand the conditions for the establishment of the theorem; cannot answer "why do this"Stop working on the paper, go back to the concept and deduce it again
programme errorThe method is correct but the steps are skipped, the order is messed up, and the proof is missing linksCopy the standard solution three times to establish a fixed writing format
Wrong reviewMissing conditions, answering questions incorrectly, units or formats not matchingBefore answering, circle the requirements and conditions given.
Wrong calculationPositive and negative signs, rounding timing, computer inputEstablish verification process (substitution to original formula) and computer operation specifications

Methods to distinguish conceptual errors from the other three categories: After reading the answer, try to do it again without looking at the answer and explaining the reasons for each step. If you can do it, it's a calculation or programme error; if you can't, it's a conceptual error, and you have to go back.

Tool 3: Time allocation table for Paper 1 and Paper 2

Paper 1 (105 points, 135 minutes)
partFractionRecommended timereason
Part A(1)35 pointsabout 25 minutesQuestion types are fixed and should be faster than average to accumulate time
Part A(2)35 pointsabout 33 minutesModerate difficulty
Part B35 pointsabout 70 minutesThe most difficult one, requiring the time saved in the first two parts
examineabout 7 minutesTotaling exactly 135 minutes
Paper 2 (45 questions, 75 minutes, no points will be deducted for wrong answers)
roundstimedo what
first roundabout 30 minutesOnly take questions where the method can be seen at a glance; if you think for more than 20 seconds, fill in the answer first and then skip it.
about 30 minutesHandle questions that require calculations; skip ahead if a single question exceeds 3 minutes
third roundabout 15 minutesSolve the problem; stop solving the problem in the last 3 minutes and confirm that there are no spaces

Conversion basis: Each question in Paper 1 takes about 1.29 minutes (105 minutes ÷ 135 minutes); the average question in Paper 2 takes about 1 minute and 40 seconds. After deducting the answer time, a question-solving budget of about 90 seconds is recommended. For detailed rules and threshold for abandoning questions, see time allocation.

Tool 4: Test Day Checklist

  • Computer model in HKEAA then In the published approved list (check the complete model including suffix)
  • The fuselage has a clear "H.K.E.A.A. APPROVED" or "H.K.E.A. APPROVED" label printed on it that has not faded.
  • There are no stickers, writing or markings on the body
  • New dry batteries have been replaced and backup batteries or backup machines have been prepared.
  • All pre-stored programmes have been tested and work and do not contain any text data.
  • Angle mode set to degrees (display D)
  • Statistics memory cleared
  • Write the clock reading at the time checkpoint in the scratch space (e.g. "8:45 → Question 15")
  • Rules for abandoning questions have been established and implemented on a daily basis

See the complete rules and five common operating mistakes Computer strategy.

Tool 5: Five skills checklist before entering senior secondary

Using these five self-checks before moving from Form 3 to Form 4 is more reliable than looking at scores - because the scoring standards of different schools are not comparable.

  • When you see a quadratic expression, you can determine which factoring method to use within a few seconds.
  • All three methods of solving quadratic equations of one variable (factorization method, formula method, and combination method) can be used, and the meaning of the discriminant can be understood
  • Understand that the combination method and the vertex expression are the same thing
  • Able to deduce equations from parabola graphs (not just draw graphs from equations)
  • Write the complete name of the property at each step of the geometric proof.
  • The exchange of negative exponents and fractional exponents is a no-brainer
  • Have the habit of checking the calculation after solving the problem (substituting back to the original formula)
  • There are errors in the question book and record the error classification

See the levels and curriculum scope of each grade.Overview of grade classes and Form 3 maths tuition.

Tool Six: Dependency Chain Reverse Diagnosis Table

Usage: When a certain topic continues to make mistakes, look to the left to see its prerequisites, test them one by one, and find the first unstable link - that is where you should invest your time.

From prerequisites to subsequent topics
Preconditionsdirect impact
Algebraic simplification, algebra with letters (Form 1)Almost all algebra units
factoring (Form 2 to Form 3)Algebraic fractions, quadratic equations, continued polynomials, functions and their graphs (finding intercepts)
Algebraic Fractions (Form 2)Fractional equations in continued equations
Linear equation of two variables (Form 2)Continuation Equations; Linear Equations and Matrix Solutions of M2
Pythagorean theorem, similarity and congruence (Form 2 to Form 3)Continued equations of triangles, lines and circles
trigonometric ratio (Form 2 to Form 3)Continuous Trigonometry (sine formula, cosine formula, three-dimensional problems)
Exponential laws include negative exponents and fractional exponents (Form 3)Exponential and logarithmic functions; basic calculus operations for M1 and M2
Writing of Geometric Proofs (Form 2 to Form 3)Proof of basic properties of circles; mathematical induction and vector proof of M2
Statistical charts, frequency distribution (Form 1 to Form 3)Measurement of dispersion, application of statistics; statistical field of M1

A complete cross-grade dependency map is available at Overview of grade classes.

5. The correct way to organize formulas

We do not offer ready-made formula sheets for download, this is a deliberate decision.

Reason: Copying a ready-made formula sheet is of little help to memory. The process of organizing is itself a process of memory formation; and a list made by others cannot reflect your personal error-prone points. What's more important is that you don't actually need to memorize most of the formulas. You only need to understand where they come from, because even if you forget the formulas you have understood, you can still push them back in the exam field.

Effective organizing framework

according to official unit of study Group, not by textbook chapter. Core has a total of 17 learning units, which fall into three learning areas:

Grouping framework for formula organization
Learning scopeLearning Units (17 in total)
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 UnitComprehensive application of three areas to solve cross-topic problems

Three things should be written next to each formula

  1. Establishment conditions: For example, the true number of a logarithm must be positive; a certain formula only applies to right triangles. This item is the main source of conceptual errors.
  2. Applicable question types: Whenever I see any question, I think of this formula. This item determines whether you can access it in time in the examination room.
  3. The location I remembered wrongly: For example, "I tried writing the minus sign in the cosine formula as a plus sign." This item cannot be provided by the general formula sheet.

Three classification suggestions

  • Must memorize: Those that cannot be derived quickly but are used frequently (such as quadratic formulas, sine and cosine formulas).
  • Just understand: Can be derived from other formulas (for example, the multiple angle formula can be derived from the compound angle formula).
  • It is enough to know that it exists: Rarely tested and can be checked.

If you take Extended Modules, the formulas for M1 and M2 should be organized separately - the course scope of the two subjects is different, and mixing them together will cause the wrong range. Scope analysis M1 complete guide and M2 complete guide.

6. About computer programmes

It is not recommended to directly copy the code circulating on the Internet. Two reasons: 1. Different models and firmware versions have different command writing methods, variable upper limits, and symbol input methods. If you copy it, it may not work on your machine, and you may even find it in the exam room after making a mistake. 2. Compliance issues – stored programmes No text data may be stored (Including text versions of theorems, formula explanations or prompts), this needs to be checked word for word, and copying and pasting just bypasses this checking step.

Four types of computing aids worth mastering

Practical calculation functions for DSE mathematics
typeuseCorresponding topics
Substitution function (CALC)Substitute special values ​​into calculations containing variables, and use the special value method in Paper 2Algebraic simplification, identities
Equation SolvingQuadratic equations, simultaneous equationsQuadratic equations, continued equations, equations of straight lines and circles
Trigonometric calculationsNumerical calculation of sine formula and cosine formulaContinuation triangle
Statistics functionmean, standard deviation, quartilesmeasure of dispersion

Correct establishment process

  1. Confirm model number at HKEAA then is on the approved list and has the APPROVED label on the fuselage.
  2. Compare it with the model you have manual Enter step by step.
  3. Test with example questions with known answers - e.g. x² − 8x + 15 = 0 Test the quadratic equation and get 5 and 3.
  4. The itemized confirmation does not contain any textual information.
  5. Use it regularly during regular time-limited exercises until the operation becomes muscle memory.

For a comparison of approved models, five common operating errors and complete rules, see DSE Mathematics Computer Guide.

7. Resource usage sequence by stage

What resources should be used at each stage?
stageofficial resourcesTools on this page
Form 3 to Form 4 Education Bureau Curriculum Interpretation (Confirmation Scope); Assessment Outline Five skills checklist; error book format; four types of error classification cards
Form 5 Sample test paper (understand the structure); questions from previous test papers are selected according to topics Wrong question book; dependency chain reverse diagnosis table
Form 6 last semester Previous examination papers are compiled according to year; reference for marking (gradual correction) Time allocation table; four types of error classification card
Form 6 next semester Practice papers; exam reports and test question albums (check the year you have done them) Time allocation table; review of wrong question book
before exam List of computers allowed to be used (check); retained test papers from the last 2 to 3 sessions Exam Day Checklist

A principle that runs through all stages: the review time should be no less than the paper writing time. Doing 30 papers without reviewing them is not as effective as doing 10 papers and analyzing each wrong question in depth - because the improvement in score comes from the elimination of errors, not from the number of questions done. For detailed methods, see Past Paper practice method.

Want organized teaching materials?

The above official resources plus the tools on this page are enough to support self-study - our chief tutor used this method as a self-study student to obtain 5** in Core, M1 and M2. But self-study has a structural limitation:Mark your own Paper 1 according to the grading requirements External assistance is almost necessary, because you have to use the wrong set of judgment standards to judge where you are lacking.

Enroll Math Insight Course Available:

  • Instructor’s own notes and teaching materials: Arranged according to the actual weaknesses of students in the class, not a general handout.
  • Three levels of difficulty exercises: The first level is basic concepts and single-step questions, the second level is intensive deepening and cross-topic synthesis, and the third level is Past Paper from famous schools and previous public examination questions.
  • Mock Paper Closed Loop: Form 6 is distributed in each class and reviewed in the next class, forming "practice → correction → explanation → redo".
  • Correction according to scoring requirements: Compare the marking reference to point out which steps are missing reasons and which sentences should be written but are not.
  • Misclassification feedback: The teaching assistant sorts out the errors and gives feedback to the lecturer to adjust the content of the next lesson.
  • WhatsApp to ask about homework after class: If you get stuck during review, you don’t have to wait until the next class.

The fee is HK$1,360 for 4 Core lessons per month (each lesson is 1.5 hours); additional courses are compulsory M1 or M2 (2 hours per class) HK$1,600; junior secondary 4 classes per month HK$1,280. The first trial lesson is half price, and the first month's tuition will be deducted for daily reading. See details Charge page and FAQ.

The class location is Room A, 9/F, Landmark City, 761 Nathan Road, Prince Edward, Kowloon (About 2 minutes’ walk from Exit C1 of MTR Prince Edward Station), WhatsApp 9651 3910. Please see the instructor’s qualifications Maths Tutors.

Free Resources FAQ

What are the most useful free resources?

The HKEAA's assessment syllabus, sample test papers and practice papers, previous test papers, marking reference, "Examination Report and Question Album", list of approved computers, performance statistics; as well as the Education Bureau's curriculum and assessment guidelines and explanations of each part of the curriculum. These are the only authoritative and free sources.

Which one is the most ignored?

"Examination Reports and Questions Album". It contains the markers' comments on the performance of this year's candidates and analysis of common mistakes. It is the only official information that can help you avoid "the pitfalls that most people fall into."

Why not provide formula sheet download?

Copying a sheet of ready-made formulas is of little help to memorization. An effective way is to organize it yourself: group it into official learning units, indicate the conditions and applicable question types next to each formula, and mark the positions where you have remembered mistakes. The organizing process itself is the process of memory formation.

Can the resources from the aggregation website be used?

There are three risks: the scope is not updated (the course has been revised), the answers may be wrong (no moderation mechanism), and the scoring rubric is not visible (only the official marking reference shows how marks are distributed across the steps). It is recommended to focus on official resources.

Can computer programmes be downloaded online?

Not recommended for copying. The command writing methods of different models are different and may not work; and the stored programme must not store any text data and needs to be checked word for word. You should enter step by step according to the instructions and test with example questions with known answers.

Which documents need to be rechecked annually?

Assessment outline and list of approved computer models. The former is about whether the range is correct, and the latter is about whether it can be brought into the examination room - missing the APPROVED label may result in points being deducted, and bringing in unapproved models may result in disqualification from the entire examination.

Can the old system examination questions be used?

Supplements can be made, but out-of-scope questions must first be eliminated against the current assessment syllabus. Priority should be given to completing DSE previous papers, sample papers and practice papers.

How many previous examination papers are there?

DSE was first held in 2012 and will run for 15 times until 2026. It is recommended that the last 5 to 7 sessions be carefully reviewed and completely reviewed, and the last 2 to 3 sessions be reserved for final simulation one month before the exam.

Resource usage instructions

The copyright of the official documents listed on this page belongs to the Hong Kong Examinations and Assessment Authority (HKEAA) or the Education Bureau. The links are for reference only; the latest official version shall prevail for the content of the documents. The review tools provided on this page (error book format, time allocation table, checklist, etc.) are in the format used in Math Insight classroom. You are welcome to copy and use them yourself.

Official documents and rules will be updated from time to time, especially Assessment outline and List of approved computer models The version published by the HKEAA in that year shall prevail. If there is any discrepancy between the content of this page and official documents, the official document shall prevail.

Related strategies and courses

Official resources plus these tools are enough for self-study

But to correct your paper 1 according to the grading requirements, someone almost needs help · Half price for the first trial lesson · WhatsApp 9651 3910

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