- Official Structure and Scoring Rules for Paper 2
- "No points will be deducted for wrong answers" How to determine the strategy for the entire paper
- Time management: three-round answering strategy
- Four quick fixes
- Compliant use of computers
- Two mistakes that will lead to loss of points
- Common pitfalls across topics
- Practice methods
1. Official structure and scoring rules of Paper 2
Paper 2 is a multiple-choice question paper of DSE Mathematics Core, accounting for the subject 35%, exam time 1 hour 15 minutes,common 45 questions, 1 point for each question,No points will be deducted for wrong answers.
Differences in scope between Part A and Part B
| part | Occupy the whole volume | Question scope |
|---|---|---|
| Part A | About two-thirds (about 30 questions) | in Core Basic topics and in Mathematics from Form 1 to Form 3 basic part |
| Part B | About one-third (about 15 questions) | Core and entire Form 1 to Form 3 Mathematics Course |
This table has an important meaning: junior secondary topics are directly testable in Paper 2. Factoring, percentages and interest, similarity and congruence, Pythagorean theorem, quadrature method, basic statistics and probability - they not only appear in Part A, but are also covered in Part B entire Form 1 to Form 3 courses. Therefore, it is wrong to say "Junior secondary students will not be tested"; students with unstable foundation should first look back rather than catch up. See Mathematics supplementary courses.
Difficulty distribution
The questions in Paper 2 are roughly arranged in increasing difficulty. The first part corresponds to the basic topics of Part A, and the second part corresponds to the broader scope of Part B. The practical implications are:The accuracy of the questions in the first section determines the basic market, and the questions in the latter section determine whether you can move up to the next level.. If the target is level 4 or above, almost all of the points lost in the early stages are avoidable careless mistakes - the least points worth losing.
Regarding "How many questions must be answered correctly in Paper 2 to achieve a certain level": There is no such correspondence.never announced The raw scores or percentages corresponding to each level of any subject; Level 5 and above are further subdivided with norm reference. There is no official basis for statements such as "5** requires more than 40 correct answers, 5* requires 36 to 38 questions" circulated on the Internet. For details, see DSE Mathematics 5** Strategy.
2. "No points will be deducted for wrong answers" How to determine the strategy for the entire paper
This is the most important rule of Paper 2, and its corollary is hard and undiscussable:Never leave blank.
Calculate once with expected value
Assume that there are still 5 unanswered questions before closing the paper:
| practice | expected score | illustrate |
|---|---|---|
| Leave all blank | 0 points | Zero points for sure |
| Answer 5 questions randomly (choose one from four) | About 1.25 minutes | 5 × 25% without any downside risk |
| Eliminate an option before answering | About 1.67 minutes | 5 × 33% |
| Eliminate two options before answering | About 2.5 minutes | 5 × 50% |
Since there is no deduction, the expected score for completing the answer never less than Leave blank. Therefore, the correct finishing process is: stop solving problems for the last 3 minutes and confirm that there are no spaces on the answer sheet one by one.
This also changes the criteria for judging abandoned questions. In Paper 1, if you encounter a question you don’t know how to solve, you should write a formula to get method points; in Paper 2, if you encounter a question you don’t know how to solve, you should write down a formula to get method points;Mark and fill in an answer now Skip again - it only takes two seconds to fill in the answer, but it saves 25% of the chance and avoids forgetting to go back to fill in the answer in the end.
3. Time management: Three rounds of answering strategies
45 questions, 75 minutes, average time per question is about 1 minute 40 seconds. However, the difficulty of the questions varies widely, with easy questions taking 40 seconds to complete and difficult questions taking up to 3 minutes. The worst way to do it is to answer questions one by one in order of question number - you will be stuck on a question in the middle for five minutes, and you will not have time to do the easy questions in the later part.
- Round 1 (~30 minutes): Scan and harvest. Proceed from question 1 in order, only do You can see the method at a glance topic. Any questions that require you to stop and think for more than 20 seconds are marked and skipped (remember to fill in an answer first). The goal of this round is to complete most of the questions in Part A.
- Round 2 (approximately 30 minutes): Calculation and processing. Go back to the marked questions and work on the parts that require actual calculations. In this round, substitution method, special value method and computer programme can be used. Any question that takes more than 3 minutes will be skipped again.
- Round 3 (approximately 15 minutes): Puzzle and finishing. Tackle the toughest remaining problems, narrowing them down using elimination and estimation techniques. Stop solving problems in the last 3 minutes.Make sure there are no spaces in each question.
The three segments total exactly 75 minutes. It is recommended to set a time checkpoint:By the 30th minute you should have completed approximately 25 to 30 questions; If you are obviously lagging behind, it means that the threshold for skipping questions in the first round is set too loosely.
marking system
Use three simple marks next to the question number on the test paper to instantly locate the second and third rounds:
✓Done and confident, never look back.?Answers that have been filled in but are not certain will be processed first in the second round.✗There was no direction at all and it was only dealt with in the third round.
The key is Answers have been filled in for all three marks. Marking only determines the priority of review, not whether to answer. For complete time management and question abandonment rules, see DSE maths Time Allocation.
4. Four quick-solving techniques
Paper 2 does not look at the process, only the options. this means Any method that leads to the correct option is scored equally— Including methods that are not "formal solutions".
Tip 1: Substitution method (substitute the options back into the question)
principleInstead of solving the problem forward, it is better to go back to the four options one by one to verify the question. Suitable for finding unknown numbers, finding values that satisfy conditions, and solving equations and inequalities.
demonstrationIf 3x + 5 = 2x + 12, find x. A. 5 B. 6 C. 7 D. 8 Substitute into C (x = 7): Left = 3(7) + 5 = 26 Right = 2(7) + 12 = 26 Both sides are equal → the answer is CProductivity Tips
Substitute in B or C first (the middle value). If the result is too small, try in the bigger direction; if it is too big, try in the smaller direction - so you only need to try twice on average.
Tip 2: Special Value Method (Customized Variables)
principleWhen the question does not provide specific numerical values (for example, it requires simplifying an algebraic expression or judging an identity relationship), substitute a set of simple numerical values by yourself, calculate the original formula and each option, and choose the one with the same numerical value.
demonstrationSimplify (x + y)² − 2xy Take x = 2, y = 3: Original formula = (2 + 3)² − 2(2)(3) = 25 − 12 = 13 Enter each option one by one and get the same result as 13.Value selection rules
- Avoid 0 and 1: Multiple options may match at the same time and cannot be distinguished.
- Choose asymmetric small integers: For example, 2 and 3, do not use 2 and 2.
- Trigonometric problems use 30° or 60°, Avoid 45°— Because the sine and cosine values are equal at 45°, it is easy for different options to produce the same result.
- If the two options match at the same time, change to the second set of values and test again.
Tip Three: Elimination Method
principleWhen it's difficult to find a direct answer, it's often much easier to eliminate options that are obviously impossible. And since there are no points deducted for wrong answers, every time you eliminate an option, your expected score will actually increase.
Four grounds for exclusion- rationality: Length, area, and volume cannot be negative; probability must be between 0 and 1; variance is non-negative.
- Units and magnitude: Estimate the approximate magnitude of the answer and exclude those who deviate significantly.
- extreme value test: Push the variables in the question to extremes (approaching 0, approaching very large) to see which options behave unreasonably.
- formal judgment: The answer should be an integer or a fraction, contain radicals or not, be positive or negative.
Tip 4: Sketching and Estimating
principleFor problems such as coordinate geometry, function graphs, and linear programming, drawing a proportional sketch is often faster than calculating.
Correct approach- Redraw it yourself based on known data, and try to be in proportion.
- Take the title and substitute the coordinates of the known points into the equations of each option to verify - the correct equation should satisfy all known points.
- Function graph questions examine key features: intercepts, vertices, opening directions, asymptotes.
- Sketch only Auxiliary verification, used to eliminate obviously erroneous options, should not replace calculations to arrive at the final answer.
See the second item in the next section -Do not measure the shapes printed on the test paper.
5. Compliant use of computers
The nature of Paper 2 is most suitable for making good use of computers: as long as you get the correct value, no writing process is required. But the rules must be clarified first.
The computer must be HKEAA Approved model And printed with "H.K.E.A.A. APPROVED" or "H.K.E.A. APPROVED" label, otherwise There is a chance of points being deducted; If you bring in a computer that is not authorized and can gain an unfair advantage by retrieving data,May be disqualified from the entire exam. Can use pre-stored For calculation programme, but programme No text data may be stored— Including text versions of theorems, formula explanations or prompts. The rules and approved list are published by the HKEAA every year, and the latest version should prevail.
Features and programme Types Particularly Useful for Paper 2
| type | use | Corresponding topics |
|---|---|---|
| CALC substitution function | Substitute special values into calculations containing variables and use the special value method | Algebraic simplification, identities |
| Solving simultaneous equations | Find the intersection point of two straight lines and solve the system of equations | Continued equations, equations of straight lines and circles |
| Finding roots of quadratic equation | Quickly get the discriminant of two roots and | Quadratic equations of one variable, quadratic functions |
| Trigonometric calculations | Numerical calculation of sine formula and cosine formula | Continuation triangle |
| Statistics function | mean, standard deviation, quartiles | measure of dispersion |
| Sequence calculation | The nth item, the first n items, and |
Three must-follow operating habits
- Unwind and confirm the angle mode is degrees (display D). Setting it to radians will make the entire trigonometric problem wrong, but the answer will still look like a reasonable number.
- Clear the statistics memory before entering a new set of statistics. Errors caused by residual data are the most insidious.
- Always add parentheses. Different models may handle omitted multiplication signs differently, so do not rely on the default priority.
Comparison of approved models, programme entry and five common operating errors, see DSE Mathematics Computer Guide. You can bring a backup machine to prevent failure, but if the models of the two machines are different, you should pay attention to the differences in button positions and operation sequences. You should use both Form 1 before the exam.
6. Two wrong practices that will lead to loss of points
These two items are widely circulated in the public, but they will cause the originally correct answers to be corrected.
Wrong approach 1: Using "average answer distribution" as the basis for checking
popular saying"A, B, C, and D each account for about 11 to 12 questions. If one option appears only 5 times and another option appears 15 times, you should re-examine the question that you are not sure about."
why unreliableHKEAA no promises The occurrences of each option are evenly distributed. The actual distribution of any given paper can deviate from the mean, and the deviation itself has no diagnostic significance. What's more serious is that this approach will encourage students to Correct the correct answer— Because the basis for the change is not mathematics, but an unfounded statistical expectation.
Correct approachChecks are always based on Mathematical calculation: Substitute the answer back into the question, use the second method to recalculate, or check the rationality (positive or negative, magnitude, unit). Don't change your answer without a mathematical reason.
Mistake 2: Measure the graphics printed on the test paper
popular saying"Use a ruler to measure the length in the picture, use a protractor to measure the angle, and then compare the options to choose the closest one."
why unreliableGraphics on the test paper Not necessarily drawn to scale, the question usually states that the figures are not necessarily to scale. Question makers may even draw misleading graphics to test whether candidates rely on vision rather than reasoning. Measuring the printed graph directly is giving the answer to an untrustworthy source.
Correct approachIf you want to use graphics assistance, you should Redraw it yourself based on known data A sketch that is to scale and should only be used to eliminate obviously incorrect options or to check whether an answer makes sense - it should not be used to arrive at an answer directly. The real solution is still calculation.
7. Common pitfalls in various topics
The pitfalls unique to Paper 2 are listed below by topic. For a complete diagnostic framework for score loss (concept errors, procedural errors, question review errors, and calculation errors), see Common points lost and errors counted.
| Topic | Common pitfalls | Check action |
|---|---|---|
| Exponential and logarithmic | Confusing exponential operations with coefficient operations; confusing addition and subtraction of logarithms with multiplication and division of real numbers; forgetting to check that real numbers are positive | Substitute special values to verify identity relationships |
| Factoring and Algebra | Negative sign assignment;(a + b)² Missing middle term; omitting "term" instead of "factor" |
Expand and enter x = 2 Check |
| Functions and Images | Confuse f(x) and f(−x) image relationship; reverse the translation direction; ignore domain restrictions |
Take two specific points and substitute them into the verification |
| Continuation triangle | The angle mode is set incorrectly; the quadrant symbol is incorrectly judged; solutions are missing within the specified range; the application of the sine formula and the cosine formula is confused. | Confirm D mode; after solving the equation check for other solutions in the range |
| Equations of Lines and Circles | The sign of the slope is wrong when judging parallel and perpendicular; the equation of the circle is not standardized to read the centre and radius of the circle. | Substitute the known points into the option equation to verify |
| measure of dispersion | Standard deviation is confused with variance; group boundaries are used for grouped data instead of group midpoints; the direction of the standard score formula is wrong | The statistical memory is cleared first; whether the answer magnitude is reasonable |
| Continuation probability | Misuse of addition and multiplication rules; confusion between mutual exclusion and independence; "at least once" no complement event | The probability answer must be between 0 and 1 |
| Arrangement and combination | Misjudgment of whether order is important; double counting or omission of calculations | Use small-scale case counting to verify once |
| quadrature method and similarity | Misapplication of area ratio and volume ratio (similar ratios of squares and cubes); non-linear unit conversion | Remember that the area ratio is the square of the length ratio and the volume ratio is the cube |
| Errors and Estimates | Wrong judgment of upper and lower limits; confusion between absolute error and relative error | Write the range first and then answer |
8. Practice methods
By subject and by year
- Form 5 to Form 6 last semester were mainly based on topics: Each time you complete a study unit, focus on the past questions in Paper 2 of that unit to build up your ability to identify question types.
- Form 6 will be converted to year-based next semester: The entire volume is limited to 75 minutes to complete, with training rhythm and cross-topic switching.
- DSE was first held in 2012 and has accumulated 15 previous examination papers as of 2026, as well as sample examination papers and practice papers from the HKEAA.
About the old HKCEE test questions: Supplementary exercises are available, but please note that the course scope and question types are different from those of DSE, and some content is no longer included in the current course. Priority will be given to previous DSE papers and supplementary sources will be considered only if resources are insufficient.
Three special trainings for Paper 2
- Time-limited practice: Practice 15 questions first with a time limit of 25 minutes, and then do the entire 45 questions after getting used to the rhythm. You often don’t learn rhythm control by jumping directly to the entire volume.
- pure speed exercise: Find 20 simple questions that you already know how to do, and have a time limit of 15 minutes to complete them. This training is not about problem-solving ability, but operation speed and computer proficiency.
- Skill specific exercises: Require yourself to only use the substitution method or only the special value method to complete a set of questions, forcing you to become proficient in the judgment timing of this technique.
Wrong question record
The wrong questions in Paper 2 should have been recorded as follows:Is this question "I don't know how to do it" or "I know how to do it but I'm wrong". The former is a concept or scope gap, the latter is a speed or carelessness problem - and the methods for correcting them are completely different. For the four-column format (source of the question, what was my original mistake, classification of errors, record of repeated offenses) see Common points lost and errors counted.
Courses and Tutors
There are two main areas for improvement in Paper 2:Skill Judgment Proficiency (You will know which method is fastest when you see the question) and time discipline (The threshold for skipping questions and the closing process). Both require repeated practice under time pressure rather than reading from a skill list.
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. In the Form 6 stage, Mock Paper is distributed in each class and reviewed in the next class, forming a closed loop of "practice → correction → explanation → redo"; the judgment timing and computer operation of various quick solving techniques will be demonstrated in class. The teacher-student ratio in small classes is no more than 1:7, and each class has about 12 to 14 people taught by two instructors at the same time.
- TOLL: Core 4 classes per month (1.5 hours each) HK$1,360; compulsory M1 or M2 (2 hours per class) HK$1,600. See details Charge page.
- Other courses: junior secondary maths tuition, IB/GCE maths tuition, Summer Courses, One to one and online courses.
- Class location: 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/Phone: 9651 3910; Email: terrybgwan@gmail.com.
Students mainly come from Band 1 secondary schools in Kowloon district, including Diocesan Boys' School, Diocesan Girls' School, La Salle College, Maryknoll Convent School, Wah Yan College, Kowloon and Heep Yunn School. See centre background About Math Insight, please see the instructor’s qualifications Maths Tutors, actual results are shown in Results.
Paper 2 Frequently Asked Questions
How many questions are there in Paper 2? How is it scored?
45 multiple-choice questions, 1 hour and 15 minutes, accounting for 35% of the subject, each question is worth 1 point,No points will be deducted for wrong answers. Therefore it should never be left blank.
Is there any difference in the scope of Part A and Part B?
have. Part A accounts for about two-thirds, covering the basic topics of Core and the basic parts of Form 1 to Form 3 courses; Part B accounts for about one-third, covering Core and entire Form 1 to Form 3 courses.
How many questions do you need to answer correctly to get 5**?
There is no such correspondence. Grades are assessed based on overall subject performance weighted by Paper 1 and Paper 2, and the HKEAA never publishes the raw marks or percentages corresponding to each grade.
How is time allocated?
Three-round strategy: 30 minutes in the first round to collect questions with obvious methods; 30 minutes in the second round to deal with those that require calculation; 15 minutes in the third round to deal with difficult questions and confirm all answers. By the 30th minute you should have completed approximately 25 to 30 questions.
Can I measure the graphics on the test paper?
Unreliable. Exam paper figures may not be drawn to scale, and questions usually indicate that figures are not necessarily to scale. You should redraw it yourself based on known data and only use it for auxiliary verification.
Is ABCD evenly distributed?
HKEAA does not commit to equal distribution. There is no basis for using the distribution frequency as a basis for checking. Instead, it may correct the correct answer. The inspection should be based on mathematical calculations.
What values should be substituted into the special value method?
Choose asymmetric small integers (such as 2 and 3), avoid 0 and 1; use 30° or 60° for trigonometric problems, avoid 45° (because the sine and cosine values are equal at this time).
Can I use a computer programme?
available For calculation programme, but the computer must be of approved model and bear the APPROVED label, the programme No text data may be stored. See details Computer strategy.
Which is easier to improve, Paper 2 or Paper 1?
Paper 2 usually yields quicker results because its improvement mainly comes from skill and speed and does not rely on writing standards. However, Paper 1 accounts for 65% and the weight is nearly twice that of Paper 2. In the long run, Paper 1 should still be the focus. See Paper 1 Strategy.