Solving complex problems on Hong Kong’s Diploma of Secondary Education (DSE) mathematics exam can be quite demanding, but don’t be overwhelmed.
We spoke to Dick Hui, a mathematics tutor at Defining Education and King’s Glory Education, who shared tips for the maths exam on April 13.
According to Hui, students should take note of a few major adjustments to the syllabus.
The theorem of three perpendiculars is a new learning focus for this year, but he noted that similar concepts had appeared in past exams. Several topics have been removed, mainly polar coordinates, the hexadecimal number system, and algebraic identities involving the sum and difference of cubes.
Whether you are aiming for a top grade or just hoping to secure a solid pass, these strategies will guide you through the exam with ease.
Paper 1
Hui expects the difficulty of this year’s paper to remain consistent with recent years.
“Last year’s difficulty was already high. I believe it may not be harder than last year, probably similar,” he said.
Paper 1 lasts for two hours and 15 minutes, and it includes Sections A(1), A(2) and B. The difficulty increases in later sections.
Time management
For students targeting level 5 or above, Hui suggested completing Section A(1) in 15 to 25 minutes and Section A(2) in 30 to 40 minutes, leaving enough time for Section B and review.
“For those aiming for level 5 [or higher], the most challenging questions are definitely the last two questions [in Section B],” the tutor said.
He noted that Section B would usually have two easier questions and two complex ones. The hardest problems usually cover 3D trigonometry, coordinate geometry, arithmetic sequences and geometric sequences.
Other topics, such as logarithms, transformations of graphs, and permutations and combinations, also appear throughout the paper but are more straightforward to solve.
Students aiming to pass can spend more time on Sections A(1) and A(2) to secure marks: 25 to 35 minutes for A(1) and 40 to 50 minutes for A(2). If needed, they can skip the harder parts of Section B.
“Part A for each question from Section B is supposed to be relatively straightforward and direct,” Hui said. “Try to do about one-third of the Section B points ... Attempt every question’s Part A.”
The tutor added: “Performing well means completing all the questions you know how to do, not necessarily every question.”
Tackling different question types
Hui advised students to pay special attention to “explain why”, proof-based and statistics-related questions.
He noted that “explain why” questions would appear in every section.
“[They] are not really explanation questions; it’s another way of asking you to calculate something,” the tutor said. “[Students] should think about what to compare and calculate that.”
He added: “For example, it might ask you to explain whether pouring some water into a cup will overflow ... It’s just calculating the cup’s volume and the amount of water. The most important explanation is a comparison – which one is bigger or smaller.”
For proof-based questions, Hui noted that students should proceed carefully.
“Even if they write a lot, they can still get a zero because they made the wrong assumptions,” he explained.
Proofs may appear in diagram-type questions for solving geometric problems, such as proving similar triangles or congruent triangles.
Hui recommended spending more time preparing for statistics questions, which can be worth 10 to 20 points in Paper 1.
“[They] are relatively easier. But they can carry very heavy marks,” he said.
Paper 2
You have 75 minutes to complete 45 multiple-choice questions for Paper 2, which gives you roughly 100 seconds per question.
Start with the easy questions
The tutor advised students to divide questions into three categories: “confident”, “in-between” and “unable”.
“Finish all the questions you are confident in and skip those you don’t know ... Then, revisit the skipped questions,” Hui said.
The tutor noted that Paper 2’s hardest questions would usually be around Questions 15 to 23, with about eight geometry-related questions in that part of the exam.
“Questions 24 to 30 are relatively more straightforward, involving coordinate geometry, probability or statistics,” Hui said, adding that students should aim to complete the probability and statistics questions near the end of Sections A and B since these would be easier.
Useful strategies
Hui also encouraged students to be strategic in their use of substitution methods in Paper 2.
“The key is choosing the right number to substitute,” he said. “The substituted number must help distinguish the answers and should not affect known conditions.”
The tutor added: “If a question has multiple-choice answers [A, B, C, D] and involves a variable K, students might substitute K with a number to simplify or solve it.”
The tutor added that substitution could also be useful if it helps you work faster.
Another way to improve your efficiency is by using different calculator programs.
“[Students] should have certain basic programs, such as quadratic programs,” Hui said, noting they could also be used to verify answers.
He pointed out that students could set up additional programs to speed up their calculations, such as those for determining vertices and fixed points.
Final reminders for students
As the exam approaches, Hui urged students to practise each past paper from start to end, rather than focusing only on specific topics. He suggested they find their pace to know the time they need for different types of questions.
“They must get used to exam mode, tools, environment [and] timing, and probably start [doing the paper] at a fixed time, like 8.30am daily,” he said, stressing the importance of reviewing after each practice exam.
“Review means, first, an overall assessment of what can be improved if they redo the paper. Second, focus on correcting mistakes. Third, analyse slow questions to find faster methods,” he said.
The tutor also told students to avoid learning new topics at the last minute and cramming just two days before the exam.
For students feeling anxious, Hui suggested a simple technique: “Write down all your worries and then put them aside. This helps let go of fixed thoughts.”
He added: “Before the exam ... be confident and believe that you are well-prepared and will perform well.”
