# HKDSE 2021: Maths exam Paper 2 more difficult than usual, while Paper 1 relatively easy

- Tutors and students said while Paper 1 only had a few tricky questions, the multiple-choice questions in Paper 2 required students to combine multiple skills within one question
- Despite this, a Beacon College tutor remarked that students could score a Level 4 if they studied past papers

This year’s HKDSE maths exam saw the most challenging Paper 2 in recent years, tutors believe, while Paper 1 was generally easy.

A total of 47,813 candidates took part in the HKDSE maths exam today. We spoke to students and tutors for their take on this year’s exam.

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Student Bowie Tang, 18, from Ying Wa College, who aimed for a Level 4 result in the exam, felt Paper 1 was generally easy.

“My strategy was to get full marks in part A, and part B was a bonus for me. Part A was generally easy, similar to past paper questions. There were no tricky questions,” he says, adding that he spent two thirds of his time on Part A and the rest on Part B.

But he found Paper 2 “of fair difficulty”. He said he finished 30 questions with confidence, but he could only guess the answers for the remaining 15 multiple-choice questions.

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Achudha Bala Selva Sathish, 16, from St. Margaret’s Co-Educational English Secondary and Primary School, agrees with Bowie’s assessment of the difficulty level of Paper 2.

“HKEAA found new ways to test students on different concepts, so I couldn’t use standard formulas. I especially found the geometry questions in Paper 2 more time-consuming than expected,” she says.

### Paper 1 was relatively easy this year

Dick Hui a tutor from Modern Education, who took the exam himself this year, felt that this year’s Paper 1 was “generally easy”, saying, “Only three questions in Paper 1 are tricky. The others are all generally straightforward."

Despite having many repeated questions in Paper 1, Hui said that Q.12, Q.18, and Q.19 presented more challenges this year.

Q.12 asked candidates to solve a polynomial. “Normally, it appears as a cubic polynomial, but this year it appeared as a fourth degree polynomial,” he said.

Q.18 required candidates to solve a 3D trigonometry problem on paper folding, in which students needed to match up all the sides and angles with those in part A of Q.18, and determine all the right angles to solve the question. He explains, “3D problems are usually not very hard, but the steps were very tedious and troublesome."

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As for Q.19, which is the hardest question for students who desire to get top grades, it required candidates to solve a coordinate geometry problem that touched on a variety of other topics: completing the square, transformation of graphs, circle and tangent properties, and trigonometry.

“To tackle this question, candidates need quite a number of geometry skills and similar triangles. And they need to actively find the relations between the lines and circles without any given diagrams. Besides drawing the diagram, students needed to figure out that the question is about an isosceles triangle, and then apply the corresponding properties to solve the problems,” he explains.

Ken Tai, a tutor from Beacon College, agrees as well that Paper 1, especially Part A, was relatively easy, saying, “It is comparatively easy to get a Level 4 if one has worked hard on studying past papers."

Tai noted that Q.16 tests linear programming without providing figures, which would require students to draw the figures themselves, hence, using more time.

### Paper 2 was much more difficult this year

In agreement with students, Bowie and Achudha, all the tutors noted a spike in difficulty in Paper 2, the multiple-choice paper.

Hui says, “It was harder than usual. About seven out of the 45 questions would have been tricky and unfamiliar to most students. Even simple questions like the polynomial in Q.8 were more difficult than usual.”

He added that students may have been unable to finish all the questions within 75 minutes.

“Q.37 had an inequality question, but it also required students’ knowledge of the discriminant in quadratic equations,” he says, adding that many questions did not focus on testing one specific skill, but that they required knowledge across different topics.

He noted Q.21 and Q.33 were new question types which students may have been unfamiliar with. He advises students who are taking next year’s exam to attempt a variety of question types and crossover questions.

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As for Tai, he said some questions might have posed potential traps for students, saying, “Q.25, Q.26, and Q.27 required deeper knowledge on circles and loci, which is quite uncommon compared to previous years."

“For Q.25, there was a trap to confuse students into thinking that the locus was a straight line like in previous years, but instead, it was actually a circle if you paid attention,” he explains.

Meanwhile, online tutor Herman Yeung, said one of the challenges in Paper 2 was that candidates had to draw their own diagrams, which was more time consuming.

“In the past, HKEAA would provide the figures and diagrams for some of the questions in Paper 2, but this year, it required students to draw their own to understand the question,” he says, adding that this was the case for Q.33 from Paper 2.

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He also noted that the question setting of Q.8 was similar to pure mathematics from the old syllabus, which was unusual to see in the HKDSE.

“In Q.42 in Paper 2, nCr and nPr were tested in a more aggressive way than before,” he says.

“Although the tricky questions might not hold a lot of points, it would be more difficult for candidates to get full marks,” he says, adding that he expects to see a lower cut-off point for 5** this year. However, he says, over 30 multiple-choice questions out of the 45 were standard, so “overall it was not too challenging”.