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The question on the final page of the most challenging HSC maths exam is famed for its difficulty, intended to stretch the state’s most talented maths students beyond their comfort zone.
About 3300 students filed into exam rooms this week to attempt the gruelling three-hour maths extension 2 paper, many flipping straight to the last page to weigh up the difficulty of the toughest problems.
“Questions 14 to 16 were harder than normal,” said Vivian Xu, 17, from James Ruse Agricultural High School. “I was super tight on time, and think I finished with two minutes left on the clock.”
Her classmate, Sizhe Pan, said the higher-level exam was more challenging than the previous years’ papers he completed in the lead up to the test, but felt the first ten multiple choice questions – on algebra, mechanics and proofs – had eased him into the trickier final pages.
“Overall it was pretty hard, and a higher concentration of medium to hard questions, but I finished on time,” said Pan.
This year’s final question involved complex numbers, an extension of the real number system that involves combining real and imaginary numbers. They can be used in physics, pure maths, aeronautics and electrical engineering.
Miriam Lees, a consultant for the Mathematical Association of NSW, said complex numbers can be viewed as mysterious and challenging, but “form the basis of a lot of our modern life”, including computing currents and voltages. “To be able to turn on a fluorescent light, we need complex numbers.”
Questions 15 and 16 of the extension 2 paper are designed to challenge the top students, Lees explains, and few of the students walk into the exam “expecting to complete the paper in the way extension 1 and advanced students do”.
“Unlike complex number questions from 20 years ago, where students could use their algebra brain to get the answer, this year you needed to use geometry, advanced trigonometry and visual representations to solve it. You needed to use them flexibly to move and transform objects on the diagram. I’ve not seen a question like this in an extension 2 paper.”
“What we’re wanting from our graduates of mathematics is critical, flexible and creative thinking. It’s hard to assess in an exam; and in a question like this you need all of those skills.”
Sizhe Pan and Vivian Xu from James Ruse Agricultural High School attempt the final question from the maths extension 2 paper.Credit: Wolter Peeters
Fairvale High’s head of maths, Stephen Barbuto, who has been teaching the subject for 45 years, said it was “largely a textbook paper” apart from the last challenging questions.
“There was a lot of scope for students who had prepared, and had done their homework, to demonstrate their understanding. Having said that, there are quite a few challenging questions, but that gives students the chance to show us what they know.”
“Sometimes in extension 2 the answer isn’t always the goal, sometimes it’s about their proof or interpretations.”
Barbuto said the second last question on the paper was on geometry with vectors, and would stretch the knowledge of some students.
“This cohort going through were in year 10 when we were in lockdown. What we’ve found is there are gaps from that, particularly in geometry. I’m not quite sure how my students will go with this.”
Hubert Lam, a maths teacher at Normanhurst Boys High, said over the past few years the final question in the extension 2 paper has become similar to the problems students would face in mathematics competitions.
“Students really need to use their creative mathematical thinking to get the answer. These questions are a bit like a scavenger hunt, the entry point isn’t always obvious, and I don’t think this year’s last question has shown up in previous exams.”
Maths extension 2 enrolments have hovered at about 3200 for the past decade, with twice the number of boys taking the subject this year compared with girls. It is the fourth year students have sat exams under the new maths syllabuses.
From next year, a new maths syllabus will be rolled out which eliminates a three-tiered course structure in years 9 and 10 in favour of a single “core” unit of work. It is intended to abolish the rigid pathways that mean students can be streamed in the early years of high school and may not attempt trickier concepts before entering years 11 and 12.
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