With less than a week to go before this year’s DSE Compulsory Mathematics exams, Young Post asked two top tutors, Modern Education’s Dick Hui and King’s Glory Education Centre’s Wilson Liu, what key knowledge you’ll need to get you through the ordeal.
According to Liu, there’s a good chance that this year’s Paper One will include questions on three-dimensional trigonometry. In particular, it’s worth revising the following concepts: coordinate geometry related to centres of triangle; how to find the angle between two planes; and how to find the vertex of a quadratic graph by completing the square.
“Students should also pay special attention to topics like logarithmic graphs, polar coordinates, and arithmetic and geometric sequences,” Liu adds.
In addition, the last question of the paper – which is also the longest question and worth the most points (13) – may also be based on one of these topics, says Hui.
“There is a high chance that students will be tested on concepts related to arithmetic and geometric sequence, three-dimensional geometry and trigonometry, as well as probability,” he says.
Both Hui and Liu suggest using visual aids to answer questions.
“Students should always sketch diagrams or plot graphs using the information given in the problems before solving them. This is especially important for questions about coordinate geometry, polar coordinates, and mensuration,” says Hui.
Key question phrases
Maths is obviously a numbers game, so if a question asks you to “explain” your answer, it isn’t usually looking for a written explanation.
“When students are asked to ‘explain why’, they are usually expected to calculate a maximum or minimum value, rather than verbally explain their answer,” says Hui.
“The only exception is when the phrase appears in questions related to statistics. In that case, students are supposed to make their own judgments and explain them by referring to the concepts they’ve learned.”
Liu adds that “do you agree” is another key phrase that will crop up in some questions. “Students should state their stance and give a full explanation based on the results of their calculation.”
Finally, if you see sub-questions that start with the word “hence”, it means the question is related to the previous question, so you’ll need to use both parts to help you work out the answer – even if you know it without using them.
“There are usually more than one way to solve these problems, but students will get no scores for attempting them without using the answer from the previous sub-question,” Hui says.
If you’re stuck
If you’re struggling to solve a problem, double check that you’ve used every single piece of information provided in the question. If you haven’t, says Hui, “think about how you can use the remaining data to solve the question”.
Again, remember that if a question has sub-parts, these parts shouldn’t be treated as totally separate problems.
“Most of the time, the second part of a long question is closely related to the first part. For instance, results from the former parts may offer new information that is essential for solving the sub-questions that follow,” says Liu.
In addition, sub-questions which require students to “show” or “prove” something are usually there for a reason. “Very often you are expected to use what you’ve proved – be it a formula or the properties of a diagram – to solve the sub-questions following them,” says Liu.
The way you manage your time in these exams depends on where you hope to gain the most points.
“Students aiming for Level Five or above should spend no more than 20 minutes on Section A1 and 40 minutes on Section A2, so that they can spend the rest of time on [the more complicated, high-mark questions in] Section B,” said Hui.
But students who are less certain about how well they’ll do on the tricky Section B should allocate their time differently. “They should spend more time on Section A1 and A2, and ensure they get at least 80 per cent of their Section A1 answers right,” he said. “That’s because students with a weak foundation might only get a single-digit score in Section B.”
If you’ve been stuck on a question for more than two minutes, Liu suggests giving up and moving on.
This paper consists of 45 multiple-choice questions. Although each question is worth the same score, it doesn’t mean you should spend an equal amount of time on each one, Hui said.
“The difficulty level of the questions varies a lot; some can be solved in 10 to 30 seconds, while some might take three minutes,” he said.
The tutors added that as a general rule, it’s best to spend no more than 90 seconds on each question.
“Do not give up the whole forest for one tree,” said Hui. “Completing Paper Two should be a top priority.”
Other tips and advice
“Write down every step you take when solving an equation, and never make false assumptions,” says Hui. “For example, never assume a triangle is an isosceles when it is not mentioned in the question, unless you can prove it.”
Another common slip-up is to give non-answers or incomplete calculations. “It happens when students are too caught up in the calculation process, especially in Paper Two,” he says.
To ensure you have your wits about you, both tutors recommend getting into a healthy sleep pattern a few days before the exam, so that you can wake up easily on the morning of the real thing. Liu also advises against attempting any really tough practice questions the day before the exam, as this will only cause unnecessary anxiety.