The basic university admission requirement for the HKDSE Compulsory Maths exam is Level 2, but some undergraduate programmes make it clear that you need to get a higher score in this paper. For example, you need at least Level 4 in maths to study actuarial science at the University of Hong Kong.
So how do you get a higher score? Last year’s top scorer Moses Lam Ka-nam, and C. Cheung, a tutor from Modern Education, share some last-minute tips.
- Cheung says many of the questions in last year’s DSE maths exam were text-based and didn’t give students any visual clues.
Students will lose marks if they mix up the different types of shapes or don’t understand key words. For example, some students mistook a cone for a cylinder in one question in last year’s Paper One,” he says.
Cheung also noticed a trend towards asking students to analyse the shapes and graphs they have drawn. For instance, in last year’s Paper One Q18, students needed to explain the geometric meaning of the transformation of shapes.
- If diagrams are not provided, Cheung suggests you follow these steps before trying to solve the problem.
First, read the question carefully. Make sure you understand what you are being asked to find or answer. Next, sketch out the shape, diagram or graph based on the information provided. Finally, work out which theories or formulas you need to use to solve the problem.
In Q7 last year, the key words were “polar coordinate system”. Recognising that would have allowed you to plot out the coordinates, which would have made it simpler to work out the angles and perimeter.
- Moses says it is important not to skip memorising basic theories and formulas when you’re revising
Cheung agrees, adding that you should also make sure you don’t mix them up. He said the following formulas were confused particularly often: the sum of roots; the product of roots; x-intercept; y-intercept; the vertex formula; and the quadratic formula.
- Cheung says some students are not familiar with approximation methods. Rounding a number to the nearest whole number, nearest 10, nearest 100, or nearest 1,000, for example, is a way that you can estimate a solution. An easy way to think of it is that all numbers to the right of the place (e.g. 10s, 100s) you are rounding to become zeros.
If the number you are rounding is followed by 5, 6, 7, 8, or 9, you “round up”; e.g. 3,578 to the nearest 10 is 3,580; to the nearest 100 is 3,600; and to the nearest 1,000 is 4,000.
If the number you are rounding is followed by a 1, 2, 3 or 4, you “round down”; e.g. 3,443 to the nearest 10 is 3,440; to the nearest 100 is 3,400; and to the nearest 1,000 is 3,000.
For front-end estimation, you round only the first (left-most) digit, and turn the other numbers into zeros. For example, to use front-end estimation to determine the product of 578 x 233, you’d round 578 up to 600, and 233 down to 200, i.e. 600 x 200 , for an estimate of 120,000. Your calculations will be wrong if you do not round correctly.
- Cheung says many students have problems with simplification. For example, it is important to always reduce a fraction to its lowest terms, e.g. 4/6 should be rewritten as 2/3.
- Moses says in deductive geometry questions, it’s important not to waste time explaining proofs, but just answer the question.
“For this topic, focus on calculating and finding the angles. Most exam questions in previous years only asked students to find the unknown angles, not to present proof,” he says.
- Cheung says for some topics, such as coordinates geometry, you can always use the first few parts of the questions to help you answer the following, harder, parts.
“Get some points in the easier sub-questions as the answers will help you calculate the next difficult one,” he says.
- Moses recommends practising rare questions. It’s a good idea to prepare for topics that didn’t appear in last year’s Paper One, such as linear programming. Take a look at the questions on this topic in the 2012-2015 past papers.
“You should also do old A-Level or HKCEE papers to practise certain topics, such as geometry of the circle, and trigonometry, which are included in the compulsory maths exam. Practising past papers is the ideal way to become familiar with different question types,” he says.