Chapter 3: How to Study, How to Be Examined
How learning works: what the research shows
Educational psychology has tested many study techniques. A major review by Dunlosky et al. (2013) rated them by their usefulness across students, materials, and tasks. It found that practice testing (trying to recall or solve without looking at notes) and distributed practice (spreading study over time) had high utility, while rereading and highlighting were of low utility. The classic experiment of Roediger and Karpicke (2006) showed that students who practised retrieving material remembered more a week later than students who spent the same time rereading. Cepeda et al. (2006) found that spacing study sessions improves long-term retention.
What this means for you.
Do problems, do not just read solutions. Mathematics and physics are learned by doing.
Test yourself. After studying a topic, close the book and write out the key ideas, definitions, derivations, and formulae from memory.
Space your study. Revisit each topic after one day, one week, and one month.
Mix topics. When practising, shuffle problem types so that you must decide which method to use, as you will in the examination.
Explain aloud. Teaching a friend, or explaining to yourself, shows what you do not understand.
Keep an error log. For each mistake, record the problem, the error, the correct method, and the reason you went wrong. Review the log weekly.
Solving problems: a method
Polya (1945) described four steps that apply to problems in mathematics, physics, and chemistry:
Understand the problem. What is given? What is wanted? Draw a diagram.
Devise a plan. Which principle or formula applies? Have you seen a similar problem?
Carry out the plan. Work step by step, with units.
Look back. Check the answer: sign, size, units, and whether it makes sense.
A weekly study plan
| Time | Activity |
|---|---|
| School and tuition | Learn new content; take notes |
| Same day (30–45 min per subject) | Rework examples without notes; do 5–10 problems |
| End of week | Review the error log; a mixed set of problems from earlier topics |
| Weekend | One timed practice paper section; repair weak areas |
| Monthly | A full paper under exam conditions |
Sleep, exercise, and breaks are part of the plan. Memory consolidation depends on sleep, and long unbroken study sessions are less effective than shorter focused ones.
Examination technique
Before the exam. Know the format, time, and marking scheme of each paper. Papers typically combine multiple-choice questions with structured and essay-type questions, and the exact format is set by the Department of Examinations, so confirm it from the latest past papers and circulars. Prepare your calculator, pens, ruler, and set squares, and learn the permitted equipment.
During the exam.
Read the whole paper first and plan your time by marks.
Start with questions you can do, to build confidence and bank marks.
Show your working. Marks are given for method, not only for the answer.
Write units and significant figures correctly.
Draw clear, labelled diagrams.
Do not leave blanks. Partial credit is often available.
Check your answers if you have time, especially signs and arithmetic.
For multiple-choice, eliminate wrong options, mark the best answer, and avoid spending too long on one item.
Past papers. Work through past papers by topic first and then as full timed papers. Mark your own work strictly against the official marking scheme. The pattern of the questions, and the way marks are given, are best learned from the Department of Examinations’ past papers and marking schemes.
Using computers and calculators
A scientific calculator is a tool, not a substitute for understanding. Learn its functions (trigonometric, logarithmic, exponential, statistical), check that it is in the correct mode (degrees or radians), and practise doing quick estimates so that you can catch errors. Spreadsheets and simple programs, which you will meet in ICT, can help you explore relationships and check results.
Wellbeing
The A/L is stressful, and sustained pressure harms both health and performance. Keep regular sleep, meals, physical activity, and social contact. Talk to a teacher, family member, or counsellor if the pressure feels overwhelming. Success in the A/L is important, but it is not the measure of a person, and there are several pathways to a good career.
Common mistakes
Spending hours rereading and highlighting rather than solving problems.
Memorizing solutions without understanding the method.
Ignoring the marking scheme and losing marks for missing units, steps, or diagrams.
Practice questions
Explain, using the evidence in this chapter, why self-testing is better than rereading.
Draw up a two-week study plan for one subject with spaced review.
Part Two: Combined Mathematics
Combined Mathematics joins Pure Mathematics and Applied Mathematics in one subject (GCE Advanced Level in Sri Lanka, n.d.). It is the language in which physics and engineering are written. The four chapters in this part cover the main ideas and methods; standard university-level texts such as Stewart (2016), Croft and Davison (2019), and Riley et al. (2006) develop them further. Topic lists follow the usual structure of the subject, and the NIE syllabus sets the exact scope.