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Singapore Math

Monday, November 18, 2013

General Paper and Math Essays

A six-year series of past exam GP papers

In many Commonwealth countries, high school students sitting for the Cambridge G.C.E. 'A' Level/Higher School Certificate Examination are required to sit for the "General Paper," a paper that "tests the candidate's understanding and use of English and the extent to which he has achieved a maturity of thought appropriate to sixth-form (or high-school) students in their second year."

The three hours "General Paper," which is primarily not a test of general knowledge, is made up of two parts:

Paper 1 contains topics for composition on a number of disciplines, ranging from geography and history to literature and language to arts and crafts to mathematics and science. From a dozen questions, students choose one to write an essay between 500 and 800 words in length.

Paper 2, which lasts one hour 30 minutes, tests comprehension of one passage of continuous prose, or of two different passages that allow for comparative analysis.

University of Cambridge Math Essays

Let's look at some math-related topics that have appeared in Paper 1 of the General Paper in the last half century.

7. Consider the view that mathematics possesses not only truth, but supreme beauty. (2012)

12. Can mathematics be seen as anything more than a useful tool in everyday life? (2010)

9. Discuss the view that too much faith is placed in statistics. (2008)

?. Consider the view that the study of mathematics is intellectually satisfying, but of little practical use. (2005)

5. How important is numeracy in today's society? (2004)
?. Statistics measure everything but prove nothing. Discuss. (2003)

A ten-year series of past exam GP papers

7. Can mathematics be made fun, interesting and worthwhile? (2003)

10. 'An education is incomplete without a sound understanding of mathematics.' Do you agree? (2002)

6. What is the relevance of Mathematics? (2000)
5. What is the value of mathematics? (1992)

7. 'Mathematics is the most perfect language of all.' Discuss. (1991) 

6. How could the teaching of science and mathematics be improved in schools on your country? (1991)

5. How necessary is it for the non-scientist to have some knowledge of mathematics? (1987)

7. 'Statistics can be both helpful and misleading.' Discuss, with examples. (1984)

6. What mathematical knowledge should all young people have acquired by the time they leave school? (1979)

6. 'Neither Physics nor Chemistry could have reached its present level without Mathematics.' Explain this statement, giving examples from either Physics or Chemistry. (1969)

8. Write simply, in non-technical language as far as possible on one of the following:
(a) logarithms;  (b) genetic code;  (c) the internal combustion engine;  (d) the metric system. (1967)

Mathematical Writing vs. Mathematics Writing

The General Paper (GP) provides high-school math students an opportunity to write about their love for the language of science and of technology—they write about instead of on mathematics. In other words, they're to showcase their mathematical writing skills, as compared to professional mathematicians who focus on mathematics writing, which grace the pages of journals and periodicals.

One wonders what percent of GP students would choose to write on these math-related themes, even if they're doing well in the subject? How many pre-university students would be confident or motivated to write an essay about the beauty, utility, or ubiquity of mathematics? It would be interesting to get some information on the popularity of math essays among GP students, from the Cambridge Examining Board.

The General Paper also provides a good opportunity for both arts and science students to be mathematically cultured, as they write about the beauty and power of mathematics. Encouraging more students to write math essays would indirectly lead them to learn more about the story or history of mathematicshow mathematics and mathematical ideas have enriched the lives of humankind over the centuries. In other words, how the evolution and revolution of mathematical results or breakthroughs have helped shape civilization. At the least, GP math essay questions could help bring humanities, arts, and math closer.

Some Questions on GP Math Essays

1. Assuming that the essays are free of grammatical and spelling mistakes, what would make one's "math essay" stand head-and-shoulders above the rest of the competition?

2. Compare and contrast the GP essay with a 500-hundred-word college admissions essay. Which one promotes a higher degree of critical thinking?

3. How does the General Paper encourage students to explore and appraise mathematical, scientific, and technological issues?

4. Most GP or English language teachers are known not to like math. Would they give math composition a miss? Or, would they make an effort to learn more about the subject, so that they in turn would be confident to assign and mark these math-related essays?


Fairfield Book Publishers Pte Ltd. (2013). General paper: Answers with explanations. Singapore: Fairfield Books Publishers Pte Ltd.

Rajamanikam, J. (ed.) (1985). General Paper. Singapore: Redspot.

SEAB/UCLES (2005). General Paper Yearly Questions G.C.E. A-Level Nov. Examination Paper 1 & 2 2001-2005. Singapore: Dyna Publisher Pte Ltd.
Singapore Asia Publishers Pte Ltd. (2013). H1 A Level General Paper. Singapore: SAP Education.

Web Publications Pte Ltd (2004). A-Level General Paper Past Examination Questions. Singapore: Web Publications.

Past-exam papers with modeled solutions

© Yan Kow Cheong, Nov. 17, 2013.