Hi,
Unconventional questions have been asked in the 2008 & 2009 exams. In preparation for the 2010 exam, here are two questions for you to practise:
Q1 Solve the inequality |x + 3a| > 2|x - 2a|, where a is a positive constant. Hence deduce the solution to the inequality |sin x + 3/2| > 2|sin x - 1|.
Q2 A set of 20 pairs of bivariate data (x, y) is summarised by
sum x = 200, sum x^2 = 2125, sum y = 240, sum y^2 = 8245.
The product moment correlation coefficient is -0.992.
Find the equation of the regression line of y on x.
Thanks.
Cheers,
Wen Shih
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Hi,
In the H2 Maths 2010 exam, an unconventional minimisation problem (P1/Q9) was asked in which an arbitrary constant was involved.
Go try it! Thanks.
Cheers,
Wen Shih
Hi,
Here are some interesting trigo-related problems. Solve them without the use of a calculator.
1. Find the value of (sin pi/8)^4 + (sin 3pi/8)^4 + (sin 5pi/8)^4 + (sin 7pi/8)^4.
2. Find the value of [ (tan 40 deg) x (tan 60 deg) x (tan 80 deg) ] / [ (tan 40 deg) + (tan 60 deg) + (tan 80 deg) ].
3. Let m = sqrt(2). Find the value of [ log_m (cos 20 deg) + log_m (cos 40 deg) + log_m (cos 80 deg) ]^2. Note: log_m k refers to the logarithm of k with base m.
4. If cos 2A = -sqrt(5) / 3, find the value of 6 (sin A)^6 + 6 (cos A)^6.
Enjoy!
Cheers,
Wen Shih
Hi,
This problem is about complex partial fractions:
Students who have done Complex Numbers can give it a shot!
Cheers,
Wen Shih
Hi,
Interesting results can result from a very simple one. Read:
http://johnmayhk.wordpress.com/2011/03/17/just-a-question-on-square-root/
Enjoy and be thrilled!
Cheers,
Wen Shih