Blogs about: Hkal
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A nice coordinate geometry problem (suitable for Form 7 pure)
Let be a point on the curve Let be the tangent line at Given intersects the curve again at Prove that… more →
Mathematics in HKCEE, HKAL, and Beyond
A nice coordinate geometry problem (suitable for Form 7 pure)
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koopakoo wrote 3 weeks ago: Let be a point on the curve Let be the tangent line at Given intersects the curve again at Prove tha … more →
For my Form 7 Pure students: A proof of the Rational Root Theorem
koopakoo wrote 1 month ago: Let Suppose , where is a rational root. Then we have . Multiplying both sides by yields: Since , we … more →
To my Form 7 students: I am impressed!
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koopakoo wrote 1 month ago: Just finished my CB class tonight and I am impressed by two students. They both expressed interests … more →
Selected solutions for my F7 Pure (Polynomials)
koopakoo wrote 1 month ago: Book 2, pg 14. (00IQ12)(c) (i) Let y = x^2, then we have ay^2 – by + a. Considering the discri … more →
Challenging problem in Linear Algebra
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koopakoo wrote 3 months ago: Let Solve the following matrix equation where … more →
Mental exercises for my Pure Complex Class (1)
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koopakoo wrote 3 months ago: Dear Students, Please avoid as much calculations as possible. In ideal situation, you should not do … more →
Selected Solutions to My Pure Complex Class (1)
koopakoo wrote 3 months ago: Lesson 1: Page 26 where the last line follows from part a(ii). Page 27 (i) Hence Note that we have i … more →
Concept Check for my Linear Algebra Students
koopakoo wrote 3 months ago: Let (E) be the following system: Let be the augmented matrix. Determine whether the following statem … more →
Solution to "Possible HKAL Pure Problems"
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koopakoo wrote 7 months ago: 1(a) Expanding along the last row, we have: Therefore, is a cubic in with leading coefficient 1(b) N … more →
Possible HKAL Pure Problem (2)
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koopakoo wrote 7 months ago: Prove by contradiction or otherwise, show that is not a polynomial with real coefficients. … more →
A possible HKAL Pure problem?
koopakoo wrote 8 months ago: Let (a) By expanding the determinant along the last row (or otherwise), show that det(A) is a cubic … more →
Vandermonde Determinant
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koopakoo wrote 10 months ago: The matrix is of special interests and it is given a name called the Vandermonde matrix. It shows up … more →
An Interesting Game in IMO Training Session
koopakoo wrote 1 year ago: I once played the following game at an IMO training session for the advanced candidates. I simply as … more →
Polynomial Practice for AL Pure
koopakoo wrote 1 year ago: Suppose are roots of Compute Hint: There is a three-line-solution. My solution will be given in 2 da … more →
Answer to "Another HKAL Problem".
koopakoo wrote 1 year ago: Here is an intuitive answer given by Katherine Chiu (my high school math teacher): Let It is clear t … more →
Another AL problem?
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koopakoo wrote 1 year ago: I am not sure whether the following is an actual AL problem, but it can definitely be solved using t … more →
HKAL 2008 problem
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koopakoo wrote 1 year ago: Here is a pure math problem in HKAL 2008: 證明方程 沒有實根. This is discussed in the mathdb blog: http://ma … more →
