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Comprehensive Revision Guide for High School Mathematics

This document serves as a revision guide covering key topics in high school mathematics, including basic math, calculus, and logarithms. It offers structured induction proofs, polynomial factorization techniques, and practical applications of integrals and differentiation. Key problems such as calculating compound interest on deposits, finding quotients and remainders, and demonstrating arithmetic progressions are included to enhance understanding. Intended for students preparing for examinations or seeking a solid foundation in math concepts.

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Comprehensive Revision Guide for High School Mathematics

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  1. Revision on High School Maths Leo Cheung

  2. About me • Leo Cheung • Office: SHB117 • Office Hours: Friday 9:30-12:30 • Email: hycheung@cse

  3. Agenda • Revision on basic Maths • Induction • Calculus

  4. Logarithm • Given , express b in terms of a • Prove (HKCEE 92)

  5. Polynomials • Find quotient and remainder of • Factorize

  6. Arithmetic Progression • Calculate 1 + 3 + 6 + 8 + 11 + 13 + 16 + 18 + … + 48 + 51

  7. Interest • $1000 deposited • 10% interest rate per year (compound) • What is the balance after 5 years?

  8. Interest • $1000 deposited in the beginning of each year • 10% interest rate per year (compound) • What is the balance at the end of the 5th years?

  9. Induction • Prove 2+6+10+…2(2n-1) = 2n2 • Using induction, we have to prove • It is true for n=1 • If is true for n=k, then it is true for n=k+1

  10. Differentiation • Slope of a function • Useful in CSCI2800

  11. Integration • Inverse of differentiation • Area under a curve • Useful in ENGG2040

  12. Integration

  13. References • Additional mathematics : an exploratory approach • By S.W. Li, W.H. Wong, C.M. Yeung. • Hong Kong Educational Pub. Co. • Additional Mathematics : a guided course • By C.K. Chan, O.K. Fok, L.S. Ko. • Canotta Pub.

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