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    • About
    • Twitch Office Hours
    • Writing
      • KES Physics Newsletter
      • Notes & Handouts
    • Problems
      • Questions & Answers
      • Year 9 +
      • Year 11 +
      • Year 12 +
      • Problem Authorship
    • Useful Stuff
      • Revision & Further Study
      • University Admissions
      • Blogs & Other Webpages
      • UG Research Internships
      • UG & PG Notes
      • LGBTQ+
    • Fun Stuff
      • Misc Webpages
      • Physics & Maths Memes
      • Physics & Maths GIFs
    • Contact
  • About
  • Twitch Office Hours
  • Writing
    • KES Physics Newsletter
    • Notes & Handouts
  • Problems
    • Questions & Answers
    • Year 9 +
    • Year 11 +
    • Year 12 +
    • Problem Authorship
  • Useful Stuff
    • Revision & Further Study
    • University Admissions
    • Blogs & Other Webpages
    • UG Research Internships
    • UG & PG Notes
    • LGBTQ+
  • Fun Stuff
    • Misc Webpages
    • Physics & Maths Memes
    • Physics & Maths GIFs
  • Contact

Problems - Year 11 +

Divisibility Problem

Prove that for any odd integer (a whole number) larger than 1,  d² -1 is divisible by 8.


(Hint: An odd integer can be written as 2n+1, where n is an integer)

Clockface Problem

At which time(s) of day do the second, minute and hour hands all line up on the clockface?

Click the figure

Nested Square Root Problem

Find the numerical value of the expression pictured. (Where the '...' indicates the pattern continuing indefinitely)


(Hint: Try squaring both sides)

Polygon inside a Circle Problem

Find a general expression for the area of an n-sided regular polygon embedded inside of a circle of unit radius. What happens as n becomes very large? Think about what should happen, before going through the algebra. 


You may find the following identity useful for the case of large n:  when x is small,  sin(x) ≈  x 

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