DP Further Mathematics HL Questionbank

• Syllabus

6.5

Sub sections and their related questions

Representation of integers in different bases.

• 11M.1.hl.TZ0.3a: Prove that the number \(14 641\) is the fourth power of an integer in any base greater than \(6\).
• 13M.1.hl.TZ0.1b: Consider the base \(15\) number CBA, where A, B, C represent respectively the digits ten, eleven,...
• 12M.1.hl.TZ0.6a: Using mathematical induction or otherwise, prove that the number \({(1020)_n}\) , that is the...
• 12M.1.hl.TZ0.6b: Explain briefly why the case \(n = 2\) has to be excluded.
• SPNone.1.hl.TZ0.3a: Determine the value of \(b\) .
• SPNone.1.hl.TZ0.3b: Find the representation of \(N\)   (i) in base \(10\);   (ii) in base \(12\).
• 14M.1.hl.TZ0.1: Find the positive square root of the base 7 number \({(551662)_7}\), giving your answer as a base...
• 15M.1.hl.TZ0.9a: In base \(5\) an integer is written \(1031\). Express this integer in base \(10\).
• 15M.1.hl.TZ0.9b: Given that \(N = 365,{\text{ }}r = 10\) and \(s = 7\) find the values of...
• 15M.1.hl.TZ0.9c: (i)     Given that \(N = 899,{\text{ }}r = 10\) and \(s = 12\) find the values of...
• 15M.1.hl.TZ0.9d: Show that \(121\) is always a square number in any base greater than \(2\).
• 16M.1.hl.TZ0.10b: Hence show that an integer is divisible by 3 if and only if the difference between the sum of its...
• 16M.1.hl.TZ0.10c: Express the hexadecimal (base 16) number \({\text{ABB}}{{\text{A}}_{{\text{16}}}}\) in binary.
• 18M.1.hl.TZ0.3a: A number written in base 5 is 4303. Find this as a number written in base 10.
• 18M.1.hl.TZ0.3b: 1000 is a number written in base 10. Find this as a number written in base 7.