DP Mathematics HL Questionbank

• Syllabus

10.5

Sub sections and their related questions

Representation of integers in different bases.

• 08M.3dm.hl.TZ1.3a: Show that when p = 2 , N is even if and only if its least significant digit, \({a_0}\) , is 0.
• 08M.3dm.hl.TZ1.3b: Show that when p = 3 , N is even if and only if the sum of its digits is even.
• 08N.3dm.hl.TZ0.1a: Convert the decimal number 51966 to base 16.
• 11M.3dm.hl.TZ0.3c: The positive integer M is expressed in base 9. Show that M is divisible by 4 if the sum of its...
• 09N.3dm.hl.TZ0.4a: Show that a positive integer, written in base 10, is divisible by 9 if the sum of its digits is...
• 09N.3dm.hl.TZ0.4b: The representation of the positive integer N in base p is denoted by \({(N)_p}\) . If...
• 10M.3dm.hl.TZ0.3: The positive integer N is expressed in base 9 as \({({a_n}{a_{n - 1}} \ldots {a_0})_9}\). (a)  ...
• 10N.3dm.hl.TZ0.4: (a)     Write down Fermat’s little theorem. (b)     In base 5 the representation of a natural...
• 13M.3dm.hl.TZ0.3a: By writing down an appropriate polynomial equation, determine the value of n.
• 13M.3dm.hl.TZ0.3b: Rewrite the above equation with numbers in base 7.
• 14M.3dm.hl.TZ0.2a: Consider the integers \(a = 871\) and \(b= 1157\), given in base \(10\). (i)     Express...
• 13N.3dm.hl.TZ0.3: Consider an integer \(a\) with \((n + 1)\) digits written as...
• 15N.3dm.hl.TZ0.5b: Hence determine whether the base \(3\) number \(22010112200201\) is divisible by \(8\).
• 16M.3dm.hl.TZ0.3a: (i)     Given that \({(43)_n} \times {(56)_n} = {(3112)_n}\), show that...
• 16M.3dm.hl.TZ0.3b: Determine the set of values of \(n\) satisfying \({(13)_n} \times {(21)_n} = {(273)_n}\).
• 16M.3dm.hl.TZ0.3c: Show that there are no possible values of \(n\) satisfying...
• 16N.3dm.hl.TZ0.1a: (i)     By converting the base 7 number to base 10, find the value of \(x\), in base 10. (ii)  ...
• 16N.3dm.hl.TZ0.1b: Let \(y\) be the base 9 number \({({a_n}{a_{n - 1}} \ldots {a_1}{a_0})_9}\). Show that \(y\) is...
• 16N.3dm.hl.TZ0.1c: Using the method from part (b), find the unit digit when the base 9 number \({(321321321)_9}\) is...
• 17N.3dm.hl.TZ0.5a: Convert the decimal number 1071 to base 12.
• 17N.3dm.hl.TZ0.5b: Write the decimal number 1071 as a product of its prime factors.
• 17N.3dm.hl.TZ0.5c.i: Using your answers to part (a) and (b), prove that there is only one possible value for \(b\) and...
• 17N.3dm.hl.TZ0.5c.ii: Hence state the value of \(a\).