DP Mathematics HL Questionbank

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• 18M.3dm.hl.TZ0.4b.ii: State the value of \({\text{gcd}}\left( {4k + 2,\,3k + 1} \right)\) for even positive...
• 18M.3dm.hl.TZ0.4b.i: State the value of \({\text{gcd}}\left( {4k + 2,\,3k + 1} \right)\) for odd positive integers \(k\).
• 18M.3dm.hl.TZ0.4a: Show that...
• 16M.3dm.hl.TZ0.1a: Use the Euclidean algorithm to show that 1463 and 389 are relatively prime.
• 12M.3dm.hl.TZ0.1a: Use the Euclidean algorithm to express gcd (123, 2347) in the form 123p + 2347q, where...
• 12N.3dm.hl.TZ0.3b: Hence find integers A and B such that 861A + 957B = h .
• 12N.3dm.hl.TZ0.3a: Using the Euclidean algorithm, find h .
• 08M.3dm.hl.TZ1.1: Use the Euclidean Algorithm to find the greatest common divisor of 7854 and 3315. Hence state...
• 08M.3dm.hl.TZ2.1: (a)     Use the Euclidean algorithm to find the gcd of 324 and 129. (b)     Hence show that...
• 08N.3dm.hl.TZ0.1b: (i)     Using the Euclidean algorithm, find the greatest common divisor, d , of 901 and...
• 11M.3dm.hl.TZ0.1a: Use the Euclidean algorithm to find the greatest common divisor of the numbers 56 and 315.
• 09M.3dm.hl.TZ0.2: (a)     Use the Euclidean algorithm to find gcd(\(12\,306\), 2976) . (b)     Hence give the...
• SPNone.3dm.hl.TZ0.1a: Use the Euclidean algorithm to find the greatest common divisor of 259 and 581.
• 13M.3dm.hl.TZ0.1a: Using the Euclidean algorithm, show that \(\gcd (99,{\text{ }}332) = 1\).
• 11N.3dm.hl.TZ0.2a: Use the Euclidean algorithm to find \(\gcd (752,{\text{ }}352)\).
• 15M.3dm.hl.TZ0.5b: Use the Fundamental theorem of arithmetic, applied to \(5577\) and \(99\,099\), to calculate...
• 14N.3dm.hl.TZ0.1d: By factorizing \(f(n)\) explain why it is always exactly divisible by \(6\).
• 14N.3dm.hl.TZ0.1e: Determine the values of \(n\) for which \(f(n)\) is exactly divisible by \(60\).
• 14N.3dm.hl.TZ0.1a: Find the values of \(f(3)\), \(f(4)\) and \(f(5)\).
• 14N.3dm.hl.TZ0.1b: Use the Euclidean algorithm to find (i)     \(\gcd \left( {f(3),{\text{ }}f(4)} \right)\); (ii)...