DP Mathematics HL Questionbank

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Directly related questions

• 16M.3srg.hl.TZ0.5: The group $\{ G,{\text{ }} * \}$ is defined on the set $G$ with binary operation $*$....
• 16M.3srg.hl.TZ0.1e: Solve the equation $2 * x * 4 * x * 4 = 2$.
• 16M.3srg.hl.TZ0.1d: (i)     Find the two proper subgroups of $\{ S,{\text{ }} * \}$. (ii)     Find the coset of...
• 17N.3srg.hl.TZ0.1b: Write down the elements in set $K$.
• 12M.3srg.hl.TZ0.1b: The Cayley table for the binary operation $\odot$ defined on the set T = {p, q, r, s, t} is...
• 08M.3srg.hl.TZ2.1: (a)     Draw the Cayley table for the set of integers G = {0, 1, 2, 3, 4, 5} under addition...
• 08M.3srg.hl.TZ2.4b: Given the group $(G,{\text{ }} * )$, a subgroup $(H,{\text{ }} * )$ and...
• 11M.3srg.hl.TZ0.1c: The set T is defined by $\{ x * x:x \in S\}$. Show that {T , $*$} is a subgroup of {S ,...
• 09N.3srg.hl.TZ0.5: Let {G , $*$} be a finite group of order n and let H be a non-empty subset of G . (a)    ...
• SPNone.3srg.hl.TZ0.5: Let $\{ G,{\text{ }} * \}$ be a finite group and let H be a non-empty subset of G . Prove that...
• 10N.3srg.hl.TZ0.4: Set...
• 10N.3srg.hl.TZ0.5: Let $\{ G,{\text{ }} * \}$ be a finite group that contains an element a (that is not the...
• 13M.3srg.hl.TZ0.2e: Find the proper subgroups of $\{ G,{\text{ }}{ \times _{14}}\}$.
• 13M.3srg.hl.TZ0.5: H and K are subgroups of a group G. By considering the four group axioms, prove that $H \cap K$...
• 11N.3srg.hl.TZ0.1b: The Cayley table for the set...
• 13N.3srg.hl.TZ0.2b: State, with a reason, whether or not it is necessary that a group is cyclic given that all its...
• 15N.3srg.hl.TZ0.3a: Find the order of $\{ G,{\text{ }} \circ \}$.
• 15M.3srg.hl.TZ0.1c: Write down the subgroups containing (i)     $r$, (ii)     $u$.
• 15M.3srg.hl.TZ0.5b: Assuming that $(H,{\text{ }} + )$ forms a group, show that it is a proper subgroup of...
• 14N.3srg.hl.TZ0.1c: Write down the three sets that form subgroups of order 2.
• 14N.3srg.hl.TZ0.1d: Find the three sets that form subgroups of order 4.