DP Mathematics HL Questionbank

• Syllabus

8.4

Sub sections and their related questions

Binary operations.

• 12M.3srg.hl.TZ0.1b: The Cayley table for the binary operation \( \odot \) defined on the set T = {p, q, r, s, t} is...
• 12N.3srg.hl.TZ0.3b: Construct the Cayley table for \(P(A)\) under \(\Delta \) .
• 12N.3srg.hl.TZ0.4a: Simplify \(\frac{c}{2} * \frac{{3c}}{4}\) .
• 08M.3srg.hl.TZ1.1: (a)     Determine whether or not \( * \) is (i)     closed, (ii)     commutative, (iii)    ...
• 08N.3srg.hl.TZ0.2: A binary operation is defined on {−1, 0, 1}...
• 11M.3srg.hl.TZ0.1a: Copy and complete the following operation table.
• 09M.3srg.hl.TZ0.2a: (i)     Show that \( * \) is commutative. (ii)     Find the identity element. (iii)     Find...
• 09M.3srg.hl.TZ0.2b: The binary operation \( \cdot \) is defined on \(\mathbb{R}\) as follows. For any elements a ,...
• 10M.3srg.hl.TZ0.3: (a)     Consider the set A = {1, 3, 5, 7} under the binary operation \( * \), where \( * \)...
• 10N.3srg.hl.TZ0.4: Set...
• 13M.3srg.hl.TZ0.1a: is closed;
• 13M.3srg.hl.TZ0.2a: Copy and complete the following Cayley table for this binary operation.  
• 11N.3srg.hl.TZ0.1a: Consider the following Cayley table for the set G = {1, 3, 5, 7, 9, 11, 13, 15} under the...
• 14M.3srg.hl.TZ0.1: The binary operation \(\Delta\) is defined on the set \(S =\) {1, 2, 3, 4, 5} by the following...
• 15M.3srg.hl.TZ0.1b: (i)     State the inverse of each element. (ii)     Determine the order of each element.
• 15M.3srg.hl.TZ0.2a: Find the element \(e\) such that \(e * y = y\), for all \(y \in S\).
• 16M.3srg.hl.TZ0.1a: Copy and complete the table.
• 17N.3srg.hl.TZ0.4a: Show that \(x * y \in S\) for all \(x,{\text{ }}y \in S\).
• 17N.3srg.hl.TZ0.4b.i: Show that the operation \( * \) on the set \(S\) is commutative.

Operation tables (Cayley tables).

• 12M.3srg.hl.TZ0.1b: The Cayley table for the binary operation \( \odot \) defined on the set T = {p, q, r, s, t} is...
• 12N.3srg.hl.TZ0.3b: Construct the Cayley table for \(P(A)\) under \(\Delta \) .
• 08N.3srg.hl.TZ0.2: A binary operation is defined on {−1, 0, 1}...
• 11M.3srg.hl.TZ0.1a: Copy and complete the following operation table.
• 09M.3srg.hl.TZ0.1: (a)     Show that {1, −1, i, −i} forms a group of complex numbers G under multiplication. (b)  ...
• 09N.3srg.hl.TZ0.1: The binary operation \( * \) is defined on the set S = {0, 1, 2, 3}...
• 10M.3srg.hl.TZ0.3: (a)     Consider the set A = {1, 3, 5, 7} under the binary operation \( * \), where \( * \)...
• 14N.3srg.hl.TZ0.1a: Find the values represented by each of the letters in the table.
• 15M.3srg.hl.TZ0.1a: Complete the following Cayley table [5 marks]
• 15N.3srg.hl.TZ0.4a: Copy and complete the following Cayley table for \(\{ T,{\text{ }} * \} \).
• 16M.3srg.hl.TZ0.1a: Copy and complete the table.