DP Mathematics HL Questionbank

• Syllabus

2.4

Sub sections and their related questions

The rational function \(x \mapsto \frac{{ax + b}}{{cx + d}}\) and its graph.

• 13M.1.hl.TZ2.12a: Express \(f(x)\) in the form \(A + \frac{B}{{x + 2}}\), where \(A\) and \(B \in \mathbb{Z}\).
• 13M.1.hl.TZ2.12c: State the range of f.
• 13M.1.hl.TZ2.12d: (i)     Find an expression for \({f^{ - 1}}(x)\). (ii)     Sketch the graph of \(y = f(x)\),...

The function \(x \mapsto {a^x}\) , \(a > 0\) , and its graph.

The function \(x \mapsto {\log _a}x\) , \(x > 0\) , and its graph

• 08N.1.hl.TZ0.2: Write \(\ln ({x^2} - 1) - 2\ln (x + 1) + \ln ({x^2} + x)\) as a single logarithm, in its simplest...
• 09M.1.hl.TZ1.3: Let \(g(x) = {\log _5}\left| {2{{\log }_3}x} \right|\) . Find the product of the zeros of g .
• 10M.2.hl.TZ2.4: (a)     Find the solution of the...
• 13N.1.hl.TZ0.3c: Given that \(f(x) = \ln (ax + b),{\text{ }}x > 1\), find the value of \(a\) and the value of...
• 14N.1.hl.TZ0.11b: The function \(g\) is defined as \(g(x) = \ln x,{\text{ }}x \in {\mathbb{R}^ + }\). The graph of...
• 15M.1.hl.TZ2.9a: State the set of values of \(a\) for which the function \(x \mapsto {\log _a}x\) exists, for all...
• 15M.1.hl.TZ2.9b: Given that \({\log _x}y = 4{\log _y}x\), find all the possible expressions of \(y\) as a function...