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...