DP Mathematics HL Questionbank

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Directly related questions

• 18M.1.hl.TZ2.10c: The function $h$ is defined by $h\left( x \right) = \sqrt x$, for $x$ ≥ 0. State the...
• 18M.1.hl.TZ2.10a: Find the inverse function ${f^{ - 1}}$, stating its domain.
• 18M.2.hl.TZ2.10a.iv: Explain why $f$ is not a function for...
• 18M.2.hl.TZ2.10a.iii: Explain why $f$ has no inverse on the given domain.
• 18M.2.hl.TZ2.10a.ii: With reference to your graph, explain why $f$ is a function on the given domain.
• 18M.2.hl.TZ2.10a.i: Sketch the graph of $y = f\left( x \right)$...
• 16M.2.hl.TZ1.5b.ii: Write down the range of $f$.
• 16M.2.hl.TZ1.5b.i: Sketch the graph $y = f(x)$.
• 16M.2.hl.TZ1.5a: Prove that $f$ is an even function.
• 16M.2.hl.TZ1.2b: If $f(x) = x + 2$ and $(g \circ f)(x) = {x^2} + 4x - 2$ write down $g(x)$.
• 16M.2.hl.TZ1.2a: Express ${x^2} + 4x - 2$ in the form ${(x + a)^2} + b$ where $a,{\text{ }}b \in \mathbb{Z}$.
• 16N.2.hl.TZ0.2: Find the acute angle between the planes with equations $x + y + z = 3$ and $2x - z = 2$.
• 17N.1.hl.TZ0.11a: Determine whether ${f_n}$ is an odd or even function, justifying your answer.
• 12N.1.hl.TZ0.12d: (i)     State ${F_n}(0){\text{ and }}{F_n}(1)$ . (ii)     Show that ${F_n}(x) < x$ ,...
• 09N.1.hl.TZ0.4: Consider the function f , where $f(x) = \arcsin (\ln x)$. (a)     Find the domain of f . (b)...
• 13M.1.hl.TZ1.12d: Find the range of f.
• 11N.1.hl.TZ0.9b: Hence determine the range of the function $f:x \to \frac{{x + 1}}{{{x^2} + x + 1}}$.
• 11M.1.hl.TZ1.10a: Find the largest possible domain of the function $g$ .
• 09N.2.hl.TZ0.9: (a)     Given that the domain of $g$ is $x \geqslant a$ , find the least value of $a$ such...
• 11M.1.hl.TZ1.8b: Find the coordinates of the point where the graph of $y = f(x)$ and the graph of...
• 11M.1.hl.TZ1.8a: (i)     Find $\left( {g \circ f} \right)\left( x \right)$ and write down the domain of the...
• 15M.1.hl.TZ1.9b: Find the range of $g \circ f$.
• 15M.1.hl.TZ1.6b: Given that $f(x)$ can be written in the form $f(x) = A + \frac{B}{{2x - 1}}$, find the values...
• 15M.1.hl.TZ2.13b: Hence show that $\sqrt 2  - 1 < \frac{1}{{\sqrt 2 }}$.
• 15M.1.hl.TZ2.13a: Show that $\frac{1}{{\sqrt n  + \sqrt {n + 1} }} = \sqrt {n + 1}  - \sqrt n$ where...
• 15N.1.hl.TZ0.12d: Find the range of $f$.
• 15N.2.hl.TZ0.12a: The functions $u$ and $v$ are defined as $u(x) = x - 3,{\text{ }}v(x) = 2x$ where...