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...