DP Mathematics HL Questionbank

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Directly related questions

• 12M.1.hl.TZ1.12a: Show that \(f'(x) = \frac{1}{2}{x^{ - \frac{1}{2}}}{(1 - x)^{ - \frac{3}{2}}}\) and deduce that f...
• 12N.1.hl.TZ0.8a: Find the gradient of the tangent to the curve at the point \((\pi ,{\text{ }}\pi )\) .
• 12N.2.hl.TZ0.12c: Let a = 3k and b = k . Find \(\frac{{{\text{d}}L}}{{{\text{d}}\alpha }}\).
• SPNone.1.hl.TZ0.12a: Show that \(f''(x) = 2{{\text{e}}^x}\sin \left( {x + \frac{\pi }{2}} \right)\) .
• SPNone.1.hl.TZ0.13b: Show that f is a one-to-one function.
• SPNone.1.hl.TZ0.9a: (i)     Find an expression for \(f'(x)\) . (ii)     Given that the equation \(f'(x) = 0\) has...
• SPNone.1.hl.TZ0.12b: Obtain a similar expression for \({f^{(4)}}(x)\) .
• SPNone.2.hl.TZ0.13a: Obtain an expression for \(f'(x)\) .
• SPNone.3ca.hl.TZ0.1a: Show that \(f''(x) = - \frac{1}{{(1 + \sin x)}}\) .
• 13M.2.hl.TZ1.13a: Verify that this is true for \(f(x) = {x^3} + 1\) at x = 2.
• 13M.2.hl.TZ1.13b: Given that \(g(x) = x{{\text{e}}^{{x^2}}}\), show that \(g'(x) > 0\) for all values of x.
• 13M.2.hl.TZ1.13c: Using the result given at the start of the question, find the value of the gradient function of...
• 13M.2.hl.TZ2.13d: Show that...
• 11N.1.hl.TZ0.8b: Find the value of \(\theta \) for which \(\frac{{{\text{d}}t}}{{{\text{d}}\theta }} = 0\).
• 11N.3ca.hl.TZ0.5a: Given that \(y = \ln \left( {\frac{{1 + {{\text{e}}^{ - x}}}}{2}} \right)\), show that...
• 11M.1.hl.TZ1.12b: Show that there is a point of inflexion on the graph and determine its coordinates.
• 11M.1.hl.TZ1.12c: Sketch the graph of \(y = f(x)\) , indicating clearly the asymptote, x-intercept and the local...
• 11M.1.hl.TZ1.12a: (i)     Solve the equation \(f'(x) = 0\) . (ii)     Hence show the graph of \(f\) has a local...
• 14M.1.hl.TZ2.14c: Given that \(f(x) = h(x) + h \circ g(x)\), (i)     find \(f'(x)\) in simplified form; (ii)    ...
• 13N.1.hl.TZ0.10a(i)(ii): (i)     Find an expression for \(f'(x)\). (ii)     Hence determine the coordinates of the point...
• 15N.3ca.hl.TZ0.2a: Show that \(f''(x) = 2\left( {f'(x) - f(x)} \right)\).
• 15M.1.hl.TZ1.11a: Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 15M.1.hl.TZ2.11c: Let \(y = g \circ f(x)\), find an exact value for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) at the...
• 15M.2.hl.TZ1.6: A function \(f\) is defined by \(f(x) = {x^3} + {{\text{e}}^x} + 1,{\text{ }}x \in \mathbb{R}\)....
• 15N.1.hl.TZ0.4a: Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 15N.1.hl.TZ0.8b: Consider \(f(x) = \sin (ax)\) where \(a\) is a constant. Prove by mathematical induction that...
• 14N.2.hl.TZ0.10b: (i)     State \(\frac{{{\text{d}}A}}{{{\text{d}}x}}\). (ii)     Verify that...