DP Mathematics HL Questionbank

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Directly related questions

• 18M.1.hl.TZ2.6a.ii: Find \(g'\left( x \right)\).
• 18M.1.hl.TZ2.6a.i: Find \(f'\left( x \right)\).
• 18M.1.hl.TZ1.7a: Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 18M.1.hl.TZ1.2b: Hence find the values of θ for which \(\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2y\).
• 18M.1.hl.TZ1.2a: Find \(\frac{{{\text{d}}y}}{{{\text{d}}\theta }}\)
• 16M.2.hl.TZ2.12c: (i)     Show that \(t'(x) = \frac{{{{[f(x)]}^2} - {{[g(x)]}^2}}}{{{{[f(x)]}^2}}}\) for...
• 16M.1.hl.TZ2.11b: (i)     Given that \(\frac{{{\text{d}}V}}{{{\text{d}}h}} = \pi {(3\cos 2h + 4)^2}\), find an...
• 16M.2.hl.TZ1.12e: Given that \(v = {y^3},{\text{ }}y > 0\), find \(\frac{{{\text{d}}v}}{{{\text{d}}x}}\) at...
• 16M.1.hl.TZ1.9: A curve is given by the equation \(y = \sin (\pi \cos x)\). Find the coordinates of all the...
• 16N.2.hl.TZ0.6: An earth satellite moves in a path that can be described by the curve...
• 16N.2.hl.TZ0.10c: Show that \(f'(x) =  - \frac{{3{{\text{e}}^x}}}{{{{(2{{\text{e}}^x} - 1)}^2}}}\).
• 16N.1.hl.TZ0.11a: Find an expression for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 17M.2.hl.TZ1.12g.ii: Hence, show that there are no solutions to \(({g^{ - 1}})'(x) = 0\).
• 17M.2.hl.TZ1.12g.i: Hence, show that there are no solutions to \(g'(x) = 0\);
• 17M.2.hl.TZ1.12f: Find \(g'(x)\).
• 17M.2.hl.TZ1.8b: Calculate \(\frac{{{\text{d}}\theta }}{{{\text{d}}t}}\) when \(\theta = \frac{\pi }{3}\).
• 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 \(\frac{{{\text{d}}L}}{{{\text{d}}\alpha }}\).
• 08N.2.hl.TZ0.12: The function f is defined by...
• 13M.1.hl.TZ2.5a: Show that...
• 13M.1.hl.TZ2.12b: Hence show that \(f'(x) > 0\) on D.
• 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.TZ1.11a: Show that \(f'(x) = \frac{{1 - \ln x}}{{{x^2}}}\).
• 14M.2.hl.TZ1.10d: Find the equation of the line \({L_2}\).
• 14M.1.hl.TZ2.13c: Find \(f''(x)\) expressing your answer in the form \(\frac{{p(x)}}{{{{({x^2} + 1)}^3}}}\), where...
• 13N.1.hl.TZ0.10a(i)(ii): (i)     Find an expression for \(f'(x)\). (ii)     Hence determine the coordinates of the point...
• 14M.1.hl.TZ2.13a: Find \(f'(x)\).
• 14M.2.hl.TZ1.10b: (i)     Find \(f'(x)\). (ii)     Show that the curve has exactly one point where its tangent is...
• 14M.2.hl.TZ1.10c: Find the equation of \({L_1}\), the normal to the curve at the point where it crosses the y-axis.
• 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...
• 15N.1.hl.TZ0.12b: Find \(f'(x)\).
• 15N.2.hl.TZ0.13a: Find \(f''(x)\).
• 14N.1.hl.TZ0.7a: \(p'(3)\);
• 14N.1.hl.TZ0.5: A tranquilizer is injected into a muscle from which it enters the bloodstream. The concentration...