DP Mathematics HL Questionbank

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Directly related questions

• 18M.2.hl.TZ2.11a: Show...
• 16M.2.hl.TZ2.7a: Use implicit differentiation to show that...
• 16M.2.hl.TZ1.12b: Show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{2y - {{\text{e}}^x}}}{{2(y - x)}}\).
• 16N.1.hl.TZ0.9a: Find an expression for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) in terms of \(x\) and \(y\).
• 17N.1.hl.TZ0.7: The folium of Descartes is a curve defined by the equation \({x^3} + {y^3} - 3xy = 0\), shown in...
• 17M.2.hl.TZ2.2a: Find the equation of the normal to the curve at the point \(\left( {1,{\text{ }}\sqrt 3 } \right)\).
• 17M.2.hl.TZ1.2a: Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) in terms of \(x\) and \(y\).
• 12M.1.hl.TZ1.9: The curve C has equation \(2{x^2} + {y^2} = 18\). Determine the coordinates of the four points on...
• 12M.1.hl.TZ2.8: Let \({x^3}y = a\sin nx\) . Using implicit differentiation, show...
• 12N.2.hl.TZ0.6: A particle moves along a straight line so that after t seconds its displacement s , in...
• 12N.1.hl.TZ0.8a: Find the gradient of the tangent to the curve at the point \((\pi ,{\text{ }}\pi )\) .
• 08M.2.hl.TZ1.6: Find the gradient of the tangent to the curve \({x^3}{y^2} = \cos (\pi y)\) at the point (−1, 1) .
• 08M.1.hl.TZ2.5: Consider the curve with equation \({x^2} + xy + {y^2} = 3\). (a)     Find in terms of k, the...
• 11M.2.hl.TZ2.10: The point P, with coordinates \((p,{\text{ }}q)\) , lies on the graph of...
• 09M.1.hl.TZ2.5: Consider the part of the curve \(4{x^2} + {y^2} = 4\) shown in the diagram below.     (a)  ...
• 13M.1.hl.TZ2.8b: Find the value of \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) at the point on C where y = 1 and...
• 13M.1.hl.TZ2.8a: Express \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) in terms of x and y.
• 13M.1.hl.TZ1.7: A curve is defined by the equation \(8y\ln x - 2{x^2} + 4{y^2} = 7\). Find the equation of the...
• 11M.1.hl.TZ1.9: Show that the points (0, 0) and (\(\sqrt {2\pi } \) , \( - \sqrt {2\pi } \)) on the curve...
• 09N.2.hl.TZ0.8: Find the gradient of the curve...
• 14M.1.hl.TZ1.9: A curve has equation \(\arctan {x^2} + \arctan {y^2} = \frac{\pi }{4}\). (a)     Find...
• 14M.2.hl.TZ2.10a: Use implicit differentiation to find an expression for \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 13N.1.hl.TZ0.5: A curve has equation \({x^3}{y^2} + {x^3} - {y^3} + 9y = 0\). Find the coordinates of the three...
• 15N.1.hl.TZ0.7a: Show that there is no point where the tangent to the curve is horizontal.
• 15M.2.hl.TZ2.11a: Show that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{{5y - 2x}}{{2y - 5x}}\).