DP Mathematics SL Questionbank

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Directly related questions

• 17M.1.sl.TZ2.6b: Find \(h'(8)\).
• 17M.1.sl.TZ2.6a: Find \(h(1)\).
• 16M.1.sl.TZ1.10d: Let \(h(x) = f(x) \times g(x)\). Find the equation of the tangent to the graph of \(h\) at the...
• 16M.1.sl.TZ1.10c: Find \(g(1)\).
• 16M.1.sl.TZ1.10b: Write down \(g'(1)\).
• 16M.1.sl.TZ1.10a: Find \(f'(1)\).
• 16N.1.sl.TZ0.10c: (i)     Find \(h'(x)\). (ii)     Hence, show that \(h'(\pi ) = \frac{{ - 21!}}{2}{\pi ^2}\).
• 12N.1.sl.TZ0.10a: Find \(f'(x)\) .
• 12M.1.sl.TZ2.10a: Use the quotient rule to show that \(f'(x) = \frac{{2{x^2} - 2}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\) .
• 12M.1.sl.TZ2.10b: Hence find the coordinates of B.
• 12M.1.sl.TZ2.10c: Given that the line \(y = k\) does not meet the graph of f , find the possible values of k .
• 12N.1.sl.TZ0.10c: Let \(h(x) = \frac{1}{{x(x + 1)}}\) . The area enclosed by the graph of h , the x-axis and the...
• 08N.2.sl.TZ0.9a: Show that \(f'(x) = {{\rm{e}}^{2x}}(2\cos x - \sin x)\) .
• 08M.2.sl.TZ2.9a: Show that \(f'(x) = {{\rm{e}}^x}(1 - 2x - {x^2})\) . 
• 10M.1.sl.TZ1.9a: Use the quotient rule to show that \(f'(x) = \frac{{ - 1}}{{{{\sin }^2}x}}\) .
• 10M.1.sl.TZ1.9c: Find the value of p and of q.
• 10M.1.sl.TZ1.9b: Find \(f''(x)\) .
• 10M.1.sl.TZ1.9d: Use information from the table to explain why there is a point of inflexion on the graph of f...
• 09N.2.sl.TZ0.2c: Let \(h(x) = f(x) \times g(x)\) . Find \(h'(x)\) .
• 09M.1.sl.TZ1.3: Let \(f(x) = {{\rm{e}}^x}\cos x\) . Find the gradient of the normal to the curve of f at...
• 09M.1.sl.TZ2.8b: Let \(h(x) = {{\rm{e}}^{ - 3x}}\sin \left( {x - \frac{\pi }{3}} \right)\) . Find the exact value...
• 10M.2.sl.TZ1.3b: On the grid below, sketch the graph of \(y = f'(x)\) .
• 10M.2.sl.TZ1.3a: Find \(f'(x)\) .
• 10M.2.sl.TZ2.10b: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Show that...
• 10M.2.sl.TZ2.10a(i) and (ii): Let P and Q be points on the curve of f where the tangent to the graph of f is parallel to the...
• 10M.2.sl.TZ2.10c: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Sketch the graph of \(g'\) .
• 10M.2.sl.TZ2.10d: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Consider \(g'(x) = w\) ....
• 11N.2.sl.TZ0.10a: Sketch the graph of f .
• 11N.2.sl.TZ0.10c: Show that \(f'(x) = \frac{{20 - 6x}}{{{{\rm{e}}^{0.3x}}}}\) .
• 11N.2.sl.TZ0.10b(i) and (ii): (i)     Write down the x-coordinate of the maximum point on the graph of f . (ii)    Write down...
• 11N.2.sl.TZ0.10d: Find the interval where the rate of change of f is increasing.
• 11M.1.sl.TZ1.5a: Use the quotient rule to show that \(g'(x) = \frac{{1 - 2\ln x}}{{{x^3}}}\) .
• 11M.1.sl.TZ1.5b: The graph of g has a maximum point at A. Find the x-coordinate of A.
• 11M.1.sl.TZ2.4: Let \(h(x) = \frac{{6x}}{{\cos x}}\) . Find \(h'(0)\) .
• 13M.1.sl.TZ1.3a: Find \(f'(x)\) .
• 13M.1.sl.TZ2.10d: find the equation of the normal to the graph of \(h\) at P.
• 14M.2.sl.TZ1.7: Let \(f(x) = \frac{{g(x)}}{{h(x)}}\), where \(g(2) = 18,{\text{ }}h(2) = 6,{\text{ }}g'(2) = 5\),...
• 14M.1.sl.TZ2.10a: Use the quotient rule to show that \(f'(x) = \frac{{10 - 2{x^2}}}{{{{({x^2} + 5)}^2}}}\).