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 $f'(x) = \frac{{10 - 2{x^2}}}{{{{({x^2} + 5)}^2}}}$.