DP Mathematics SL Questionbank

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• 16M.2.sl.TZ2.9e: There is a value of $x$, for $1 < x < 4$, for which the graphs of $f$ and $g$ have...
• 16M.2.sl.TZ2.9d: Given that $g'(1) =  - e$, find the value of $a$.
• 16M.2.sl.TZ2.9c: Write down the value of $b$.
• 16M.2.sl.TZ2.9b: Find $f'(x)$.
• 16M.2.sl.TZ2.9a: Write down the equation of the horizontal asymptote of the graph of $f$.
• 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 $f'(1)$.
• 12N.1.sl.TZ0.10a: Find $f'(x)$ .
• 12N.1.sl.TZ0.10b: Let $g(x) = \ln \left( {\frac{{6x}}{{x + 1}}} \right)$ , for $x > 0$ . Show that...
• 12M.2.sl.TZ2.2b: On the grid below, sketch the graph of $f'(x)$ .
• 12M.2.sl.TZ2.2a: Find $f'(x)$ .
• 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.TZ1.10b(i) and (ii): (i)     Find $f'(x)$ . (ii)    Find $g'(x)$ .
• 08M.1.sl.TZ2.9b: Find $f'(x)$ , giving your answer in the form $a{\sin ^p}x{\cos ^q}x$ where...
• 10N.1.sl.TZ0.2a: Find $g'(x)$ .
• 10N.1.sl.TZ0.2b: Find the gradient of the graph of g at $x = \pi$ .
• 09N.1.sl.TZ0.9a: (i)     Find the coordinates of A. (ii)    Show that $f'(x) = 0$ at A.
• 09N.2.sl.TZ0.2a: Find $f'(x)$ .
• 09N.2.sl.TZ0.2b: Find $g'(x)$ .
• 09M.1.sl.TZ2.8a: Write down (i)     $f'(x)$ ; (ii)    $g'(x)$ .
• 09M.2.sl.TZ2.10d: Write down one value of x such that $f'(x) = 0$ .
• 09M.2.sl.TZ2.6a: Write down the gradient of the curve at P.
• 10M.2.sl.TZ1.9a: Show that $A = 10$ .
• 10M.2.sl.TZ1.9b: Given that $f(15) = 3.49$ (correct to 3 significant figures), find the value of k.
• 10M.2.sl.TZ1.9c(i), (ii) and (iii): (i)     Using your value of k , find $f'(x)$ . (ii)    Hence, explain why f is a decreasing...
• 10M.2.sl.TZ1.9d: Let $g(x) = - {x^2} + 12x - 24$ . Find the area enclosed by the graphs of f and g .
• 11N.1.sl.TZ0.9c: Find $f'(x)$ .
• 11N.1.sl.TZ0.9a(i), (ii) and (iii): Use the graph to write down the value of (i)     a ; (ii)    c ; (iii)   d .
• 11N.1.sl.TZ0.9b: Show that $b = \frac{\pi }{4}$ .
• 11N.1.sl.TZ0.9d: At a point R, the gradient is $- 2\pi$ . Find the x-coordinate of R.
• 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.2.sl.TZ1.9b(i) and (ii): (i)     Find $f'(x)$ . (ii)    Show that $f''(x) = (4{x^2} - 2){{\rm{e}}^{ - {x^2}}}$ .
• 11M.2.sl.TZ1.9a: Identify the two points of inflexion.
• 11M.2.sl.TZ1.9c: Find the x-coordinate of each point of inflexion.
• 11M.2.sl.TZ1.9d: Use the second derivative to show that one of these points is a point of inflexion.
• 13M.2.sl.TZ1.9d: Show that $f'(x) = \frac{{1000{{\rm{e}}^{ - 0.2x}}}}{{{{(1 + 50{{\rm{e}}^{ - 0.2x}})}^2}}}$ .
• 13M.2.sl.TZ2.10b: Consider all values of $m$ such that the graphs of $f$ and $g$ intersect. Find the value of...
• 13N.1.sl.TZ0.10a: Show that $f'(x) = \frac{{\ln x}}{x}$.
• 18M.1.sl.TZ2.10c: Let L2 be the tangent to the graph of g at P. L1 intersects L2 at the point Q. Find the...
• 18M.1.sl.TZ2.10b: Show that the graph of g has a gradient of 6 at P.
• 18M.1.sl.TZ2.10a.ii: Find $f\left( 2 \right)$.
• 18M.1.sl.TZ2.10a.i: Write down $f'\left( 2 \right)$.
• 18M.1.sl.TZ1.7: Consider f(x), g(x) and h(x), for x∈$\mathbb{R}$ where h(x) = \(\left( {f \circ g}...
• 17M.2.sl.TZ1.6: Let $f(x) = {({x^2} + 3)^7}$. Find the term in ${x^5}$ in the expansion of the derivative,...
• 15N.1.sl.TZ0.10d: The following diagram shows the shaded regions $A$, $B$ and $C$. The regions are...