DP Mathematics HL Questionbank

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Directly related questions

• 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 $\frac{{{\text{d}}L}}{{{\text{d}}\alpha }}$.
• SPNone.1.hl.TZ0.12a: Show that $f''(x) = 2{{\text{e}}^x}\sin \left( {x + \frac{\pi }{2}} \right)$ .
• SPNone.1.hl.TZ0.13b: Show that f is a one-to-one function.
• SPNone.1.hl.TZ0.9a: (i)     Find an expression for $f'(x)$ . (ii)     Given that the equation $f'(x) = 0$ has...
• SPNone.1.hl.TZ0.12b: Obtain a similar expression for ${f^{(4)}}(x)$ .
• SPNone.2.hl.TZ0.13a: Obtain an expression for $f'(x)$ .
• SPNone.3ca.hl.TZ0.1a: Show that $f''(x) = - \frac{1}{{(1 + \sin x)}}$ .
• 13M.2.hl.TZ1.13a: Verify that this is true for $f(x) = {x^3} + 1$ at x = 2.
• 13M.2.hl.TZ1.13b: Given that $g(x) = x{{\text{e}}^{{x^2}}}$, show that $g'(x) > 0$ for all values of x.
• 13M.2.hl.TZ1.13c: Using the result given at the start of the question, find the value of the gradient function of...
• 13M.2.hl.TZ2.13d: Show that...
• 11N.1.hl.TZ0.8b: Find the value of $\theta$ for which $\frac{{{\text{d}}t}}{{{\text{d}}\theta }} = 0$.
• 11N.3ca.hl.TZ0.5a: Given that $y = \ln \left( {\frac{{1 + {{\text{e}}^{ - x}}}}{2}} \right)$, show that...
• 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.TZ2.14c: Given that $f(x) = h(x) + h \circ g(x)$, (i)     find $f'(x)$ in simplified form; (ii)    ...
• 13N.1.hl.TZ0.10a(i)(ii): (i)     Find an expression for $f'(x)$. (ii)     Hence determine the coordinates of the point...
• 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...
• 15M.2.hl.TZ1.6: A function $f$ is defined by $f(x) = {x^3} + {{\text{e}}^x} + 1,{\text{ }}x \in \mathbb{R}$....
• 15N.1.hl.TZ0.4a: Find $\frac{{{\text{d}}y}}{{{\text{d}}x}}$.
• 15N.1.hl.TZ0.8b: Consider $f(x) = \sin (ax)$ where $a$ is a constant. Prove by mathematical induction that...
• 14N.2.hl.TZ0.10b: (i)     State $\frac{{{\text{d}}A}}{{{\text{d}}x}}$. (ii)     Verify that...