DP Mathematics HL Questionbank

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Directly related questions

• 18M.1.hl.TZ2.6a.ii: Find $g'\left( x \right)$.
• 18M.1.hl.TZ2.6a.i: Find $f'\left( x \right)$.
• 18M.1.hl.TZ1.7a: Find $\frac{{{\text{d}}y}}{{{\text{d}}x}}$.
• 18M.1.hl.TZ1.2b: Hence find the values of θ for which $\frac{{{\text{d}}y}}{{{\text{d}}\theta }} = 2y$.
• 18M.1.hl.TZ1.2a: Find $\frac{{{\text{d}}y}}{{{\text{d}}\theta }}$
• 16M.2.hl.TZ2.12c: (i)     Show that $t'(x) = \frac{{{{[f(x)]}^2} - {{[g(x)]}^2}}}{{{{[f(x)]}^2}}}$ for...
• 16M.1.hl.TZ2.11b: (i)     Given that $\frac{{{\text{d}}V}}{{{\text{d}}h}} = \pi {(3\cos 2h + 4)^2}$, find an...
• 16M.2.hl.TZ1.12e: Given that $v = {y^3},{\text{ }}y > 0$, find $\frac{{{\text{d}}v}}{{{\text{d}}x}}$ at...
• 16M.1.hl.TZ1.9: A curve is given by the equation $y = \sin (\pi \cos x)$. Find the coordinates of all the...
• 16N.2.hl.TZ0.6: An earth satellite moves in a path that can be described by the curve...
• 16N.2.hl.TZ0.10c: Show that $f'(x) =  - \frac{{3{{\text{e}}^x}}}{{{{(2{{\text{e}}^x} - 1)}^2}}}$.
• 16N.1.hl.TZ0.11a: Find an expression for $\frac{{{\text{d}}y}}{{{\text{d}}x}}$.
• 17M.2.hl.TZ1.12g.ii: Hence, show that there are no solutions to $({g^{ - 1}})'(x) = 0$.
• 17M.2.hl.TZ1.12g.i: Hence, show that there are no solutions to $g'(x) = 0$;
• 17M.2.hl.TZ1.12f: Find $g'(x)$.
• 17M.2.hl.TZ1.8b: Calculate $\frac{{{\text{d}}\theta }}{{{\text{d}}t}}$ when $\theta = \frac{\pi }{3}$.
• 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 $\frac{{{\text{d}}L}}{{{\text{d}}\alpha }}$.
• 08N.2.hl.TZ0.12: The function f is defined by...
• 13M.1.hl.TZ2.5a: Show that...
• 13M.1.hl.TZ2.12b: Hence show that $f'(x) > 0$ on D.
• 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.TZ1.11a: Show that $f'(x) = \frac{{1 - \ln x}}{{{x^2}}}$.
• 14M.2.hl.TZ1.10d: Find the equation of the line ${L_2}$.
• 14M.1.hl.TZ2.13c: Find $f''(x)$ expressing your answer in the form $\frac{{p(x)}}{{{{({x^2} + 1)}^3}}}$, where...
• 13N.1.hl.TZ0.10a(i)(ii): (i)     Find an expression for $f'(x)$. (ii)     Hence determine the coordinates of the point...
• 14M.1.hl.TZ2.13a: Find $f'(x)$.
• 14M.2.hl.TZ1.10b: (i)     Find $f'(x)$. (ii)     Show that the curve has exactly one point where its tangent is...
• 14M.2.hl.TZ1.10c: Find the equation of ${L_1}$, the normal to the curve at the point where it crosses the y-axis.
• 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...
• 15N.1.hl.TZ0.12b: Find $f'(x)$.
• 15N.2.hl.TZ0.13a: Find $f''(x)$.
• 14N.1.hl.TZ0.7a: $p'(3)$;
• 14N.1.hl.TZ0.5: A tranquilizer is injected into a muscle from which it enters the bloodstream. The concentration...