DP Mathematics HL Questionbank

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Directly related questions

• 18M.1.hl.TZ2.11c: The region R, is bounded by the graph of the function found in part (b), the x-axis, and...
• 18M.2.hl.TZ1.9d: The shaded region is rotated by 2$\pi$ about the $y$-axis. Find the volume of the solid formed.
• 18M.1.hl.TZ1.7b: Find $\int_0^1 {{\text{arccos}}\left( {\frac{x}{2}} \right){\text{d}}x}$.
• 18M.1.hl.TZ1.4b: $\int_{ - 2}^0 {f\left( {x{\text{ + 2}}} \right){\text{d}}x}$.
• 18M.1.hl.TZ1.4a: $\int_{ - 2}^0 {\left( {f\left( x \right){\text{ + 2}}} \right){\text{d}}x}$.
• 16M.1.hl.TZ2.11a: Calculate the value of the volume generated.
• 16N.2.hl.TZ0.10f: Consider the region $R$ enclosed by the graph of $y = f(x)$ and the axes. Find the volume of...
• 17N.2.hl.TZ0.10d: This region is now rotated through $2\pi$ radians about the $x$-axis. Find the volume of...
• 12M.1.hl.TZ1.2b: Hence state the value of (i)     $f'( - 3)$; (ii)     $f'(2.7)$; (iii)  ...
• 12M.1.hl.TZ1.6a: Find the area of region A in terms of k .
• 12M.1.hl.TZ1.6b: Find the area of region B in terms of k .
• 12M.1.hl.TZ1.6c: Find the ratio of the area of region A to the area of region B .
• 12M.1.hl.TZ2.10c: The region bounded by the graph, the x-axis and the y-axis is denoted by A and the region bounded...
• 12N.2.hl.TZ0.9: Find the area of the region enclosed by the curves $y = {x^3}$ and $x = {y^2} - 3$...
• 08M.1.hl.TZ1.6: Find the area between the curves $y = 2 + x - {x^2}{\text{ and }}y = 2 - 3x + {x^2}$ .
• 08M.2.hl.TZ2.3: The curve $y = {{\text{e}}^{ - x}} - x + 1$ intersects the x-axis at P. (a)     Find the...
• 11M.1.hl.TZ2.13a: (i)     Sketch the graphs of $y = \sin x$ and $y = \sin 2x$ , on the same set of axes, for...
• 11M.1.hl.TZ2.13c: The increasing function f satisfies $f(0) = 0$ and $f(a) = b$ , where $a > 0$ and...
• 09M.1.hl.TZ2.11: A function is defined as $f(x) = k\sqrt x$, with $k > 0$ and $x \geqslant 0$ . (a)    ...
• 10M.2.hl.TZ1.10: The diagram below shows the graphs of $y = \left| {\frac{3}{2}x - 3} \right|,{\text{ }}y = 3$...
• 10M.2.hl.TZ2.11: The function f is defined...
• 10N.1.hl.TZ0.13: Consider the curve $y = x{{\text{e}}^x}$ and the line \(y = kx,{\text{ }}k \in...
• 11N.1.hl.TZ0.7: The graphs of $f(x) = - {x^2} + 2$ and $g(x) = {x^3} - {x^2} - bx + 2,{\text{ }}b > 0$,...
• 11N.2.hl.TZ0.1b: Find the area of the region bounded by the graph and the x and y axes.
• 13M.2.hl.TZ2.12b: A different solution of the differential equation, satisfying y = 2 when $x = \frac{\pi }{4}$,...
• 11M.1.hl.TZ1.7: Find the area enclosed by the curve $y = \arctan x$ , the x-axis and the line $x = \sqrt 3$ .
• 14M.1.hl.TZ1.6: The first set of axes below shows the graph of $y = {\text{ }}f(x)$ for...
• 14M.1.hl.TZ1.11e: The graph of $y = {\text{ }}f(x)$ crosses the $x$-axis at the point A. Find the area...
• 14M.1.hl.TZ2.13e: Find the area of the shaded region. Express your answer in the form...
• 14M.2.hl.TZ2.3b: Find the area enclosed between the two graphs for...
• 13N.1.hl.TZ0.10f: Find an exact value for the area of the region bounded by the curve $y = g(x)$, the x-axis and...
• 15M.1.hl.TZ2.11d: Show that the area bounded by the graph of $y = g \circ f(x)$, the $x$-axis and the lines...
• 15N.1.hl.TZ0.12g: Show that...
• 15N.1.hl.TZ0.12f: Find the area of the region enclosed by the graph of $y = f(x)$ and the $x$-axis for...
• 15N.2.hl.TZ0.5a: (i)     Express the area of the region $R$ as an integral with respect to $y$. (ii)    ...
• 14N.1.hl.TZ0.11d: A region $R$ is bounded by the graphs of $y = g(x)$, the tangent $T$ and the line...
• 17M.2.hl.TZ2.2b: Find the volume of the solid formed when the region bounded by the curve, the $x$-axis for...
• 17M.2.hl.TZ1.4b: Calculate the area of $A$.
• 17M.2.hl.TZ1.4a: Write down a definite integral to represent the area of $A$.