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 \(A\).