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.
• 16M.1.hl.TZ1.13d: Find the volume of the solid formed when the region \(R\) is rotated through \(2\pi \) about the...
• 16N.2.hl.TZ0.10f: Consider the region \(R\) enclosed by the graph of \(y = f(x)\) and the axes. Find the volume of...
• 16N.1.hl.TZ0.11f: Find the area of the region enclosed by the graph of \(f\) and the \(x\)-axis. The curvature at...
• 17N.2.hl.TZ0.10d: This region is now rotated through \(2\pi \) radians about the \(x\)-axis. Find the volume of...
• 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 \(A\).
• 17M.1.hl.TZ1.11f: Determine the area of the region enclosed between the graph of...
• 12M.2.hl.TZ1.8: A cone has height h and base radius r . Deduce the formula for the volume of this cone by...
• 08M.1.hl.TZ1.10: The region bounded by the curve \(y = \frac{{\ln (x)}}{x}\) and the lines x = 1, x = e, y = 0 is...
• 08N.2.hl.TZ0.12: The function f is defined by...
• 09M.1.hl.TZ2.5: Consider the part of the curve \(4{x^2} + {y^2} = 4\) shown in the diagram below.     (a)  ...
• 09N.1.hl.TZ0.10: A drinking glass is modelled by rotating the graph of \(y = {{\text{e}}^x}\) about the y-axis,...
• 13M.2.hl.TZ1.4: Find the volume of the solid formed when the region bounded by the graph of \(y = \sin (x - 1)\),...
• 10M.1.hl.TZ1.8: The region enclosed between the curves \(y = \sqrt x {{\text{e}}^x}\) and...
• 10N.2.hl.TZ0.13: Let \(f(x) = \frac{{a + b{{\text{e}}^x}}}{{a{{\text{e}}^x} + b}}\), where \(0 < b <...
• 11N.1.hl.TZ0.4c: find the volume of the solid formed when the graph of f is rotated through \(2\pi \) radians...
• 11M.2.hl.TZ1.14a: When the glass contains water to a height \(h\) cm, find the volume \(V\) of water in terms of...
• 09M.2.hl.TZ1.12: (a)     If A, B and C have x-coordinates \(a\frac{\pi }{2}\), \(b\frac{\pi }{6}\) and...
• 14M.2.hl.TZ1.5b: The region \(S\) is rotated by \(2\pi \) about the \(x\)-axis to generate a solid. (i)     Write...
• 13N.1.hl.TZ0.12f: S is rotated through \(2\pi \) radians about the x-axis. Find the value of the volume generated.
• 13N.2.hl.TZ0.13b: The domain of \(f\) is now restricted to \(x \geqslant 0\). (i)     Find an expression for...
• 13N.1.hl.TZ0.12e: Hence find the value of \(\int_0^{\frac{\pi }{2}} {{{\cos }^6}\theta {\text{d}}\theta } \).
• 15M.2.hl.TZ1.1: The region \(R\) is enclosed by the graph of \(y = {e^{ - {x^2}}}\), the \(x\)-axis and the lines...
• 15N.2.hl.TZ0.5b: Find the exact volume generated when the region \(R\) is rotated through \(2\pi \) radians about...
• 15M.2.hl.TZ2.6b: The region bounded by the graph of \(y = \ln (5x + 10)\), the \(x\)-axis and the lines...
• 14N.2.hl.TZ0.13a: If the container is filled with water to a depth of \(h\,{\text{cm}}\), show that the volume,...