DP Mathematical Studies Questionbank

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Directly related questions

• 16N.2.sl.TZ0.6d: Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).
• 18M.2.sl.TZ2.6f: Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.
• 18M.2.sl.TZ2.6e: Show that the stationary points of the curve are at x = 1 and x = 2.
• 18M.2.sl.TZ2.6d: Find \(\frac{{{\text{dy}}}}{{{\text{dx}}}}\).
• 18M.2.sl.TZ2.6c: Find the value of y when x = 1 .
• 18M.2.sl.TZ2.6b: A teacher asks her students to make some observations about the curve. Three students...
• 18M.2.sl.TZ2.6a: Sketch the curve for −1 < x < 3 and −2 < y < 12.
• 18M.1.sl.TZ2.14c: Find the x-coordinate of the point at which the normal to the graph of f has...
• 18M.1.sl.TZ2.14b: Find the gradient of the graph of f at \(x =  - \frac{1}{2}\).
• 18M.1.sl.TZ2.14a: Find f'(x)
• 18M.2.sl.TZ1.6f: The designer claims that the new trash can has a capacity that is at least 40% greater than the...
• 18M.2.sl.TZ1.6e: Using your graphic display calculator, find the value of r which maximizes the value of V.
• 18M.2.sl.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by \(V = 110\pi {r^3}\).
• 18M.2.sl.TZ1.6c: Find the height of the cylinder, h , of the new trash can, in terms of r.
• 18M.2.sl.TZ1.6b: Find the total volume of the trash can.
• 18M.2.sl.TZ1.6a: Write down the height of the cylinder.
• 17N.2.sl.TZ0.5e: Write down the coordinates of the point of intersection.
• 17N.2.sl.TZ0.5d: Draw the graph of \(f\) for \( - 3 \leqslant x \leqslant 3\) and...
• 17N.2.sl.TZ0.5c: Use your answer to part (b)(ii) to find the values of \(x\) for which \(f\) is increasing.
• 17N.2.sl.TZ0.5b.ii: Find \(f’(x)\).
• 17N.2.sl.TZ0.5b.i: Expand the expression for \(f(x)\).
• 17N.2.sl.TZ0.5a: Find the exact value of each of the zeros of \(f\).
• 17N.1.sl.TZ0.14b: Find the point on the graph of \(f\) at which the gradient of the tangent is equal to 6.
• 17N.1.sl.TZ0.14a: Write down the derivative of \(f\).
• 16M.2.sl.TZ2.5g: Sketch the graph of \(V = 4{x^3} - 51{x^2} + 160x\) , for the possible values of \(x\) found...
• 16M.2.sl.TZ2.5f: Calculate the maximum volume of the tray.
• 16M.2.sl.TZ2.5e: Using your answer from part (d), find the value of \(x\) that maximizes the volume of the tray.
• 16M.2.sl.TZ2.5d: Find \(\frac{{dV}}{{dx}}.\)
• 16M.2.sl.TZ2.5c: Show that the volume, \(V\,{\text{c}}{{\text{m}}^3}\), of this tray is given...
• 16M.2.sl.TZ2.5b: (i)     State whether \(x\) can have a value of \(5\). Give a reason for your answer. (ii)  ...
• 16M.2.sl.TZ2.5a: Hugo is given a rectangular piece of thin cardboard, \(16\,{\text{cm}}\) by \(10\,{\text{cm}}\)....
• 16M.1.sl.TZ2.15b: There are two points at which the gradient of the graph of \(f\) is \(11\). Find...
• 16M.1.sl.TZ2.15a: Consider the function \(f(x) = {x^3} - 3{x^2} + 2x + 2\) . Part of the graph of \(f\) is shown...
• 16M.2.sl.TZ1.3f: The nearest coastguard can see the flare when its height is more than \(40\) metres above sea...
• 16M.2.sl.TZ1.3e: i)     Show that the flare reached its maximum height \(40\) seconds after being fired. ii)  ...
• 16M.2.sl.TZ1.3d: Find \(h'\,(t)\,.\)
• 16M.2.sl.TZ1.3c: The flare fell into the sea \(k\) seconds after it was fired. Find the value of \(k\) .
• 16M.2.sl.TZ1.3b: Find the height of the flare \(15\) seconds after it was fired.
• 16M.2.sl.TZ1.3a: A distress flare is fired into the air from a ship at sea. The height, \(h\) , in metres, of the...
• 16M.1.sl.TZ1.15b: Calculate the value of \(r\) that minimizes the surface area of a can.
• 16M.1.sl.TZ1.15a: A company sells fruit juices in cylindrical cans, each of which has a volume of...
• 16M.1.sl.TZ1.11c: Find the value of \(c\) .
• 16M.1.sl.TZ1.11b: Point \({\text{A}}( - 2,\,5)\)  lies on the graph of \(y = f(x)\) . The gradient of the tangent...
• 16M.1.sl.TZ1.11a: Consider the function \(f(x) = a{x^2} + c\). Find \(f'(x)\)  
• 16N.2.sl.TZ0.6h: Find the least number of cans of water-resistant material that will coat the area in part (g).
• 16N.2.sl.TZ0.6g: Find the value of this minimum area.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 16N.2.sl.TZ0.6e: Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).
• 16N.2.sl.TZ0.6c: Write down, in terms of \(r\) and \(h\), an equation for the volume of this water container.
• 16N.2.sl.TZ0.6b: Express this volume in \({\text{c}}{{\text{m}}^3}\).
• 16N.2.sl.TZ0.6a: Write down a formula for \(A\), the surface area to be coated.
• 16N.1.sl.TZ0.14b: Find the coordinates of P.
• 16N.1.sl.TZ0.14a: Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 10M.2.sl.TZ1.3b: Write down f ′(x).
• 10N.2.sl.TZ0.5b: Find \(f'(x)\).
• 11N.1.sl.TZ0.14a: Find \(f'(x)\) .
• 12N.1.sl.TZ0.15a: Find f'(x).
• 12N.2.sl.TZ0.5b: Write down g′(x) .
• 12M.2.sl.TZ1.5d: Find f '(x).
• 10M.2.sl.TZ2.5c: Differentiate A in terms of x.
• 12M.1.sl.TZ2.13a: Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 12M.2.sl.TZ2.5c: Find \( \frac{{\text{d}V}}{{\text{d}x}}\).
• 09N.1.sl.TZ0.6a: Find \(f'(x)\).
• 11N.2.sl.TZ0.4b: Find  \(f'(x)\) .
• 09N.2.sl.TZ0.5B, b, i: The gradient of the curve \(y = p{x^2} + qx - 4\) at the point (2, –10) is 1. Find...
• 09M.1.sl.TZ1.15b: Sarah wishes to draw the tangent to \(f (x) = x^4\) parallel to L. Write down \(f ′(x)\).
• 09M.2.sl.TZ1.5a: Differentiate \(f (x)\) with respect to \(x\).
• 11M.2.sl.TZ1.3c: Find \(f'(x)\) .
• 09M.2.sl.TZ2.5a: Write down an expression for \(f ′(x)\).
• 09M.1.sl.TZ2.11a: Find \(f ′(x)\).
• 11M.1.sl.TZ2.11a: Differentiate \(f(x)\) with respect to \(x\) .
• 11M.1.sl.TZ2.11b: Differentiate \(g(x)\) with respect to \(x\) .
• 13M.1.sl.TZ1.15a: Find \(f ' (x) \).
• 13M.2.sl.TZ1.4b: Find \(f ′(x)\).
• 11M.2.sl.TZ2.5b: Find \(f'(x)\) .
• 13M.1.sl.TZ2.11a: Find \(f ' (x) \).
• 13M.2.sl.TZ2.5b: Find the derivative of \(y = \frac{{ - {x^2}}}{{10}} + \frac{{27}}{2}x\).
• 07M.1.sl.TZ0.11a: (i) Differentiate \(f_1 (x) \) with respect to x. (ii) Differentiate \(f_2 (x) \) with respect...
• SPM.1.sl.TZ0.9a: Write down \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• SPM.1.sl.TZ0.14a: Write down \(f'(x)\) .
• SPM.1.sl.TZ0.15b: Find the number of machines that should be made and sold each month to maximize \(P(x)\) .
• 07M.2.sl.TZ0.3i.b: Find \(f ′(x)\).
• 07M.2.sl.TZ0.3ii.b: Find \(\frac{{dy}}{{dx}}\).
• SPM.2.sl.TZ0.6e: Write down \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).
• 07N.1.sl.TZ0.15a: Find \(f ′(x)\) .
• 07N.2.sl.TZ0.5b: Differentiate \(f (x)\) .
• 08N.2.sl.TZ0.5c: Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\) .
• 08M.1.sl.TZ1.3a: Find \(f'(x)\).
• 08M.2.sl.TZ1.5ii.d: Find \(\frac{{{\text{d}}V}}{{{\text{d}}x}}\).
• 08M.1.sl.TZ2.12a: Find \(f'(x)\).
• 08M.1.sl.TZ2.12b: Find \(f''(x)\).
• 08M.2.sl.TZ2.4ii.a: Find \(C'(x)\).
• 14M.1.sl.TZ2.15a: Write down the derivative of the function.
• 14M.2.sl.TZ2.5e: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
• 13N.1.sl.TZ0.9b: Differentiate \(f(x) = x(2{x^3} - 1)\).
• 13N.2.sl.TZ0.4b: Find \(f'(x)\).
• 14M.1.sl.TZ1.10a: Write down \(f'(x)\).
• 14M.1.sl.TZ1.15a: Write down \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 14M.2.sl.TZ1.6d: The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\). Find...
• 15M.1.sl.TZ1.15b: Find the value of \(x\) that makes the volume a maximum.
• 15M.2.sl.TZ1.5a: Write down \(f'(x)\).
• 15M.2.sl.TZ2.5b: Find \(f'(x)\).
• 14N.1.sl.TZ0.15a: Find \(\frac{{{\text{d}}y}}{{{\text{d}}x}}\).
• 14N.2.sl.TZ0.3e: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
• 17M.2.sl.TZ2.6g: The equation \(f(x) = m\), where \(m \in \mathbb{R}\), has four solutions. Find the possible...
• 17M.2.sl.TZ2.6f: Write down the number of possible solutions to the equation \(f(x) = 5\).
• 17M.2.sl.TZ2.6e: Write down the range of \(f(x)\).
• 17M.2.sl.TZ2.6d.ii: Write down the intervals where the gradient of the graph of \(y = f(x)\) is positive.
• 17M.2.sl.TZ2.6d.i: Write down the \(x\)-coordinates of these two points;
• 17M.2.sl.TZ2.6c.ii: Find \(f(2)\).
• 17M.2.sl.TZ2.6c.i: Show that \(a = 8\).
• 17M.2.sl.TZ2.6b: Find \(f'(x)\).
• 17M.2.sl.TZ2.6a: Write down the \(y\)-intercept of the graph.
• 17M.2.sl.TZ1.6e: Find the \(y\)-coordinate of the local minimum.
• 17M.2.sl.TZ1.6d.ii: Hence justify that \(g\) is decreasing at \(x =  - 1\).
• 17M.2.sl.TZ1.6d.i: Find \(g’( - 1)\).
• 17M.2.sl.TZ1.6b.ii: Find the equation of the tangent to the graph of \(y = g(x)\) at \(x = 2\). Give your answer in...
• 17M.2.sl.TZ1.6b.i: Show that \(k = 6\).
• 17M.2.sl.TZ1.6a: Find \(g'(x)\).