DP Mathematical Studies Questionbank

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• 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.TZ1.6c: Use your answer to part (a) and the value of \(k\), to find the \(x\)-coordinates of the...
• 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 \(g'(x)\).
• 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.
• 10M.1.sl.TZ2.15a: State whether f (0) is greater than, less than or equal to f (−2). Give a reason for your answer.
• 10N.2.sl.TZ0.5f: Lines L1 and L2 are parallel, and they are tangents to the graph of f (x) at points A and B...
• 09M.2.sl.TZ1.5g, i: On your graph draw and label the tangent T.
• 11M.2.sl.TZ1.3g: Find the gradient of the tangent to the graph of \(f\) at \(x = 1\).
• 07M.1.sl.TZ0.11c: Draw the tangent to the curved graph for this value of x on the figure, showing clearly the...
• SPM.1.sl.TZ0.5d: where the gradient of the tangent to the curve is positive;
• SPM.1.sl.TZ0.9b: The point \({\text{P}}(3{\text{, }}9)\) lies on the curve \(y = {x^2}\) . Find the gradient of...
• 07N.2.sl.TZ0.5c: Find the coordinates of the point where the tangent to P is parallel to the line L.
• 08N.2.sl.TZ0.5d: Let \({L_1}\) be the tangent to the curve at \(x = 2\). Let \({L_2}\) be a tangent to the curve,...
• 15M.2.sl.TZ2.5f: Let \(T\) be the tangent to the graph of \(f\) at \(x =  - 2\). Draw \(T\) on your sketch.
• 14N.1.sl.TZ0.15b: The gradient of the tangent to the curve is \( - 14\) when \(x = 1\). Find the value of \(a\).
• 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.1.sl.TZ1.5c: Find the equation of the line DC. Write your answer in the form ax + by + d = 0 where a , b and d...
• 18M.1.sl.TZ1.5b: Find the gradient of the line DC.
• 18M.1.sl.TZ1.5a: Write down the coordinates of C, the midpoint of line segment AB.
• 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 \(f\).