DP Mathematical Studies Questionbank

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Directly related questions

• 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.TZ2.13c: Find the number of shirts produced when the cost of production is lowest.
• 18M.1.sl.TZ2.13b: Find the value of s.
• 18M.1.sl.TZ2.13a: Find the cost of producing 70 shirts.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 17N.1.sl.TZ0.11c: Find the value of \(a\) and of \(b\).
• 17N.1.sl.TZ0.11b: Write down the value of \(c\).
• 17N.1.sl.TZ0.11a: Find the equation of the axis of symmetry of the graph of \(y = f(x)\).
• 17M.2.sl.TZ1.6b.i: Show that \(k = 6\).
• 16N.2.sl.TZ0.6a: Write down a formula for \(A\), the surface area to be coated.
• 10M.1.sl.TZ2.15c: The point P(−2, 3) lies on the graph of f (x). From the information given about f ′(x), state...
• 10M.2.sl.TZ1.3c: Find the value of the local maximum of y = f (x).
• 10N.2.sl.TZ0.5d: (i) Use f '(x) to find the x-coordinate of M and of N. (ii) Hence or otherwise write down the...
• 12N.1.sl.TZ0.15b: Find using your answer to part (a) the x-coordinate of (i) the local maximum point; (ii) the...
• 12N.2.sl.TZ0.5g: Using your graphic display calculator find the coordinates of the local minimum point of y = g(x) .
• 10M.2.sl.TZ2.5d: Find the value of x that makes A a minimum.
• 12M.2.sl.TZ2.5d: Find the value of x for which V is a maximum.
• 12M.2.sl.TZ2.5e: Find the maximum volume of the container.
• 12M.2.sl.TZ2.5f: Find the length and height of the container for which the volume is a maximum.
• 09N.2.sl.TZ0.5A, f: Use Differential Calculus to verify that your answer to (e) is correct.
• 09M.2.sl.TZ1.5e, i: The graph of f has a local minimum at point P. Let T be the tangent to the graph of f at...
• 11M.2.sl.TZ1.3e: Write down the coordinates of the local maximum point on the graph of \(f\) .
• 13M.1.sl.TZ1.15c: The function has a local maximum at x = −2. Calculate the value of a.
• 13M.2.sl.TZ1.4c: Use your answer to part (b) to show that the x-coordinate of the local minimum point of the graph...
• 11M.2.sl.TZ2.5f: \({{\text{P}}_1}\) is the local maximum point and \({{\text{P}}_2}\) is the local minimum point...
• 13M.2.sl.TZ2.5c: Use the answer in part (b) to determine if A (75, 450) is the point furthest north on the track...
• SPM.1.sl.TZ0.5a: that are local maximum points;
• 07M.2.sl.TZ0.3ii.c: (i) Use your answer to part (b) to calculate the horizontal distance the ball has travelled from...
• 07N.1.sl.TZ0.15b: The function \(f (x)\) has a local maximum at the point where \(x = −1\). Find the value of a.
• 08M.2.sl.TZ1.5ii.e: (i)     Hence find the value of \(x\) and of \(y\) required to make the volume of the box a...
• 08M.2.sl.TZ2.4ii.b: Show that the cost per person is a minimum when \(10\) people are invited to the party.
• SPM.2.sl.TZ0.6f: (i)     Find the value of \(r\) that minimizes the total external surface area of the wastepaper...
• 14M.1.sl.TZ2.13a: Label the local maximum as \({\text{A}}\) on the graph.
• 14M.1.sl.TZ2.13b: Label the local minimum as B on the graph.
• 14M.1.sl.TZ2.15b: Use your graphic display calculator to find the coordinates of the local minimum point of...
• 13N.1.sl.TZ0.9c: Find the \(x\)-coordinate of the local minimum of the curve \(y = f(x)\).
• 13N.2.sl.TZ0.4c: The graph of the function \(f(x)\) has a local minimum at the point where \(x =  - 2\). Using...
• 13N.2.sl.TZ0.4e: The graph of the function \(f(x)\) has a local minimum at the point where \(x =  - 2\). Write...
• 14M.1.sl.TZ1.15b: The curve has a local minimum at the point where \(x = 2\). Find the value of \(k\).
• 14M.1.sl.TZ1.15c: The curve has a local minimum at the point where \(x = 2\). Find the value of \(y\) at this...
• 15M.2.sl.TZ1.5c: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Find \(f(2)\).
• 15M.2.sl.TZ1.5e: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Find the equation of the...
• 15M.2.sl.TZ1.5f: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Sketch the graph of...
• 15M.2.sl.TZ1.5d: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Find \(f'(2)\)