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.
• 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 \(f\).
• 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 \(g'(x)\).
• 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.
• 11N.1.sl.TZ0.14b: Find the interval of \(x\) for which \(f(x)\) is decreasing.
• 12N.2.sl.TZ0.5h: Write down the interval for which g(x) is increasing in the domain 0 < x < 5 .
• 12M.2.sl.TZ1.5j: P and Q are points on the curve such that the tangents to the curve at these points are...
• 09M.2.sl.TZ1.5c: Use your answer to part (b) to decide whether the function, \(f\) , is increasing or decreasing...
• 11M.2.sl.TZ2.5d: Using your answer to part (c), decide whether the function \(f(x)\) is increasing or decreasing...
• SPM.1.sl.TZ0.5e: where \(f(x) > 0\) and \(f'(x) < 0\) .
• 07M.2.sl.TZ0.3i.d: Write down all intervals in the given domain for which \(f (x)\) is increasing.
• 08N.2.sl.TZ0.5e: It is known that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} > 0\) for \(x < - 2\) and...
• 08M.1.sl.TZ2.15b: State whether \(f(4)\) is greater than, equal to or less than \(f(2)\).
• 08M.1.sl.TZ2.15c: Given that \(f(x)\) is increasing for \(4 \leqslant x < 7\), what can you say about the point...
• 09M.2.sl.TZ2.5c, ii: There is a local minimum at the point Q. Find the set of values of x for which the function is...
• 14M.1.sl.TZ2.13c: Write down the interval where \(f'(x) < 0\).
• 15M.2.sl.TZ1.5h: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). State the values of \(x\) for...
• 15M.2.sl.TZ2.5e: Let \(T\) be the tangent to the graph of \(f\) at \(x =  - 2\). Sketch the graph of \(f\) for...