DP Mathematical Studies Questionbank
Models using functions of the form \(f\left( x \right) = a{x^m} + b{x^n} + \ldots \); \(m,n \in \mathbb{Z}\) .
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[N/A]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.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.TZ1.4b: Using your value of k , find f ′(x).
- 18M.2.sl.TZ1.4a: Find the value of k.
- 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 \(f\).
- 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.
- 16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
- 10M.2.sl.TZ1.3a: Write down the values of x where the graph of f (x) intersects the x-axis.
- 10N.2.sl.TZ0.5a: Write down f (0).
- 12N.2.sl.TZ0.5a: Write down the equation of the vertical asymptote of the graph of y = g(x) .
- 11N.2.sl.TZ0.4a: Write down (i) the equation of the vertical asymptote to the graph of \(y = f (x)\)...
- 09M.2.sl.TZ2.5b: Consider the graph of f. The graph of f passes through the point P(1, 4). Find the value of c.
- 09M.2.sl.TZ2.5c, i: There is a local minimum at the point Q. Find the coordinates of Q.
- 13M.2.sl.TZ1.4a: Calculate \(f (1)\).
- 07M.2.sl.TZ0.3i.a: Write down the equation of the vertical asymptote.
- 07N.2.sl.TZ0.1ii.a: Sketch the curve of the function \(f (x) = x^3 − 2x^2 + x − 3\) for values of \(x\) from −2 to 4,...
- 08N.2.sl.TZ0.5a: (i) Write down the value of \(y\) when \(x\) is \(2\). (ii) Write down the coordinates of...
- 08N.2.sl.TZ0.5b: Sketch the curve for \( - 4 \leqslant x \leqslant 3\) and \( - 10 \leqslant y \leqslant 10\)....
- 12M.2.sl.TZ1.5a: Sketch the graph of y = f (x) for −3 ≤ x ≤ 6 and −10 ≤ y ≤ 10 showing clearly the axes intercepts...
- 11M.2.sl.TZ1.3b: Sketch the graph of the function \(y = f(x)\) for \( - 5 \leqslant x \leqslant 5\) and...
- 09M.1.sl.TZ1.15c, ii: Write down the value of \(f (x)\) at this point.
- 14M.2.sl.TZ2.5d: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
- 13N.2.sl.TZ0.4a: Find \(f( - 2)\).
- 15M.2.sl.TZ2.5a: Find \(f( - 2)\).
