DP Mathematics SL Questionbank

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• 17M.2.sl.TZ2.8d: Let \(R\) be the region enclosed by the graph of \(f\) , the \(x\)-axis, the line \(x = b\) and...
• 17M.2.sl.TZ2.8c.ii: Find the the rate of change of \(f\) at B.
• 17M.2.sl.TZ1.10c: Let \(d\) be the vertical distance from a point on the graph of \(h\) to the line \(y = x\)....
• 17M.2.sl.TZ1.10b.ii: Hence, find the area of the region enclosed by the graphs of \(h\) and \({h^{ - 1}}\).
• 17M.2.sl.TZ1.10b.i: Find \(\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x} \).
• 17M.2.sl.TZ1.10a.iii: Write down the value of \(k\).
• 17M.2.sl.TZ1.10a.i: Write down the value of \(q\);
• 17M.2.sl.TZ1.10a.ii: Write down the value of \(h\);
• 16M.1.sl.TZ1.9c: The graph of \(f\) is transformed by a vertical stretch with scale factor \(\frac{1}{{\ln 3}}\)....
• 16M.1.sl.TZ1.9b: Find \(f(x)\), expressing your answer as a single logarithm.
• 16M.1.sl.TZ1.9a: Find the \(x\)-coordinate of P.
• 16N.2.sl.TZ0.10c: (i)     Find \(w\). (ii)     Hence or otherwise, find the maximum positive rate of change of \(g\).
• 16N.2.sl.TZ0.10b: (i)     Write down the value of \(k\). (ii)     Find \(g(x)\).
• 16N.2.sl.TZ0.10a: (i)     Find the value of \(c\). (ii)     Show that \(b = \frac{\pi }{6}\). (iii)     Find the...
• 08N.1.sl.TZ0.6c: Show that B corresponds to a point of inflexion on the graph of f .
• 08M.1.sl.TZ1.8c: Find the x-coordinate of N.
• 08M.2.sl.TZ1.5b: Complete the table, for the graph of \(y = f(x)\) .
• 08M.2.sl.TZ1.5c: Justify your answer to part (b) (ii).
• 10M.1.sl.TZ1.9a: Use the quotient rule to show that \(f'(x) = \frac{{ - 1}}{{{{\sin }^2}x}}\) .
• 10M.1.sl.TZ1.9c: Find the value of p and of q.
• 10M.1.sl.TZ1.9b: Find \(f''(x)\) .
• 10M.1.sl.TZ1.9d: Use information from the table to explain why there is a point of inflexion on the graph of f...
• 09N.1.sl.TZ0.9b: The second derivative \(f''(x) = \frac{{40(3{x^2} + 4)}}{{{{({x^2} - 4)}^3}}}\) . Use this...
• 09M.1.sl.TZ1.10b: Given that \(f''(x) = \frac{{2ax({x^2} - 3)}}{{{{({x^2} + 1)}^3}}}\) , find the coordinates of...
• 09M.1.sl.TZ2.6c: The point P on the graph of f has x-coordinate \(3\). Explain why P is not a point of inflexion.
• 10N.2.sl.TZ0.7a: There are two points of inflexion on the graph of f . Write down the x-coordinates of these points.
• 10N.2.sl.TZ0.7b: Let \(g(x) = f''(x)\) . Explain why the graph of g has no points of inflexion.
• 11M.2.sl.TZ1.9b(i) and (ii): (i)     Find \(f'(x)\) . (ii)    Show that \(f''(x) = (4{x^2} - 2){{\rm{e}}^{ - {x^2}}}\) .
• 11M.2.sl.TZ1.9a: Identify the two points of inflexion.
• 11M.2.sl.TZ1.9c: Find the x-coordinate of each point of inflexion.
• 11M.2.sl.TZ1.9d: Use the second derivative to show that one of these points is a point of inflexion.
• 13M.1.sl.TZ1.10c: (i)     Find \(f''(1)\) . (ii)     Hence, show that there is no point of inflexion on the graph...
• 13M.1.sl.TZ2.10b: Explain why P is a point of inflexion.
• 18M.2.sl.TZ1.10b.ii: For the graph of \(f\), write down the period.
• 18M.2.sl.TZ1.10e: Find the first time when the ball’s speed is changing at a rate of 2 cm s−2.
• 18M.2.sl.TZ1.10d: Find the maximum speed of the ball.
• 18M.2.sl.TZ1.10c: Hence, write \(f\left( x \right)\) in the form \(p\,\,{\text{cos}}\,\left( {x + r} \right)\).
• 18M.2.sl.TZ1.10b.i: For the graph of \(f\), write down the amplitude.
• 18M.2.sl.TZ1.10a: Find the coordinates of A.
• 18M.1.sl.TZ1.8c: Find the values of x for which the graph of f is concave-down.
• 18M.1.sl.TZ1.8b: The graph of f has a point of inflexion at x = p. Find p.
• 18M.1.sl.TZ1.8a: Find f (x).