DP Mathematics SL Questionbank

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• 17N.2.sl.TZ0.9d: Find the total distance travelled by P when its velocity is increasing.
• 17N.2.sl.TZ0.9c: Find an expression for the velocity of P at time \(t\).
• 17N.2.sl.TZ0.9b: Hence or otherwise, find all possible values of \(t\) for which the velocity of P is decreasing.
• 17N.2.sl.TZ0.9a: Write down the values of \(t\) when \(a = 0\).
• 16M.2.sl.TZ2.7: A particle moves in a straight line. Its velocity \(v{\text{ m}}\,{{\text{s}}^{ - 1}}\) after...
• 16M.2.sl.TZ1.9e: Find the maximum speed of P.
• 16M.2.sl.TZ1.9d: Find the acceleration of P after 3 seconds.
• 16M.2.sl.TZ1.9c: Write down the number of times P changes direction.
• 16M.2.sl.TZ1.9b: Find when P is first at rest.
• 16M.2.sl.TZ1.9a: Find the displacement of P from O after 5 seconds.
• 16N.2.sl.TZ0.9d: (i)     Find the total distance travelled by P between \(t = 1\) and \(t = p\). (ii)     Hence...
• 16N.2.sl.TZ0.9c: (i)     Find the value of \(q\). (ii)     Hence, find the speed of P when \(t = q\).
• 16N.2.sl.TZ0.9b: Find the value of \(p\).
• 16N.2.sl.TZ0.9a: Find the initial velocity of \(P\).
• 12N.1.sl.TZ0.3a: Find \(\int_4^{10} {(x - 4){\rm{d}}x} \) .
• 12N.1.sl.TZ0.3b: Part of the graph of \(f(x) = \sqrt {{x^{}} - 4} \) , for \(x \ge 4\) , is shown below. The...
• 08M.1.sl.TZ1.5b: Given that \(\int_0^3 {\frac{1}{{2x + 3}}} {\rm{d}}x = \ln \sqrt P \) , find the value of P.
• 08M.1.sl.TZ2.7a: Show that \(\int_5^1 {f(x){\rm{d}}x = - 4} \) .
• 08M.1.sl.TZ2.7b: Find the value of  \(\int_1^2 {(x + f(x)){\rm{d}}x + } \int_2^5 {(x + f(x)){\rm{d}}x} \) .
• 12M.1.sl.TZ1.6: Given that \(\int_0^5 {\frac{2}{{2x + 5}}} {\rm{d}}x = \ln k\) , find the value of k .
• 10M.1.sl.TZ1.6: The region enclosed by the curve of f and the x-axis is rotated \(360^\circ \) about the...
• 09M.2.sl.TZ2.8c: The diagram below shows a part of the graph of a quadratic function \(g(x) = x(a - x)\) . The...
• 10N.2.sl.TZ0.2a: On the grid below, sketch the graph of v , clearly indicating the maximum point.
• 10N.2.sl.TZ0.2b(i) and (ii): (i)     Write down an expression for d . (ii)    Hence, write down the value of d .
• 10M.2.sl.TZ2.6a: Write down the x-coordinate of A.
• 10M.2.sl.TZ2.6c: Find \(\int_p^q {f(x){\rm{d}}x} \) . Explain why this is not the area of the shaded region.
• 10M.2.sl.TZ2.6b(i) and (ii): Find the value of (i)     p ; (ii)    q .
• 11N.1.sl.TZ0.10b: Find the area of the region enclosed by the curve of g , the x-axis, and the lines \(x = 2\) and...
• 11N.1.sl.TZ0.10a: Find the equation of L .
• 11N.1.sl.TZ0.10c: The graph of g is reflected in the x-axis to give the graph of h . The area of the region...
• 14M.1.sl.TZ1.3a: Find \(\int_1^2 {{{\left( {f(x)} \right)}^2}{\text{d}}x} \).
• 14M.1.sl.TZ1.6: Let \(\int_\pi ^a {\cos 2x{\text{d}}x}  = \frac{1}{2}{\text{, where }}\pi  < a < 2\pi \)....
• 13N.1.sl.TZ0.4a: Find \(\int_1^6 {2f(x){\text{d}}x} \).
• 13N.1.sl.TZ0.4b: Find \(\int_1^6 {\left( {f(x) + 2} \right){\text{d}}x} \).
• 15M.2.sl.TZ1.10d: Verify that \(\ln 3 + \int_2^a {g'(x){\text{d}}x = g(a)} \), where \(0 \le a \le 10\).
• 14N.1.sl.TZ0.6: The following diagram shows the graph of \(f(x) = \frac{x}{{{x^2} + 1}}\), for \(0 \le x \le 4\),...
• 15N.1.sl.TZ0.10c: The following diagram shows the shaded regions \(A\), \(B\) and \(C\). The regions are...
• 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.TZ2.8c.i: Find the coordinates of B.
• 17M.2.sl.TZ2.8b.ii: Write down the rate of change of \(f\) at A.
• 17M.2.sl.TZ2.8b.i: Write down the coordinates of A.
• 17M.2.sl.TZ2.8a: Find the value of \(p\).
• 17M.2.sl.TZ2.7: Note:     In this question, distance is in metres and time is in seconds.   A particle moves...
• 17M.1.sl.TZ2.10d: Given that the area of triangle ABC is \(p\) times the area of \(R\), find the value of \(p\).
• 17M.1.sl.TZ2.10c: Find the area of triangle ABC, giving your answer in terms of \(k\).
• 17M.1.sl.TZ2.10b: Show that the \(x\)-coordinate of B is \( - \frac{k}{2}\).
• 17M.1.sl.TZ2.10a.ii: Find the gradient of \(L\).
• 17M.1.sl.TZ2.10a.i: Write down \(f'(x)\).
• 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.TZ1.7a.ii: Find the total distance travelled by P, for \(0 \leqslant t \leqslant 8\).