DP Mathematics SL Questionbank

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Directly related questions

• 08M.2.sl.TZ1.4b: Solve the equation \(f(x) = 1\) .
• 16M.2.sl.TZ1.9a: Find the displacement of P from O after 5 seconds.
• 17M.2.sl.TZ2.6c: The equation \((f \circ g)(x) = k\) has exactly two solutions, for...
• 12M.2.sl.TZ1.2b: Solve the equation \(f(x) = 0\) .
• 14M.2.sl.TZ2.8c: How long does it take for the number of bacteria in colony \({\text{A}}\) to reach \(400\)?
• 13N.1.sl.TZ0.10d: The graph of \(g\) intersects the graph of \(f'\) when \(x = q\). Find the value of \(q\).
• 15M.2.sl.TZ1.7b: The graph of \(f\) is translated to the graph of \(g\) by the vector...
• 16M.2.sl.TZ2.9c: Write down the value of \(b\).
• 16M.2.sl.TZ1.9d: Find the acceleration of P after 3 seconds.
• 16M.2.sl.TZ1.7b: Find the least number of whole years for which \(\frac{{{P_t}}}{{{P_0}}} < 0.75\).
• 16M.2.sl.TZ1.7a: (i)     Find the value of \(k\). (ii)     Interpret the meaning of the value of \(k\).
• 17M.2.sl.TZ2.10b.ii: Explain why the probability of drawing three white marbles is \(\frac{1}{6}\).
• 17M.2.sl.TZ2.10b.i: Write down the probability of drawing three blue marbles.
• 17M.2.sl.TZ2.10a.i: Find \(q\).
• 08M.2.sl.TZ1.10c: There are two values of x for which the gradient of f is equal to the gradient of g. Find both...
• 14N.2.sl.TZ0.4b: Solve \(f(x) = 0\).
• 15N.2.sl.TZ0.9e: During which year were the number of coyotes the same as the number of foxes?
• 16M.2.sl.TZ1.10c: Find \(\theta \).
• 16M.2.sl.TZ1.9b: Find when P is first at rest.
• 16M.2.sl.TZ1.2a: Solve \(f(x) = g(x)\).
• 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.TZ2.6a: Show that \((f \circ g)(x) = {x^4} - 4{x^2} + 3\).
• 17M.2.sl.TZ2.10d: Grant plays the game until he wins two prizes. Find the probability that he wins his second prize...
• 17N.1.sl.TZ0.8b: Find the equation of \(L\) in the form \(y = ax + b\).
• 18M.2.sl.TZ1.7b: Hence find the value of n such that \(\sum\limits_{k = 1}^n {{x_k} = 861} \).
• 12M.2.sl.TZ1.2a(i) and (ii): (i)     Write down the coordinates of the vertex. (ii)    Hence or otherwise, express the...
• 09M.2.sl.TZ2.10f: Let \(g(x) = \ln (x + 1)\) , for \(0 \le x \le \pi \) . There is a value of x, between \(0\) and...
• 13M.2.sl.TZ1.9b: Solve \(f(x) = 95\) .
• 13M.2.sl.TZ2.10b: Consider all values of \(m\) such that the graphs of \(f\) and \(g\) intersect. Find the value of...
• 14M.1.sl.TZ2.8c: The graph of \(f\) has its vertex on the \(x\)-axis. Write down the solution of \(f(x) = 0\).
• 17M.2.sl.TZ1.10a.iii: Write down the value of \(k\).
• 15M.2.sl.TZ2.7: Let \(f(x) = k{x^2} + kx\) and \(g(x) = x - 0.8\). The graphs of \(f\) and \(g\) intersect at two...
• 16M.2.sl.TZ2.9b: Find \(f'(x)\).
• 16M.2.sl.TZ2.9d: Given that \(g'(1) =  - e\), find the value of \(a\).
• 16M.2.sl.TZ1.2b: Find the area of the region enclosed by the graphs of \(f\) and \(g\).
• 16M.2.sl.TZ2.9e: There is a value of \(x\), for \(1 < x < 4\), for which the graphs of \(f\) and \(g\) have...
• 16M.2.sl.TZ1.9e: Find the maximum speed of P.
• 17M.2.sl.TZ2.B10c: Jill plays the game nine times. Find the probability that she wins exactly two prizes.
• 17N.1.sl.TZ0.8a: Show that \(f’(1) = 1\).
• 17N.1.sl.TZ0.8c: Find the \(x\)-coordinate of Q.
• 17N.2.sl.TZ0.5b: The following diagram shows part of the graph of \(f\). The region enclosed by the graph of...
• 08M.2.sl.TZ2.10b(i) and (ii): At the end of 2000 there were \(25600\) people in the city who used taxis. After n years the...
• 09M.2.sl.TZ1.6b: Find the smallest value of n for which \({S_n} > 40\) .
• 13M.2.sl.TZ2.7b: The area of the shaded region is \(25\) cm2 . Find the value of \(r\) .
• 16M.2.sl.TZ2.9a: Write down the equation of the horizontal asymptote of the graph of \(f\).
• 16N.2.sl.TZ0.4b: Hence, find the area of the region enclosed by the graphs of \(f\) and \(g\).
• 16M.2.sl.TZ1.9c: Write down the number of times P changes direction.
• 16M.1.sl.TZ2.4: Three consecutive terms of a geometric sequence are \(x - 3\), 6 and \(x + 2\). Find the...
• 16M.2.sl.TZ1.10b: Show that...
• 16M.2.sl.TZ1.10d: (i)     Show that...
• 17M.2.sl.TZ1.10a.i: Write down the value of \(q\);
• 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.TZ2.5: Consider a geometric sequence where the first term is 768 and the second term is 576. Find the...
• 18M.2.sl.TZ1.1a: Find f '(x).
• 18M.2.sl.TZ1.7a: Given that xk + 1 = xk + a, find a.
• 08M.2.sl.TZ2.10c(i) and (ii): Let R be the ratio of the number of people using taxis in the city to the number of taxis. The...
• SPNone.2.sl.TZ0.10b: Kevin thinks that the function \(g(t) = - 5.2{t^2} + 9.5t + 100\) is a better model for the data....
• 14M.1.sl.TZ1.4b: Hence, solve \({\log _3}27 + {\log _8}\frac{1}{8} - {\log _{16}}4 = {\log _4}x\).
• 14M.2.sl.TZ2.8d: The number of bacteria in colony \({\text{B}}\) after \(t\) hours is modelled by the function...
• 14N.2.sl.TZ0.9b: Another sequence \({v_n}\) is defined by \({v_n} = a{n^k}\), where...
• 14N.2.sl.TZ0.9c: Find the smallest value of \(n\) for which \({v_n} > {u_n}\).
• 15N.2.sl.TZ0.4c: Find the least value of \(n\) such that \({S_n} > 75\,000\).
• 17M.2.sl.TZ1.10a.ii: Write down the value of \(h\);
• 17M.2.sl.TZ1.10b.i: Find \(\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x} \).
• 17M.2.sl.TZ2.10a.ii: Find \(p\).
• 17M.2.sl.TZ2.10b.iii: The bag contains a total of ten marbles of which \(w\) are white. Find \(w\).
• 17N.1.sl.TZ0.8d: Find the area of the region enclosed by the graph of \(f\) and the line \(L\).
• 17N.2.sl.TZ0.5a: Find the value of \(p\).
• 08M.2.sl.TZ2.10a(i) and (ii): (i)     Find the number of taxis in the city at the end of 2005. (ii)    Find the year in...
• 09M.2.sl.TZ2.3: Solve the equation \({{\rm{e}}^x} = 4\sin x\) , for \(0 \le x \le 2\pi \) .
• SPNone.2.sl.TZ0.10a(i), (ii) and (iii): Jane thinks that the function \(f(t) = - 0.25{t^3} - 2.32{t^2} + 1.93t + 106\) is a suitable...
• 11M.2.sl.TZ1.6: Let \(f(x) = \cos ({x^2})\) and \(g(x) = {{\rm{e}}^x}\) , for \( - 1.5 \le x \le 0.5\) . Find...
• 14M.2.sl.TZ2.8e: The number of bacteria in colony \({\text{B}}\) after \(t\) hours is modelled by the function...
• 14N.1.sl.TZ0.4b: Hence or otherwise, solve \(3\ln 2 - \ln 4 =  - \ln x\).
• 16N.2.sl.TZ0.1c: Solve \((g \circ f)(x) = 0\).
• 16M.2.sl.TZ1.10a: Find \(\overrightarrow {{\text{AB}}} \).
• 17M.2.sl.TZ2.6b: On the following grid, sketch the graph of \((f \circ g)(x)\), for...
• 18M.2.sl.TZ1.1b: Find f "(x).
• 18M.2.sl.TZ1.1c: Solve f '(x) = f "(x).