DP Mathematics SL Questionbank

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• 17N.2.sl.TZ0.5b: The following diagram shows part of the graph of \(f\). The region enclosed by the graph of...
• 17N.2.sl.TZ0.5a: Find the value of \(p\).
• 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.TZ2.10a.i: Write down \(f'(x)\).
• 17M.1.sl.TZ2.10a.ii: Find the gradient of \(L\).
• 17M.1.sl.TZ2.10b: Show that the \(x\)-coordinate of B is \( - \frac{k}{2}\).
• 16M.1.sl.TZ2.10c: Let \({A_T}\) be the area of the triangle OPQ. Given that \({A_T} = k{A_R}\), find the value of...
• 16M.1.sl.TZ2.10b: Show that \({A_R} = \frac{2}{3}{a^3}\).
• 16M.1.sl.TZ2.10a: (i)     Given that \(f'(x) = \frac{{2{a^2} - 4{x^2}}}{{\sqrt {{a^2} - {x^2}} }}\), for...
• 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.TZ0.10a: Find \(f'(x)\) .
• 12N.1.sl.TZ0.10b: Let \(g(x) = \ln \left( {\frac{{6x}}{{x + 1}}} \right)\) , for \(x > 0\) . Show that...
• 12M.1.sl.TZ2.8a(i) and (ii): The function can be written in the form \(f(x) = a{(x - h)^2} + k\) . (i)     Write down the...
• 12M.1.sl.TZ2.8b: Find \(f(x)\)  , giving your answer in the form \(A{x^2} + Bx + C\) .
• 18M.2.sl.TZ2.9e: Find the total distance travelled by P.
• 18M.2.sl.TZ2.9d: Find the acceleration of P when it changes direction.
• 18M.2.sl.TZ2.9c: Write down the number of times that the acceleration of P is 0 m s−2 .
• 18M.2.sl.TZ2.9b: Find the maximum speed of P.
• 18M.2.sl.TZ2.9a: Find the initial velocity of P.
• 18M.1.sl.TZ2.2b: Find the area of the region enclosed by the graph of \(f\), the x-axis and the lines x = 1 and x...
• 18M.1.sl.TZ2.2a: Find \(\int {\left( {6{x^2} - 3x} \right){\text{d}}x} \).
• 12M.1.sl.TZ2.8c: Calculate the area enclosed by the graph of f , the x-axis, and the lines \(x = 2\) and \(x = 4\) .
• 12N.1.sl.TZ0.10c: Let \(h(x) = \frac{1}{{x(x + 1)}}\) . The area enclosed by the graph of h , the x-axis and the...
• 10M.1.sl.TZ2.10a(i) and (ii): Solve for \(0 \le x < 2\pi \) (i)     \(6 + 6\sin x = 6\) ; (ii)    \(6 + 6\sin x = 0\) .
• 10M.1.sl.TZ2.10b: Write down the exact value of the x-intercept of f , for \(0 \le x < 2\pi \) .
• 10M.1.sl.TZ2.10c: The area of the shaded region is k . Find the value of k , giving your answer in terms of \(\pi \) .
• 10M.1.sl.TZ2.10d: Let \(g(x) = 6 + 6\sin \left( {x - \frac{\pi }{2}} \right)\) . The graph of f is transformed to...
• 10M.1.sl.TZ2.10e: Let \(g(x) = 6 + 6\sin \left( {x - \frac{\pi }{2}} \right)\) . The graph of f is transformed to...
• 09N.1.sl.TZ0.10c: Find an expression for the area of R .
• 09M.1.sl.TZ1.10c: It is given that \(\int {f(x){\rm{d}}x = \frac{a}{2}} \ln ({x^2} + 1) + C\) . (i)     Find the...
• 09M.2.sl.TZ2.8a: Find the area of R.
• 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.TZ0.8a: Find the value of a and of b .
• 10N.2.sl.TZ0.8b: The graph of f has a maximum value when \(x = c\) . Find the value of c .
• 10N.2.sl.TZ0.8c: The region under the graph of f from \(x = 0\) to \(x = c\) is rotated \({360^ \circ }\) about...
• 10N.2.sl.TZ0.8d: Let R be the region enclosed by the curve, the x-axis and the line \(x = c\) , between \(x = a\)...
• 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 .
• SPNone.2.sl.TZ0.9c(i) and (ii): Let R be the region in the first quadrant enclosed by the graph of h , the x-axis and the line...
• 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...
• 11M.1.sl.TZ2.8c(i) and (ii): The shaded region R is enclosed by the graph of f , the line T , and the x-axis. (i)     Write...
• 11M.1.sl.TZ2.8a: Show that the equation of T is \(y = 4x - 2\) .
• 11M.1.sl.TZ2.8b: Find the x-intercept of T .
• 14M.1.sl.TZ2.10c: The following diagram shows part of the graph of \(f\). The shaded region is enclosed by the...
• 13M.1.sl.TZ2.7a: Find \(\int_0^2 {f(x){\rm{d}}x} \) .
• 13M.1.sl.TZ2.7b: The shaded region is enclosed by the graph of \(f\) , the \(x\)-axis, the \(y\)-axis and the line...
• 15M.1.sl.TZ1.7: Let \(f(x) = \cos x\), for \(0\) \(\le \) \(x\) \( \le \) \(2\pi \). The following diagram shows...
• 15M.2.sl.TZ1.10e: The following diagram shows the graph of \(g'\), the derivative of \(g\). The shaded region...
• 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...