DP Mathematics SL Questionbank
Composite functions of the form \(f(x) = a\sin (b(x + c)) + d\) .
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[N/A]Directly related questions
- 16M.1.sl.TZ1.3b: On the following grid sketch the graph of \(f\).
- 16M.1.sl.TZ1.3a: (i) Write down the amplitude of \(f\). (ii) Find the period of \(f\).
- 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.TZ0.10a(i), (ii), (iii) and (iv): (i) Find the value of a. (ii) Show that \(b = \frac{\pi }{6}\) . (iii) Find the value...
- 08N.1.sl.TZ0.10b: The transformation P is given by a horizontal stretch of a scale factor of \(\frac{1}{2}\) ,...
- 08N.1.sl.TZ0.10c: The graph of g is the image of the graph of f under P. Find \(g(t)\) in the form...
- 08N.1.sl.TZ0.10d: The graph of g is the image of the graph of f under P. Give a full geometric description of the...
- 08M.2.sl.TZ2.8a(i), (ii) and (iii): Use the graph to write down an estimate of the value of t when (i) the depth of water is...
- 08M.2.sl.TZ2.8b(i), (ii) and (iii): The depth of water can be modelled by the function \(y = \cos A(B(t - 1)) + C\) . (i) Show...
- 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.2.sl.TZ0.9b: Consider the graph of \(f\) . Write down (i) the x-intercept that lies between \(x = 0\) and...
- 09M.2.sl.TZ1.3b: Write down the period of \(h\) .
- 09M.2.sl.TZ1.3c: Write down the range of \(h\) .
- 09M.2.sl.TZ2.10c: Hence write \(f(x)\) in the form \(p\sin (qx + r)\) .
- 10N.2.sl.TZ0.10a: Find the height of a seat above the ground after 15 minutes.
- 10N.2.sl.TZ0.10c: The height of the seat above ground after t minutes can be modelled by the function...
- 10M.2.sl.TZ1.5a(i), (ii) and (iii): Find the value of (i) p ; (ii) q ; (iii) r.
- 10M.2.sl.TZ1.5b: The equation \(y = k\) has exactly two solutions. Write down the value of k.
- 10N.2.sl.TZ0.10b: After six minutes, the seat is at point Q. Find its height above the ground at Q.
- 10N.2.sl.TZ0.10d: The height of the seat above ground after t minutes can be modelled by the function...
- SPNone.1.sl.TZ0.10d: The function \(f(x)\) can be written in the form \(r\cos (x - a)\) . Write down the value of r...
- 11N.1.sl.TZ0.9c: Find \(f'(x)\) .
- 11N.1.sl.TZ0.9a(i), (ii) and (iii): Use the graph to write down the value of (i) a ; (ii) c ; (iii) d .
- 11N.1.sl.TZ0.9b: Show that \(b = \frac{\pi }{4}\) .
- 11N.1.sl.TZ0.9d: At a point R, the gradient is \( - 2\pi \) . Find the x-coordinate of R.
- 11M.2.sl.TZ1.8d: In the first rotation, there are two values of t when the bucket is descending at a rate of...
- 11M.2.sl.TZ1.8a: Show that \(a = 4\) .
- 11M.2.sl.TZ1.8b: The wheel turns at a rate of one rotation every 30 seconds. Show that \(b = \frac{\pi }{{15}}\) .
- 11M.2.sl.TZ1.8c: In the first rotation, there are two values of t when the bucket is descending at a rate of...
- 11M.1.sl.TZ2.10a(i) and (ii): Write down the height of P above ground level after (i) 10 minutes; (ii) 15 minutes.
- 11M.1.sl.TZ2.10b(i) and (ii): (i) Show that \(h(8) = 90.5\). (ii) Find \(h(21)\) .
- 11M.1.sl.TZ2.10c: Sketch the graph of h , for \(0 \le t \le 40\) .
- 11M.1.sl.TZ2.10d: Given that h can be expressed in the form \(h(t) = a\cos bt + c\) , find a , b and c .
- 14M.2.sl.TZ2.6a: Write down the value of \(r\).
- 14M.2.sl.TZ2.6b(i): Find \(p\).
- 14M.2.sl.TZ2.6b(ii): Find \(q\).
- 13N.1.sl.TZ0.5a: Find the value of \(k\).
- 13N.1.sl.TZ0.5b: Find the minimum value of \(f(x)\).
- 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.
- 13M.1.sl.TZ2.5a: \(p\)
- 13M.1.sl.TZ2.5c: \(r\) .
- 13M.1.sl.TZ2.5b: \(q\)
- 13M.2.sl.TZ1.10c: Find the value of \(a\) .
- 13M.2.sl.TZ1.10b: (i) Show that the period of \(h\) is \(25\) minutes. (ii) Write down the exact value of...
- 13M.2.sl.TZ1.10d: Sketch the graph of \(h\) , for \(0 \le t \le 50\) .
- 14N.2.sl.TZ0.5b: \(r\);
- 14N.2.sl.TZ0.5a: \(p\);
- 14N.2.sl.TZ0.5c: \(q\).
- 15N.1.sl.TZ0.4a: Write down the amplitude of \(f\).
- 15N.1.sl.TZ0.4b: Find the period of \(f\).
- 15N.1.sl.TZ0.4c: On the following grid, sketch the graph of \(y = f(x)\), for \(0 \le x \le 3\).
- 17M.2.sl.TZ2.4c: Use the model to find the depth of the water 10 hours after high tide.
- 17M.2.sl.TZ2.4b: Find the value of \(q\).
- 17M.2.sl.TZ2.4a: Find the value of \(p\).
