DP Mathematics SL Questionbank
Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes, symmetry, and consideration of domain and range.
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- 18M.2.sl.TZ2.7c: The line y = k, where \(k \in \mathbb{R}\) intersects the graph...
- 18M.2.sl.TZ2.7b: Write down the equation of the horizontal asymptote to the graph of f.
- 18M.2.sl.TZ2.7a: The line x = 3 is a vertical asymptote to the graph of f. Find the value of c.
- 18M.2.sl.TZ2.3b: The region enclosed by the graph of \(f\), the y-axis and the x-axis is rotated 360° about the...
- 18M.2.sl.TZ2.3a: Find the x-intercept of the graph of \(f\).
- 18M.2.sl.TZ1.4c: Find the area of the region enclosed by the graphs of f and g.
- 18M.2.sl.TZ1.4b: On the grid above, sketch the graph of g for −2 ≤ x ≤ 4.
- 18M.2.sl.TZ1.4a: Write down the coordinates of the vertex of the graph of g.
- 17N.2.sl.TZ0.2c: On the following grid, sketch the graph of \(f\).
- 17N.2.sl.TZ0.2b: The graph of \(f\) has a maximum at the point A. Write down the coordinates of A.
- 17N.2.sl.TZ0.2a: Find the \(x\)-intercept of the graph of \(f\).
- 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.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.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.1.sl.TZ1.9c: The line \(y = kx - 5\) is a tangent to the curve of \(f\). Find the values of \(k\).
- 17M.1.sl.TZ1.9b: Find the value of \(a\).
- 17M.1.sl.TZ1.9a: Find the value of \(p\).
- 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.TZ2.9d: Given that \(g'(1) = - e\), find the value of \(a\).
- 16M.2.sl.TZ2.9c: Write down the value of \(b\).
- 16M.2.sl.TZ2.9b: Find \(f'(x)\).
- 16M.2.sl.TZ2.9a: Write down the equation of the horizontal asymptote of the graph of \(f\).
- 16M.1.sl.TZ2.1c: Find the \(y\)-intercept.
- 16M.1.sl.TZ2.1b: Write down the value of \(a\) and of \(b\).
- 16M.1.sl.TZ2.1a: Write down the value of \(h\) and of \(k\).
- 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.
- 16M.1.sl.TZ1.5a: Show that the two zeros are 3 and \( - 6\).
- 16N.2.sl.TZ0.2b: (i) sketch the graph of \(f\), clearly indicating the point A; (ii) sketch the tangent to...
- 12N.2.sl.TZ0.3a: Write down the x-coordinate of P.
- 12N.2.sl.TZ0.3b: Write down the gradient of the curve at P.
- 12N.2.sl.TZ0.3c: Find the equation of the normal to the curve at P, giving your equation in the form \(y = ax + b\) .
- 12N.2.sl.TZ0.5a(i) and (ii): Write down the value of (i) \(a\) ; (ii) \(c\) .
- 12N.2.sl.TZ0.5b: Find the value of b .
- 12N.2.sl.TZ0.5c: Find the x-coordinate of R.
- 12M.1.sl.TZ2.10a: Use the quotient rule to show that \(f'(x) = \frac{{2{x^2} - 2}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\) .
- 12M.1.sl.TZ2.10b: Hence find the coordinates of B.
- 12M.1.sl.TZ2.10c: Given that the line \(y = k\) does not meet the graph of f , find the possible values of k .
- 12M.2.sl.TZ2.9a: Show that \(8a + 4b + c = 9\) .
- 12M.2.sl.TZ2.9b: The graph of f has a local minimum at \((1{\text{, }}4)\) . Find two other equations in a , b...
- 12M.2.sl.TZ2.9c: Find the value of a , of b and of c .
- 08N.2.sl.TZ0.4b: The graph of f intersects the x-axis when \(x = a\) , \(a \ne 0\) . Write down the value of a.
- 08M.2.sl.TZ2.9b: Write down the equation of the horizontal asymptote.
- 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.TZ0.9a: (i) Find the coordinates of A. (ii) Show that \(f'(x) = 0\) at A.
- 09N.1.sl.TZ0.9d: Write down the range of \(f\) .
- 09N.1.sl.TZ0.10b: Point A is the x-intercept of L . Find the x-coordinate of A.
- 09N.2.sl.TZ0.7: The fencing used for side AB costs \(\$ 11\) per metre. The fencing for the other three sides...
- 09M.2.sl.TZ2.10b: Write down (i) the amplitude; (ii) the period; (iii) the x-intercept that lies...
- 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.
- 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 .
- 10M.2.sl.TZ2.10b: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Show that...
- 10M.2.sl.TZ2.10a(i) and (ii): Let P and Q be points on the curve of f where the tangent to the graph of f is parallel to the...
- 10M.2.sl.TZ2.10c: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Sketch the graph of \(g'\) .
- 10M.2.sl.TZ2.10d: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Consider \(g'(x) = w\) ....
- SPNone.2.sl.TZ0.2a: Find the x-intercepts of the graph of f .
- SPNone.2.sl.TZ0.9b(i), (ii) and (iii): (i) Sketch the graph of h for \( - 4 \le x \le 4\) and \( - 5 \le y \le 8\) , including any...
- 11N.2.sl.TZ0.10b(i) and (ii): (i) Write down the x-coordinate of the maximum point on the graph of f . (ii) Write down...
- 11N.2.sl.TZ0.10a: Sketch the graph of f .
- 11N.2.sl.TZ0.10c: Show that \(f'(x) = \frac{{20 - 6x}}{{{{\rm{e}}^{0.3x}}}}\) .
- 11N.2.sl.TZ0.10d: Find the interval where the rate of change of f is increasing.
- 11M.1.sl.TZ1.7a: Find the value of k .
- 11M.1.sl.TZ1.7b: The line \(y = p\) intersects the graph of f . Find all possible values of p .
- 13M.2.sl.TZ1.5b.i: Find the total distance travelled by the particle in the first five seconds.
- 14M.2.sl.TZ1.9b: Find the values of \(x\) where the function is decreasing.
- 14M.2.sl.TZ2.2a: Find the \(x\)-coordinate of \({\text{A}}\) and of \({\text{B}}\).
- 13N.1.sl.TZ0.8c(i): Find the \(y\)-intercept of the graph of \(h\).
- 15M.2.sl.TZ1.7a: Find the coordinates of the local minimum point.
- 15M.2.sl.TZ1.10a: The graph of \(f\) has a local maximum point when \(x = p\). State the value of \(p\), and...
- 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...
- 15M.2.sl.TZ1.4a: For the graph of \(f\) (i) find the \(x\)-intercept; (ii) write down the equation of...
- 15M.2.sl.TZ1.7b: The graph of \(f\) is translated to the graph of \(g\) by the vector...
- 15N.2.sl.TZ0.3a: Find the equation of the vertical asymptote to the graph of \(f\).
- 15N.2.sl.TZ0.3b: Find the \(x\)-intercept of the graph of \(f\).
