DP Mathematics HL Questionbank
Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes and symmetry, and consideration of domain and range.
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- 18M.1.hl.TZ2.2a: Sketch the graphs of \(y = \frac{x}{2} + 1\) and \(y = \left| {x - 2} \right|\) on the following...
- 18M.1.hl.TZ2.10b.ii: Sketch the graph of \(y = g\left( x \right)\). State the equations of any asymptotes and...
- 18M.1.hl.TZ2.10b.i: Express \(g\left( x \right)\) in the form \(A + \frac{B}{{x - 2}}\) where A, B are constants.
- 18M.2.hl.TZ2.10c: Sketch the graph of \(y = g\left( t \right)\) for t ≤ 0. Give the coordinates of any intercepts...
- 18M.2.hl.TZ2.10b: Show that \(g\left( t \right) = {\left( {\frac{{1 + t}}{{1 - t}}} \right)^2}\).
- 18M.1.hl.TZ1.9c: Sketch the graph of \(y = f\left( x \right)\) showing clearly the position of the points A and B.
- 16M.1.hl.TZ2.2: The function \(f\) is defined as...
- 16M.2.hl.TZ1.5b.ii: Write down the range of \(f\).
- 16M.2.hl.TZ1.5b.i: Sketch the graph \(y = f(x)\).
- 16M.1.hl.TZ1.7b: Find the exact solutions to the equation \(x + 2 = \left| {\frac{7}{{x - 4}}} \right|\).
- 16M.1.hl.TZ1.7a: Sketch on the same axes the curve \(y = \left| {\frac{7}{{x - 4}}} \right|\) and the line...
- 16N.2.hl.TZ0.2: Find the acute angle between the planes with equations \(x + y + z = 3\) and \(2x - z = 2\).
- 16N.2.hl.TZ0.5a: Sketch the graph of \(f\) indicating clearly any intercepts with the axes and the coordinates of...
- 17N.1.hl.TZ0.6a: Sketch the graph of \(y = \frac{{1 - 3x}}{{x - 2}}\), showing clearly any asymptotes and stating...
- 17N.2.hl.TZ0.10b: Sketch the graph of \(y = f(x)\) showing clearly the minimum point and any asymptotic behaviour.
- 17M.1.hl.TZ1.11e: Sketch the graph of \(y = f\left( {\left| x \right|} \right)\).
- 17M.1.hl.TZ1.11c: Show that \(\frac{1}{{x + 1}} - \frac{1}{{x + 2}} = \frac{1}{{{x^2} + 3x + 2}}\).
- 17M.1.hl.TZ1.11b: Sketch the graph of \(f(x)\), indicating on it the equations of the asymptotes, the coordinates...
- 17M.1.hl.TZ1.11a.ii: Factorize \({x^2} + 3x + 2\).
- 17M.1.hl.TZ1.11a.i: Express \({x^2} + 3x + 2\) in the form \({(x + h)^2} + k\).
- 12M.1.hl.TZ1.2a: Draw the graph of y = f (x) on the blank grid below.
- 12M.2.hl.TZ1.11a: Write down the coordinates of the minimum point on the graph of f .
- 12M.1.hl.TZ2.7a: On the axes below, sketch the graph of \(y = \frac{1}{{f(x)}}\) , clearly showing the coordinates...
- 12M.1.hl.TZ2.11a: State the range of f and of g .
- 12M.2.hl.TZ2.6a: Sketch the curve...
- 12M.2.hl.TZ2.12b: Sketch the graph of v against t , clearly showing the coordinates of any intercepts, and the...
- 12N.1.hl.TZ0.3a: Using the information shown in the diagram, find the values of a , b and c .
- 08N.2.hl.TZ0.6: (a) Sketch the curve \(y = \left| {\ln x} \right| - \left| {\cos x} \right| - 0.1\) ,...
- 11M.1.hl.TZ2.3a: Sketch the graph of the function. You are not required to find the coordinates of the maximum.
- 11M.2.hl.TZ2.5: Sketch the graph of \(f(x) = x + \frac{{8x}}{{{x^2} - 9}}\). Clearly mark the coordinates of the...
- 10M.1.hl.TZ1.5: The graph of \(y = \frac{{a + x}}{{b + cx}}\) is drawn below. (a) Find the value of...
- 10N.2.hl.TZ0.8: The diagram shows the graphs of a linear function f and a quadratic function g. On the...
- 11M.1.hl.TZ1.10b: On the axes below, sketch the graph of \(y = g(x)\) . On the graph, indicate any asymptotes and...
- 14M.2.hl.TZ1.10a: Find the equations of the horizontal and vertical asymptotes of the curve \(y = f(x)\).
- 14M.2.hl.TZ1.12: Let \(f(x) = \left| x \right| - 1\). (a) The graph of \(y = g(x)\) is drawn below. ...
- 14M.2.hl.TZ2.7a: (i) Sketch the graph of \(y = f(x)\), clearly indicating any asymptotes and axes...
- 14M.2.hl.TZ2.14a: Sketch the graph of \(y = v(t)\). Indicate clearly the local maximum and write down its coordinates.
- 13N.1.hl.TZ0.3b: State the range of \({f^{ - 1}}\).
- 13N.2.hl.TZ0.3a: Sketch the graph of \(y = f(x)\), stating the coordinates of any maximum and minimum points and...
- 15M.1.hl.TZ1.11c: Find the coordinates of any local maximum and minimum points on the graph of \(y(x)\). Justify...
- 15M.1.hl.TZ1.11d: Find the coordinates of any points of inflexion on the graph of \(y(x)\). Justify whether any...
- 15M.1.hl.TZ2.10a: Sketch the graph of \(y = f(x)\), indicating clearly any asymptotes and points of intersection...
- 15N.1.hl.TZ0.12e: Sketch the graph of \(y = f(x)\) indicating clearly the coordinates of the \(x\)-intercepts and...
- 15M.2.hl.TZ2.12b: Sketch a displacement/time graph for the particle, \(0 \le t \le 5\), showing clearly where the...
- 14N.1.hl.TZ0.1b: State the equations of the asymptotes of the graph of \(g\).
