DP Mathematics HL Questionbank

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Directly related questions

• 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.2.hl.TZ1.11c: Find the coordinates of the point, on $y = f(x)$ , where the gradient of the graph is 3.
• 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 .
• 08M.2.hl.TZ1.2: (a)     Sketch the curve...
• 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.1.hl.TZ2.5a: Sketch the graph of $y = \frac{1}{{f(x)}}$.
• 11M.1.hl.TZ2.5b: Sketch the graph of  $y = x{\text{ }}f(x)$ .
• 11M.2.hl.TZ2.5: Sketch the graph of $f(x) = x + \frac{{8x}}{{{x^2} - 9}}$. Clearly mark the coordinates of the...
• 09M.1.hl.TZ2.11: A function is defined as $f(x) = k\sqrt x$, with $k > 0$ and $x \geqslant 0$ . (a)    ...
• SPNone.1.hl.TZ0.9b: Sketch the graph of f , showing clearly the coordinates of the maximum and minimum.
• SPNone.1.hl.TZ0.9c: Hence show that ${{\text{e}}^\pi } > {\pi ^{\text{e}}}$ .
• 13M.1.hl.TZ1.12c: Sketch the graph of $y = f(x)$.
• 13M.2.hl.TZ1.12a: Sketch the graph of ${v_A} = {t^3} - 5{t^2} + 6t$ for $t \geqslant 0$, with ${v_A}$ on the...
• 13M.2.hl.TZ1.12b: Write down the times for which the velocity of the particle is increasing.
• 13M.2.hl.TZ1.12c: Write down the times for which the magnitude of the velocity of the particle is increasing.
• 10M.1.hl.TZ1.5: The graph of $y = \frac{{a + x}}{{b + cx}}$ is drawn below.     (a)     Find the value of...
• 13M.1.hl.TZ2.12e: (i)     On a different diagram, sketch the graph of $y = f(|x|)$ where $x \in D$. (ii)    ...
• 13M.2.hl.TZ2.13c: Sketch the graph of $\theta$, for $0 \leqslant x \leqslant 20$.
• 11N.1.hl.TZ0.4a: sketch the graph of $f$;  
• 11N.2.hl.TZ0.1a: Sketch the graph, clearly labelling the x and y intercepts with their values.
• SPNone.2.hl.TZ0.6: The function f is of the form $f(x) = \frac{{x + a}}{{bx + c}}$, $x \ne - \frac{c}{b}$. Given...
• 11M.1.hl.TZ1.12d: Now consider the functions $g(x) = \frac{{\ln \left| x \right|}}{x}$ and...
• 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.TZ1.12: Let $f(x) = \left| x \right| - 1$. (a)     The graph of $y = g(x)$ is drawn below.      ...
• 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...
• 14M.1.hl.TZ2.5a: Sketch the graph of $y = \left| {\cos \left( {\frac{x}{4}} \right)} \right|$ for...
• 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.2.hl.TZ0.3a: Sketch the graph of $y = f(x)$, stating the coordinates of any maximum and minimum points and...
• 15N.1.hl.TZ0.12e: Sketch the graph of $y = f(x)$ indicating clearly the coordinates of the $x$-intercepts and...
• 15M.2.hl.TZ1.11a: Sketch the graph $y = f(x)$.
• 15M.2.hl.TZ2.3a: Sketch the graph of $y = {(x - 5)^2} - 2\left| {x - 5} \right| - 9,{\text{ for }}0 \le x \le 10$.
• 17N.2.hl.TZ0.10b: Sketch the graph of $y = f(x)$ showing clearly the minimum point and any asymptotic behaviour.
• 14N.3sp.hl.TZ0.1a: Sketch the graph of $y = f(x)$.