DP Mathematics HL Questionbank

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• 18M.1.hl.TZ1.8: Let $a = {\text{sin}}\,b,\,\,0 < b < \frac{\pi }{2}$. Find, in terms of b, the solutions...
• 16M.1.hl.TZ2.9b: hence find the other solution to the equation for $0 < x < \frac{\pi }{2}$.
• 16M.1.hl.TZ2.9a: verify that $x = \frac{\pi }{{12}}$ is a solution to the equation;
• 16N.1.hl.TZ0.13d: Hence or otherwise solve the equation $\sin x + \sin 3x = \cos x$ in the interval...
• 17N.2.hl.TZ0.11c: Solve the equation $f(x) = 0$, giving your answers in the form $\arctan k$ where...
• 17N.2.hl.TZ0.11b.iii: Hence show that $f(x) = 0$ can be expressed as ${u^3} - 7{u^2} + 15u - 9 = 0$.
• 17N.2.hl.TZ0.11b.ii: Express $\sin 2x$ in terms of $u$.
• 17N.2.hl.TZ0.11b.i: Express $\sin x$ in terms of $\mu$.
• 12M.2.hl.TZ1.11a: Write down the coordinates of the minimum point on the graph of f .
• 12M.2.hl.TZ1.11b: The points ${\text{P}}(p,{\text{ }}3)$ and ${\text{Q}}(q,{\text{ }}3){\text{, }}q > p$,...
• 12M.1.hl.TZ2.2: Find the values of x for which the vectors...
• 08M.2.hl.TZ1.7: A system of equations is given by \[\cos x + \cos y =...
• 08N.1.hl.TZ0.11: (a)     Sketch the curve $f(x) = \sin 2x$ , $0 \leqslant x \leqslant \pi$ . (b)     Hence...
• 11M.1.hl.TZ2.13a: (i)     Sketch the graphs of $y = \sin x$ and $y = \sin 2x$ , on the same set of axes, for...
• 10M.1.hl.TZ1.13: (a)     Show that...
• 13M.2.hl.TZ2.6a: Solve the equation $3{\cos ^2}x - 8\cos x + 4 = 0$, where...
• 13M.2.hl.TZ2.6b: Find the exact values of $\sec x$ satisfying the equation $3{\sec ^4}x - 8{\sec ^2}x + 4 = 0$.
• 11N.2.hl.TZ0.4b: Hence, or otherwise, solve the equation $\arcsin x = \arctan a$.
• 12M.1.hl.TZ1.10b: By squaring both sides of the equation in part (a), solve the equation to find the angles in the...
• 11M.1.hl.TZ1.13d: Hence solve the equation $\cos 5\theta + \cos 3\theta + \cos \theta = 0$ , where...
• 11M.1.hl.TZ1.13e: By considering the solutions of the equation $\cos 5\theta = 0$ , show that...
• 14M.2.hl.TZ1.5a: Find the coordinates of the points where the line meets the curve.
• 14M.1.hl.TZ2.5b: Solve $\left| {\cos \left( {\frac{x}{4}} \right)} \right| = \frac{1}{2}$ for...
• 15M.1.hl.TZ2.3: Find all solutions to the equation $\tan x + \tan 2x = 0$ where $0^\circ  \le x < 360^\circ$.
• 15N.1.hl.TZ0.9: Solve the equation $\sin 2x - \cos 2x = 1 + \sin x - \cos x$ for...
• 15N.2.hl.TZ0.4b: Solve $f(x) = 3$ for $0 \le x \le \pi$.
• 14N.2.hl.TZ0.14b: Robert conjectures that ${\rm{C\hat AB}}$ can have two possible values. Show that Robert’s...