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 \(\mu \).
• 17M.1.hl.TZ1.3: Solve the equation \({\sec ^2}x + 2\tan x = 0,{\text{ }}0 \leqslant x \leqslant 2\pi \).
• 15N.2.hl.TZ0.4b: Solve \(f(x) = 3\) for \(0 \le x \le \pi \).
• 15N.1.hl.TZ0.9: Solve the equation \(\sin 2x - \cos 2x = 1 + \sin x - \cos x\) for...
• 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...
• 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 \(\arcsin x = \arctan a\).
• 11M.1.hl.TZ2.13a: (i)     Sketch the graphs of \(y = \sin x\) and \(y = \sin 2x\) , on the same set of axes, for...
• 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 \(0^\circ  \le x < 360^\circ\).
• 14N.2.hl.TZ0.14b: Robert conjectures that \({\rm{C\hat AB}}\) can have two possible values. Show that Robert’s...