DP Mathematics SL Questionbank

• Syllabus

3.2

Sub sections and their related questions

Definition of \(\cos \theta \) and \(\sin \theta \) in terms of the unit circle.

• 08M.1.sl.TZ1.2a(i) and (ii): Write down an expression for (i)     \(\sin 140^\circ \) ; (ii)    \(\cos 70^\circ \) .
• 09M.1.sl.TZ1.8a: Write down an expression in terms of \(\theta \) for (i)     \(x\) ; (ii)    \(y\) .
• 18M.1.sl.TZ1.6: Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.This is...
• 18M.1.sl.TZ1.10a.i: Find an expression for r in terms of θ.
• 18M.1.sl.TZ1.10a.ii: Find the possible values of r.
• 18M.1.sl.TZ1.10b: Show that the sum of the infinite sequence...
• 18M.1.sl.TZ1.10c: Find the values of θ which give the greatest value of the sum.

Definition of \(\tan \theta \) as \(\frac{{\sin \theta }}{{\cos \theta }}\) .

• 08M.1.sl.TZ1.2c: Find an expression for \(\tan 140^\circ \) .
• 09M.1.sl.TZ2.7: Let \(f(x) = \sqrt 3 {{\rm{e}}^{2x}}\sin x + {{\rm{e}}^{2x}}\cos x\) , for \(0 \le x \le \pi \) ....
• 18M.1.sl.TZ1.6: Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.This is...
• 18M.1.sl.TZ1.10a.i: Find an expression for r in terms of θ.
• 18M.1.sl.TZ1.10a.ii: Find the possible values of r.
• 18M.1.sl.TZ1.10b: Show that the sum of the infinite sequence...
• 18M.1.sl.TZ1.10c: Find the values of θ which give the greatest value of the sum.

Exact values of trigonometric ratios of \(0\), \(\frac{\pi }{6}\), \(\frac{\pi }{4}\), \(\frac{\pi }{3}\), \(\frac{\pi }{2}\) and their multiples.

• 10M.1.sl.TZ1.9a: Use the quotient rule to show that \(f'(x) = \frac{{ - 1}}{{{{\sin }^2}x}}\) .
• 10M.1.sl.TZ1.9b: Find \(f''(x)\) .
• 10M.1.sl.TZ1.9c: Find the value of p and of q.
• 10M.1.sl.TZ1.9d: Use information from the table to explain why there is a point of inflexion on the graph of f...
• 10M.1.sl.TZ2.4a: Find \(f\left( {\frac{\pi }{2}} \right)\) .
• 10M.1.sl.TZ2.4b: Find \((g \circ f)\left( {\frac{\pi }{2}} \right)\) .
• 10M.1.sl.TZ2.4c: Given that \((g \circ f)(x)\) can be written as \(\cos (kx)\) , find the value of k,...
• 09M.1.sl.TZ2.8b: Let \(h(x) = {{\rm{e}}^{ - 3x}}\sin \left( {x - \frac{\pi }{3}} \right)\) . Find the exact value...
• SPNone.1.sl.TZ0.6b: Hence or otherwise, solve the equation \(6\sin x\cos x = \frac{3}{2}\) , for...
• SPNone.1.sl.TZ0.10c: Find the maximum value of \(f(x)\) .
• 11M.1.sl.TZ2.4: Let \(h(x) = \frac{{6x}}{{\cos x}}\) . Find \(h'(0)\) .
• 14M.1.sl.TZ1.6: Let \(\int_\pi ^a {\cos 2x{\text{d}}x}  = \frac{1}{2}{\text{, where }}\pi  < a < 2\pi \)....
• 16M.1.sl.TZ2.5a: Find \({\rm{A\hat BC}}\).
• 16M.1.sl.TZ2.5b: Find the exact area of the sector BDC.
• 17M.1.sl.TZ1.3: The following diagram shows triangle PQR. Find PR.
• 17M.1.sl.TZ1.10b: Given that \(\tan \theta  > 0\), find \(\tan \theta \).
• 18M.1.sl.TZ1.6: Six equilateral triangles, each with side length 3 cm, are arranged to form a hexagon.This is...
• 18M.1.sl.TZ1.10a.i: Find an expression for r in terms of θ.
• 18M.1.sl.TZ1.10a.ii: Find the possible values of r.
• 18M.1.sl.TZ1.10b: Show that the sum of the infinite sequence...
• 18M.1.sl.TZ1.10c: Find the values of θ which give the greatest value of the sum.