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.