• Syllabus

Prior learning topics

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Sub sections and their related questions

Number

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Sets and numbers

• 09N.1.sl.TZ0.8a: (i)     Find the number of boys who play both sports. (ii)    Write down the number of boys who...

Algebra

• 10N.1.sl.TZ0.10a(i), (ii) and (iii): (i)     Show that the gradient of [PQ] is \(\frac{{{a^3}}}{{a - \frac{2}{3}}}\) . (ii)    Find...
• 10N.1.sl.TZ0.10b: Given that the area of T is \(2k + 4\) , show that k satisfies the equation...

Trigonometry

• 12M.2.sl.TZ1.10a(i) and (ii): Find the distance between the ships (i)     at 13:00; (ii)    at 14:00.
• 12M.2.sl.TZ1.10b: Let \(s(t)\) be the distance between the ships t hours after noon, for \(0 \le t \le 4\) . Show...
• 12M.2.sl.TZ1.10c: Sketch the graph of \(s(t)\) .
• 12M.2.sl.TZ1.10d: Due to poor weather, the captain of ship A can only see another ship if they are less than 8 km...
• 10N.1.sl.TZ0.8a(i), (ii) and (iii): (i)     Show that...
• 10N.1.sl.TZ0.8b(i) and (ii): The line (AC) has equation \({\boldsymbol{r}} = {\boldsymbol{u}} + s{\boldsymbol{v}}\) . (i)    ...
• 10N.1.sl.TZ0.8c: The lines (AC) and (BD) intersect at the point \({\text{P}}(3{\text{, }}k)\) . Show that...
• 10N.1.sl.TZ0.8d: The lines (AC) and (BD) intersect at the point \({\text{P}}(3{\text{, }}k)\) . Hence find the...
• 10M.1.sl.TZ1.4a: Write down the value of \(\tan \theta \) .
• 10M.1.sl.TZ1.4b(i) and (ii): Find the value of (i)     \(\sin 2\theta \) ; (ii)    \(\cos 2\theta \) .
• 10N.2.sl.TZ0.10a: Find the height of a seat above the ground after 15 minutes.
• 10N.2.sl.TZ0.10b: After six minutes, the seat is at point Q. Find its height above the ground at Q.
• 10N.2.sl.TZ0.10c: The height of the seat above ground after t minutes can be modelled by the function...
• 10N.2.sl.TZ0.10d: The height of the seat above ground after t minutes can be modelled by the function...
• 11N.2.sl.TZ0.4a: Find the two possible values of \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .
• 11N.2.sl.TZ0.4b: Hence, find \({\rm{A}}\widehat {\rm{B}}{\rm{C}}\) , given that it is acute.
• 11M.2.sl.TZ2.10a: Show that the area of the window is given by \(y = 4\sin \theta + 2\sin 2\theta \) .
• 11M.2.sl.TZ2.10b: Zoe wants a window to have an area of \(5{\text{ }}{{\text{m}}^2}\). Find the two possible values...
• 11M.2.sl.TZ2.10c: John wants two windows which have the same area A but different values of \(\theta \) . Find all...
• 13M.2.sl.TZ2.7a: Show that \({\rm{OC}} = r\cos 1.4\) .

Geometry

• 08M.1.sl.TZ2.10c: Show that \(S = 2(\pi  - 2\sin \theta )\) .
• 14N.2.sl.TZ0.3c: Hence, find the perimeter of the shaded segment \(ABC\).

Coordinate geometry

• 10M.1.sl.TZ1.4a: Write down the value of \(\tan \theta \) .
• 10M.1.sl.TZ1.4b(i) and (ii): Find the value of (i)     \(\sin 2\theta \) ; (ii)    \(\cos 2\theta \) .
• 10M.1.sl.TZ2.5: Let \(f(x) = k{x^4}\) . The point \({\text{P}}(1{\text{, }}k)\) lies on the curve of f . At P,...
• 14M.1.sl.TZ2.4b: Find the equation of the line \(L\) in the form \(y = ax + b\).
• 14N.1.sl.TZ0.10c: The line \({L_a}\) crosses the \(x\)-axis at \({\text{Q}}(2a,{\text{ }}0)\). Let...
• 15M.2.sl.TZ1.6: Let \(f(x) = \frac{{\ln (4x)}}{x}\) for \(0 < x \le 5\). Points...

Statistics and probability

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