• 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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