Secondary 4 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.
When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It
reads the working, identifies the step that went wrong, and asks a question that points at the
correction. The worked solution is there once a genuine attempt has been made.
A particle moves along a straight line such that its displacement, <i>s</i> metres, from a fixed point O at time <i>t</i> seconds is given by s=3t3−3t2+4t. Find the velocity when t=2.
Show the worked solution
$v = \frac{ds}{dt}$
$= 9t^2 - 6t + 4$
$\text{When } t = 2:$
$v = 9(2)^2 - 6(2) + 4$
$= 36 - 12 + 4$
$= 28 \text{ m/s}$
Answer: 28
Example 2
A particle moves along a straight line such that its displacement, <i>s</i> metres, from a fixed point O at time <i>t</i> seconds is given by s=3t3+t2−t. Find the acceleration when t=1.
Show the worked solution
$v = \frac{ds}{dt}$
$= 9t^2 + 2t - 1$
$a = \frac{dv}{dt}$
$= 18t + 2$
$\text{When } t = 1:$
$a = 18(1) + 2$
$= 20 \text{ m/s}^2$
Answer: 20
Example 3
A particle moves along a straight line with velocity v=6t2+6t−1 m/s. When t=0, s=3. Find the displacement when t=1.
Show the worked solution
$s = \int v \, dt$
$= \int (6t^2 + 6t - 1) \, dt$
$= 2t^3 + 3t^2 - t + C$
$\text{When } t = 0, \, s = 3: \quad C = 3$
$s = 2t^3 + 3t^2 - t + 3$
$\text{When } t = 1:$
$s = 7 \text{ m}$
Answer: 7
Questions parents ask
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Which syllabus does this follow?
Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.
Will it just show my child the answer?
No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.