Secondary 3 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 graph of Y against X is a straight line passing through (4,−16) and (6,−22). Find the Y-intercept.
Show the worked solution
$\text{Gradient} = \frac{-22 - (-16)}{6 - 4}$
$= \frac{-6}{2}$
$= -3$
$Y = mX + c$
$\text{Using } (4,\, -16): \quad -16 = -3(4) + c$
$-16 = -12 + c$
$c = -16 - (-12)$
$= -4$
Answer: −4
Example 2
Variables x and y are related by y=a+bx2, where a and b are constants. A graph of y against x2 passes through (1,0) and (4,9). Find b.
Show the worked solution
$y = a + bx^2 \Rightarrow y = bx^2 + a$
$\text{Gradient} = \frac{9 - (0)}{4 - 1}$
$= \frac{9}{3}$
$= 3$
$\text{Using } (1,\, 0): \quad 0 = 3(1) + c$
$c = 0 - 3$
$= -3$
$\text{Comparing with } y = bx^2 + a:$
Answer: 3
Example 3
Variables x and y are related by y=aebx, where a and b are constants. A graph of lny against x passes through (2,−1) and (4,−5). Find b.
Show the worked solution
$y = ae^{bx}$
$\ln y = \ln a + bx$
$\text{Comparing with } Y = mX + c \text{ where } Y = \ln y, \; X = x:$
$\text{Gradient} = b$
$= \frac{-5 - (-1)}{4 - 2}$
$= \frac{-4}{2}$
$= -2$
Answer: −2
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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.