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Linear Law

Secondary 3 Additional Math practice

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Linear Law practice questions

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.

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What this topic covers

Worked examples

Example 1

A graph of YY against XX is a straight line passing through (3, 4)(3,\, 4) and (4, 7)(4,\, 7). Find the YY-intercept.
Show the worked solution
  • Gradient=7−(4)4−3\text{Gradient} = \frac{7 - (4)}{4 - 3}
  • =3= 3
  • Y=mX+cY = mX + c
  • Using (3, 4):4=3(3)+c\text{Using } (3,\, 4): \quad 4 = 3(3) + c
  • 4=9+c4 = 9 + c
  • c=4−9c = 4 - 9
  • =−5= -5
  • The Y-intercept is −5.\text{The } Y\text{-intercept is } -5.

Answer: −5-5

Example 2

Variables xx and yy are related by y=ax2+bxy = ax^2 + bx, where aa and bb are constants. A graph of yx\frac{y}{x} against xx passes through (2, 12)(2,\, 12) and (6, 32)(6,\, 32). Find bb.
Show the worked solution
  • y=ax2+bx⇒yx=ax+by = ax^2 + bx \Rightarrow \frac{y}{x} = ax + b
  • Gradient=32−(12)6−2\text{Gradient} = \frac{32 - (12)}{6 - 2}
  • =204= \frac{20}{4}
  • =5= 5
  • Using (2, 12):12=5(2)+c\text{Using } (2,\, 12): \quad 12 = 5(2) + c
  • c=12−10c = 12 - 10
  • =2= 2
  • Comparing with yx=ax+b:\text{Comparing with } \frac{y}{x} = ax + b:

Answer: 22

Example 3

Variables xx and yy are related by y=aebxy = ae^{bx}, where aa and bb are constants. A graph of ln⁡y\ln y against xx passes through (3, 6)(3,\, 6) and (6, 15)(6,\, 15). Find bb.
Show the worked solution
  • y=aebxy = ae^{bx}
  • ln⁡y=ln⁡a+bx\ln y = \ln a + bx
  • Comparing with Y=mX+c where Y=ln⁡y,  X=x:\text{Comparing with } Y = mX + c \text{ where } Y = \ln y, \; X = x:
  • Gradient=b\text{Gradient} = b
  • =15−(6)6−3= \frac{15 - (6)}{6 - 3}
  • =93= \frac{9}{3}
  • =3= 3

Answer: 33

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

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.

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