Direct and Inverse Proportions practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 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.

Practise direct and inverse proportions free

What this topic covers

Worked examples

Example 1

yy is directly proportional to x\sqrt{x}. When x=25x = 25, y=15y = 15. Find the value of yy when x=49x = 49.
Show the worked solution
  • Since $y \propto \sqrt{x}$, we have $y = k\sqrt{x}$ for some constant $k$.
  • Substituting $x = 25$, $y = 15$:
  • $15 = k \times \sqrt{25}$
  • $15 = k \times 5$
  • $k = 3$
  • When $x = 49$:
  • $y = 3 \times \sqrt{49}$
  • $y = 3 \times 7$

Answer: 2121

Example 2

yy is inversely proportional to x3x^3. When x=6x = 6, y=8y = 8. Find the value of yy when x=3x = 3.
Show the worked solution
  • Since $y$ is inversely proportional to $x^3$, write $y = \frac{k}{x^3}$ for some constant $k$.
  • Substitute $x = 6$, $y = 8$:
  • $8 = \frac{k}{6^3}$
  • $8 = \frac{k}{216}$
  • $k = 8 \times 216$
  • $k = 1728$
  • When $x = 3$:
  • $y = \frac{1728}{3^3}$

Answer: 6464

Example 3

A consignment of fodder can feed 250250 cattle for 1515 days. For how many days can the same consignment feed 150150 cattle?
Show the worked solution
  • $250$ cattle are fed for $15$ days
  • Total fodder $= 250 \times 15 = 3750$ cattle-days $\quad \scriptsize\textit{inverse proportion}$
  • $1$ cattle is fed for $3750$ days
  • $150$ cattle are fed for $3750 \div 150$
  • Days $= 25$

Answer: 2525

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?

O-Level Mathematics (4052), 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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