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

Direct Proportion
Inverse Proportion
Multi-Variable Word Problems
Other Forms of Direct Proportion
Other Forms of Inverse Proportion

Worked examples

Example 1

y

is directly proportional to

x^3

. When

x = 2

y = 24

. Find the value of

y

when

x = 3

Show the worked solution

Since $y \propto x^3$ , we have $y = kx^3$ for some constant $k$ .
Substituting $x = 2$ , $y = 24$ :
$24 = k \times 2^3$
$24 = k \times 8$
$k = 3$
When $x = 3$ :
$y = 3 \times 3^3$
$y = 3 \times 27$

Answer: $81$

Example 2

y

is inversely proportional to

x^2

. When

x = 4

y = 63

. Find the value of

y

when

x = 2

Show the worked solution

Since $y$ is inversely proportional to $x^2$ , write $y = \frac{k}{x^2}$ for some constant $k$ .
Substitute $x = 4$ , $y = 63$ :
$63 = \frac{k}{4^2}$
$63 = \frac{k}{16}$
$k = 63 \times 16$
$k = 1008$
When $x = 2$ :
$y = \frac{1008}{2^2}$

Answer: $252$

Example 3

4

identical taps can fill a tank in

15

minutes. Find the time taken for

15

such taps to fill the same tank.

Show the worked solution

$4$ taps fill the tank in $15$ minutes
$1$ tap fills the tank in $4 \times 15 = 60$ minutes $\quad \scriptsize\textit{inverse proportion}$
$15$ taps fill the tank in $60 \div 15$
Time taken $= 4$ minutes

Answer: $4$

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.

What this topic covers

Worked examples

Example 1

Example 2

Example 3

Questions parents ask

Is it really free?

Which syllabus does this follow?

Will it just show my child the answer?

Other Secondary 2 topics