CAMBRIDGE IGCSE MATHS (0580)

Question 1:
\( y \) is inversely proportional to \( x^2 \).
When \( x = 4 \), \( y = 3 \).
Find \( y \) when \( x = 5 \).

Question 2:
\( y \) varies directly as the square of \( (x-3) \).
When \( x = 1 \), \( y = 16 \).
Find \( y \) when \( x = 10 \).

Question 3:
The periodic time \( T \) of a pendulum varies directly as the square root of its length \( l \).
\( T = 6 \) when \( l = 9 \).
Find \( T \) when \( l = 25 \).

Question 4:
The electrical resistance \( R \) of a length of cylindrical wire varies inversely as the square of the diameter \( d \) of the wire.
\( R = 10 \) when \( d = 2 \).
Find \( R \) when \( d = 4 \).

Question 5:
The mass \( m \) of an object varies directly as the cube of its length \( l \).
\( m = 250 \) when \( l = 5 \).
Find \( m \) when \( l = 7 \).

Question 6:
\( y \) varies inversely as the square root of \( x \).
When \( x = 9 \), \( y = 6 \).
Find \( y \) when \( x = 36 \).

Question 7:
\( t \) varies inversely as the square root of \( u \).
\( t = 3 \) when \( u = 4 \).
Find \( t \) when \( u = 49 \).

Question 8:
\( y \) is inversely proportional to \( x^3 \).
\( y = 5 \) when \( x = 2 \).
Find \( y \) when \( x = 4 \).

Question 9:
The mass \( m \) of a sphere varies directly with the cube of its radius \( r \).
\( m = 160 \) when \( r = 2 \).
Find \( m \) when \( r = 5 \).

Question 10:
The speed \( v \) of a wave is inversely proportional to the square root of the depth \( d \) of the water.
\( v = 30 \) when \( d = 400 \).
Find \( v \) when \( d = 25 \).

Question 11:
\( m \) varies directly as the cube of \( x \).
\( m = 200 \) when \( x = 2 \).
Find \( m \) when \( x = 0.4 \).

Question 12:
\( w \) varies inversely as the square root of \( x \).
When \( x = 4 \), \( w = 4 \).
Find \( w \) when \( x = 25 \).

Question 13:
\( y \) varies as the cube root of \( x+3 \).
When \( x = 5 \), \( y = 1 \).
Find the value of \( y \) when \( x = 340 \).

Question 14:
\( y \) varies directly with \( \sqrt{x+5} \).
\( y = 4 \) when \( x = -1 \).
Find \( y \) when \( x = 11 \).

Question 15:
\( V \) is directly proportional to the cube of \( r+1 \).
When \( r = 1 \), \( V = 24 \).
Work out the value of \( V \) when \( r = 2 \).

Question 16:
\( y \) varies inversely as \( x+5 \).
\( y = 6 \) when \( x = 3 \).
Find \( y \) when \( x = 7 \).

Question 17:
\( p \) is inversely proportional to the square of \( q+4 \).
\( p = 2 \) when \( q = 2 \).
Find the value of \( p \) when \( q = -2 \).

Question 18:
\( y \) is directly proportional to the square of \( x-1 \).
\( y = 63 \) when \( x = 4 \).
Find the value of \( y \) when \( x = 6 \).

Question 19:
\( y \) is inversely proportional to \( (x+2)^2 \).
When \( x = 1 \), \( y = 2 \).
Find \( y \) in terms of \( x \).

Question 20:
\( y \) is directly proportional to the positive square root of \( x \).
When \( x = 9 \), \( y = 12 \).
Find \( y \) when \( x = \frac{1}{4} \).

Question 21:
\( y \) is directly proportional to \( (x+2)^2 \).
When \( x = 8 \), \( y = 250 \).
Find \( y \) when \( x = 4 \).

Question 22:
\( y \) is directly proportional to the square root of \( x+2 \).
When \( x = 7 \), \( y = 2 \).
Find \( y \) when \( x = 98 \).

Question 23:
\( d \) is inversely proportional to \( (w+1)^2 \).
\( d = 3.2 \) when \( w = 4 \).
Find \( d \) when \( w = 7 \).

Question 24:
\( y \) is inversely proportional to \( \sqrt{1+x} \).
When \( x = 8 \), \( y = 2 \).
Find \( y \) when \( x = 15 \).

Question 25:
\( h \) is directly proportional to \( \sqrt{p} \).
\( h = 5.4 \) when \( p = 1.44 \).
Find \( h \) when \( p = 2.89 \).