[Form 5] - Variation

P varies directly as the cube root of Q. Find the relation between P and Q.

• $P\propto Q^3$

• $P\propto\frac{1}{Q^3}$

• $P\propto Q^{\frac{1}{3}}$

• $P\propto\frac{1}{Q^{\frac{1}{3}}}$

It is given that S varies directly as T and inversely as the square root of U. Find the relation between S, T and U.

• $S\propto\frac{U^2}{T}$

• $S\propto\frac{T}{U^2}$

• $S\propto\frac{T}{\sqrt{U}}$

• $S\propto\frac{\sqrt{U}}{T}$

y varies directly as x and inversely as the square of z. Given that the constant is k,find the relation between x, y and z.

• $y=\frac{kx^2}{z}$

• $y=\frac{kx}{z^2}$

• $y=\frac{kx}{\sqrt{z}}$

• $y=\frac{k\sqrt{z}}{x}$

It is given that X varies directly as the square root of Y and inversely as the square of Z. Find the relation betzveen X, Y and Z.

• $X\propto\frac{\sqrt{Y}}{Z^2}$

• $X\propto\frac{\sqrt{Z}}{Y^2}$

• $X\propto\frac{Y^2}{\sqrt{Z}}$

• $X\propto\frac{Z^2}{\sqrt{Y}}$

It is given that PQ² = k, where k is a constant. Which of the following statements is true?

• P varies directly as the square of Q.

• P varies directly as the square root of Q.

• P varies inversely as the square of Q.

• P varies inversely as the square root of Q.

The table shows two sets of values of the variables D and N.

It is given that D varies directly as N. Find the value of x.

• 72

• 60

• 36

• 3

The table below some values of the variables p, q and r which satisfy  $r\propto pq$  . Calculate the value of d.

•  $\frac{1}{3}$  

•  $\frac{1}{2}$  

•  $\frac{1}{4}$  

•  $6$  

The number of words typed, a, by Saiful varies directly as the time he types, t minutes. If Saiful types 270 words in 6 minutes, calculate the time he needs to spend to type 675 words.

• 14 minutes

• 15 minutes

• 16 minutes

• 17 minutes

An object falls from a height, h m, varies directly as the square of its time, t s on planet Q. Given that the object falls from the height of 5 m in 2 s, calculate the time taken in seconds, for the object to fall from a height of 45 m on the planet.

• 9 seconds

• 8 seconds

• 7 seconds

• 6 seconds

The volume of a cone, V  $cm^3$  , varies directly as the height, h cm and the square of its base radius, r cm. A cone with a height of 21 cm and a radius of 6 cm has a volume of 792  $cm^3$  . 

Calculate the volume in  $cm^3$  , of a cone with a height of 14 cm and a radius of 15 cm.

•  $3300\ cm^3$  

•   $3030\ cm^3$ 

•  $2300\ cm^3$  

•  $2020\ cm^3$