Mathematics Form 5 Chapter 1

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 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 some values of the variables p, q and r such that p varies directly as the square of q and inversely as r.

Calculate the value of d.

• 19

• 74

• 84

• 108

The table below shows some values of the variables L and M such that M varies inversely as the square root of L.

Find the relation between M and L.

• $M=\frac{3}{L^{\frac{1}{2}}}$

• $M=3L^{\frac{1}{2}}$

• $M=\frac{3}{L^2}$

• $M=3L^2$

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 shows some values of the variables P and Q.

It is given that P varies inversely as Q. Find the value of R.

• 15

• 18

• 27

• 31

It is given that

 $a\propto\frac{b^m}{c^n}$  
and a varies directly as the cube of b and inversely as the square root of c. State the value of m and of n.

• m=3, n=2
  

• m=3,  $n=\frac{1}{2}$  
  

• m=-3, n=2
  

• m=3,  $n=-\frac{1}{2}$  
  

Given
 $E\propto F$  

F=G-3 and E = 4 when G = 9, express E in terms of F.

•  $E=\frac{2}{3}F$ 
  
  

•  $E=\frac{3}{2}F$  

• E=6F

• E=9F