5.4 Variations, SPM Paper 1 (Short Question)


Question 1:
It is given that y varies directly as the cube of x and y = 192 when x = 4. Calculate the value of x when y 24.

Solution:

y α x³
y = kx³
192 = k (4)³
192 = 64 k
k = 3
 
y = 3 x³
when y = – 24 
– 24 = 3 x³
x³ = – 8
x = – 2



Question 2:
It is given that y varies directly as the square of x and y = 9 when x = 2. Calculate the value of x when y = 16.

Solution:
y α x²
y = kx²
9 = k (2)²
k= 9 4 y= 9 4 x 2 When y=16 16= 9 4 x 2 x 2 = 64 9 x= 8 3




Question 3:
Given that y varies inversely as w and x and y = 45 when w = 2 and x = 1 6 . Find the value of x when y = 15 and w = 1 3

Solution:
y α  1 wx y= k wx 45= k ( 2 )( 1 6 ) k=45× 1 3 =15 y= 15 wx

when y=15, w= 1 3 15= 15 ( 1 3 )x x 3 =1 x=3



Question 4:
Given that   p α 1 q r and p = 3 when q = 2 and r = 16, find the value of p when q = 3 and r = 4.

Solution:
p α  1 q r p= k q r 3= k ( 2 ) 16 k=24 p= 24 q r

when q=3, r=4 p= 24 3 4 p= 24 6 =4

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