Page 17 - Mathematics_Form_Two

Rates and variations

Substuting equatiation (i) in (ii) gives, Exercise 1�4
I = 4.I 1. If y varies inversely as x and y = 3
1
The percentage change in intensity when x = 4, find y when x = 6.
4I − I
= × 100%
I 2. If x varies inversely as the square of
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3I
= × 100% y and x = 3 when y = 4, what is
I the value of x when y = 8 ?
= 300%

Therefore, the percentage change in 3. If x varies inversely as y and if Mathematics for Secondary Schools
3 __
intensity is 300%. x = 4 when y = , find the value
2
of y when x = 8.
(b) When D is increased by 30%
D = D + 0.3D 4. If y is inversely proportional to x
1
1.3D= and x = 2 when y = 2 , find the
1 _
k 2
Thus, I = . value of y when x = 4.

1
D 1 2
k 5. If x varies inversely as 2y − 1 and
=
(1.3 )D 2 x = 2 when y = 3 , find the value
k
= of y when x = 6.
1.69D 2
Therefore, the new intensity, I is 6. If q varies inversely as the square of
1
k . p and p = 8 when q = 2, find the
1.69D 2
The percentage change in I is a given by; value of q when p = 4.
I − I 7. If y is inversely proportional to x
% in I = 1 × 100%
I and x = 5 when y = 6, find the

k − k value of x when y = 20.
= 1.69D 2 D 2 × 100%
k 8. If y is inversely proportional to x
D 2 and y = 3 when x = 4, find the

= (1 1.69)k− × 100% value of y when x = 6.
1.69

=− 0.69 ×100% 9. If y varies inversely as the cube
1.69 root of x and y = 3 when x = 64,
=−40.83% find the formula connecting the

variables. Hence, find the value of
Therefore, the intensity decreased by x when y = .
15
___
40.83%. 4

11
Student's Book Form Two

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MATHEMATIC F2 v5.indd 11