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033 Chapter 1	 Direct and Inverse Proportions
7.	 The force of repulsion, F newtons (N), between two
particles is inversely proportional to the square of
the distance, d m, between the particles.
	 (i)	 Write down a formula connecting F and d.
	(ii)	When the particles are a certain distance apart,
the force of repulsion is 20 N. Find the force
when the distance is halved.
8.	 For a fixed volume, the height, h cm, of a cone is
inversely proportional to the square of the base
radius, r cm. Cone A has a base
radius of 6 cm and a height of
5 cm. The base radius of Cone B
is 3 cm and the height of Cone C
is 1.25 cm. If all the cones have
the same volume, find
	 (i)	 the height of Cone B,
	 (ii)	the base radius of Cone C.
ADVANCED LEVEL
9.	 If y is inversely proportional to 2x + 1 and the
	 difference in the values of y when x = 0.5 and x = 2
	is 0.9, find the value of y when x = 0.25.
10.	 y is inversely proportional to x2
and y = b for
	 a particular value of x. Find an expression in
	 terms of b for y when this value of x is tripled.
11.	 The force of attraction between two magnets is
	 inversely proportional to the square of the
	 distance between them. When the magnets are
	 r cm apart, the force of attraction between them
	is F newtons (N). If the distance between the
	 magnets is increased by 400%, the force of
	 attraction between them becomes cF N. Find the
	 value of c.
Exercise
1D
BASIC LEVEL
1.	 If x is inversely proportional to y3
and x = 50 when
	 y = 2,
	 (i)	 find the value of x when y = 4,
	 (ii)	find an equation connecting x and y,
	 (iii)	calculate the value of y when x = 3.2.
2.	 If z is inversely proportional to w and z = 9 when
	 w = 9,
	 (i)		find an equation connecting w and z,
	 (ii)		find the value of z when w = 16,
	 (iii)	calculate the value of w when z = 3.
INTERMEDIATE LEVEL
3.	 For each of the following equations, state the two
	 variables which are inversely proportional to
	 each other and explain your answer.
	 (a)	 y =
x
3
2
	 (b)	y =
x
1
	 (c)	 y2
=
x
5
3
	 (d)	n =
m
7
 1
	
	 (e)	 q =
( )+p
4
1
2
4.	 If z is inversely proportional to x3
and z = 5 when
	 x = 64, find the value of z when x = 216.
5.	 If q2
is inversely proportional to p + 3 and q = 5 when
	 p = 2, find the values of q when p = 17.
6.	 Given that t is inversely proportional to s3
, copy and
	 complete the table.
s 1 2 4
t 80 0.08 0.01
h cm
r cm
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READ Workshop Appendix

  • 1. 033 Chapter 1 Direct and Inverse Proportions 7. The force of repulsion, F newtons (N), between two particles is inversely proportional to the square of the distance, d m, between the particles. (i) Write down a formula connecting F and d. (ii) When the particles are a certain distance apart, the force of repulsion is 20 N. Find the force when the distance is halved. 8. For a fixed volume, the height, h cm, of a cone is inversely proportional to the square of the base radius, r cm. Cone A has a base radius of 6 cm and a height of 5 cm. The base radius of Cone B is 3 cm and the height of Cone C is 1.25 cm. If all the cones have the same volume, find (i) the height of Cone B, (ii) the base radius of Cone C. ADVANCED LEVEL 9. If y is inversely proportional to 2x + 1 and the difference in the values of y when x = 0.5 and x = 2 is 0.9, find the value of y when x = 0.25. 10. y is inversely proportional to x2 and y = b for a particular value of x. Find an expression in terms of b for y when this value of x is tripled. 11. The force of attraction between two magnets is inversely proportional to the square of the distance between them. When the magnets are r cm apart, the force of attraction between them is F newtons (N). If the distance between the magnets is increased by 400%, the force of attraction between them becomes cF N. Find the value of c. Exercise 1D BASIC LEVEL 1. If x is inversely proportional to y3 and x = 50 when y = 2, (i) find the value of x when y = 4, (ii) find an equation connecting x and y, (iii) calculate the value of y when x = 3.2. 2. If z is inversely proportional to w and z = 9 when w = 9, (i) find an equation connecting w and z, (ii) find the value of z when w = 16, (iii) calculate the value of w when z = 3. INTERMEDIATE LEVEL 3. For each of the following equations, state the two variables which are inversely proportional to each other and explain your answer. (a) y = x 3 2 (b) y = x 1 (c) y2 = x 5 3 (d) n = m 7 1 (e) q = ( )+p 4 1 2 4. If z is inversely proportional to x3 and z = 5 when x = 64, find the value of z when x = 216. 5. If q2 is inversely proportional to p + 3 and q = 5 when p = 2, find the values of q when p = 17. 6. Given that t is inversely proportional to s3 , copy and complete the table. s 1 2 4 t 80 0.08 0.01 h cm r cm