1. The document contains a review exercise with 14 problems involving rates, ratios, proportions, direct and inverse variations, and word problems. 2. It also includes activities to practice direct and inverse variations graphically. 3. There are examples of classwork and quick practice problems applying the concepts of direct and inverse variations to word problems.
9
Variations
9 Variations
Review Exercise 9 (p. 9.5)
1.
The required rate
2.
The required rate
3.
The required rate
4.
18 : 36
5.
500 g : 15 kg
6.
300 seconds : 5 minutes 20 seconds
7.
8.
9.
For the 3 kg pack of washing powder:
Price per kg
107
NSS Mathematics in Action (2nd Edition) 4B Full Solutions
For the 2 kg pack of washing powder:
Price per kg
The 2 kg pack of washing powder is more economical.
10.
The required ratio
11.
Fraction of the number of female members
Let
x
be the total number of members in the music club.
There are 104 members in the music club.
12.
13.
14.
From (2), we have
By substituting (3) into (1), we have
By substituting into (3), we have
The solution is , .
15.
:
By substituting into (1), we have
The solution is , .
16.
Let
x
cm be the length of the screen of the TV.
Then the width of the screen of the TV is
.
When , .
The length and width of the screen of the TV are
57.6 cm and 32.4 cm respectively.
Activity
Activity 9.1 (p. 9.6)
1. (a)
increase
(b)
Number of tickets
bought (
x
)
1 2 3 4 5
…
Amount of money
required ($
y
)
80 160 240 320 400
…
80 80 80 80 80
…
2. (a)
no
(b)
3. (a)
(b) (i)
a straight line
(ii)
yes
Activity 9.2 (p. 9.19)
1. (a)
decrease
(b)
Number of
1 2 3 4 5
…
108
9
Variations
people (
x
)
Amount of
soft drink
each person
gets
(
y
mL)
1500 750 500 375 300
…
1500
150
0
150
0
150
0
1500
…
2. (a)
No. The value of
remains unchanged when the
values of
x
and
y
change.
(b)
3. (a)
(b) (i)
The graph of
y
against
x
is a curve.
(ii)
No, the graph does not pass through the origin.
Activity 9.3 (p. 9.42)
1.
E
= 5000 + 2000
n
2. (a) (i)
(ii)
(b)
(c) (i)
No. Let
x
0
,
y
0
and
S
0
be the original values of
x
,
y
and
S
respectively. New value of
S
(ii)
No, Let x
0
,y
0
and S
0
be the original values of x,y
and Srespectively. New value of S
Maths Dialogue
Maths Dialogue (p. 9.14)
No. For any two quantities xandyin direct variation, the graph
ofyagainst xmust be a straight line passing through the origin.
In case 3, yandxare in direct variation.
Classwork
Classwork (p. 9.8)
(a)
y= kx
2
(b)
(c)
r
=
kw
3
(d)
W
=
kL
(e)
P
=
kr
2
Classwork (p. 9.21)
(a) (b)
(c) (d)
3
w
k
C
(e)
Classwork (p. 9.33)
(a)
X
=
kyw
2
(b)
(c) (d)
(e)
Classwork (p. 9.44)
(a)
P
=
(b)
(c) (d)
(e)
Quick Practice
Quick Practice 9.1 (p. 9.9)
(a)
p
varies directly as
q
2
.
p= kq
2
, where k
0
By substituting
and into the equation, we
have
(b)
When
q
= 7,
p
= 7(7)
2
=
Quick Practice 9.2 (p. 9.10)
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