Download Chapter 2 Functions and Graphs

1
pp.150 – 157
(d)
5  1
 5 10 
  3     
9  3
9 3 
5 3 
   
 9 10 
1

6
Level 1
1.
The numbers in ascending order are:
5  2  0  3  7
8.
2.
The numbers in descending order are:
1.2  0.6  0.5  0.7  1.1
9.
3.
(a)
<
5.
(a)
3  6  9
(b)
9  5  4
(c)
8  3  (8  3)  24
(d)
12  (6)  (12  6)  2
(a)
3.5  9.4  5.9
(b)
2.3  1.1  1.2
(c)
4  (1.2)  (4  1.2)  4.8
(d)
144  (1.2)  (144  1.2)  120
(a)
1  1
2 1
3
        
2  4
4 4
4
7.

(b)

(c)
+
(d)
+
(a)
909.9  910 (cor. to the nearest one)
(b)
909.9  910 (cor. to the nearest ten)
(c)
909.9  900 (cor. to the nearest hundred)
(d)
909.9  1000 (cor. to the nearest thousand)
(a)
5.7  6.4  2.3  1.8
 67 32
(a), (b), (c)
4.
6.
(a)
(b)
>
(c)
<
10.
8
(b)
8
11.
(a)
(c)
21  99  48  62  77
 20  100  50  60  80
 50
(b)
101  3.8  83
 100  4  80
5
(c)
(b)
5.7  6.4  2.3  1.8
 5  6  2 1
2  2 2 2
    
5  3 5 3
6 10


15 15
16

15
1
1
15
341  352  349  345  356  360
 350  6
 2100
(d)
121  101  0.26
 120  0.25  100
 3000
(e)
5  2
1
5 2 
         
6  15 
9
 6 15 
4.77  0.98  1.25  5.11
 (4  0  1  5)  (0.77  0.25)  (0.98  0.11)
 10  1  1
 12
12.
The figure occupies about 19 small squares.
Area  (19 1) cm 2
 19 cm 2
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62
1
Stage Test
13.
No. The measuring unit of a chopstick is cm. It is not
22.
k
 13
5
k
  13  20
5
k
  7
5
k  7  ( 5)
20 
appropriate to use a metre ruler to measure the length of
a chopstick.
14.
Estimated weight of 300 marbles
 25

   300  g
 20

 375 g
k  35
23.
15.
(a)
No
(b)
Yes
16.
Peter’s total expenditure
 $(17  32  31  7.4)
 $(20  35  35  8)
 $98
Let $x be the cost of each apple.
Then the cost of 10 apples = $10x.
50  10 x  20
10 x  20  50
10 x  30
x
x3
Since the value must be less than $98, Peter’s total

expenditure did not exceed $100.
17.
(a)
 30
10
Since the sum of x and y = x + y,
the required result  x  y  10
24.
The cost of each apple is $3.
Let y be the present age of Winnie’s mother.
y  12  2(12  12)
y  12  2( 24)
(b)
Since the division of a by b 
y  12  48
a
,
b
y  48  12
y  36
4a
the required result 
b
18.
19.

7 ( 4)  1
3
28  1

3
27

3
9
Level 2
u
25.
(a)
12  8  15  19
(b)
14  (2)  (10)  (14  2)  (10)
 7  (10)
 (7  10)
 70
p  (24  5)  8
 19  8
26.
 152
20.
(a)
3(5)  4(3)  6  15  12  6
3
2 x  9  15
2 x  15  9
(b)
2x  6
6
2
x3
x
21.
The present age of Winnie’s mother is 36.
27.
6 y  33  3 y
6 y  3 y  33
3 y  33
33
3
y  11
y
63
(a)
(26  4)
22

  2.2
2  (5)
10
 3 5  11  9 10  11


  

 8 12  24  24 24  24
1 11


24 24
 1 24 
   
 24 11 
1

11
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(b)
3   4   10 9   4 
 5
     2        2 
 21 14   5   42 42   5 
19  14 
   
42  5 
32.
(a)
In the figure, the height of the door is about
times the height of Jacky.

 19 14 
   
 42 5 
19

15
(b)
28.
(a)
(b)
4
3
(0.8  1)  (4.5  0.5)  (0.2)  9
 1.8
Estimated height of the door
4

  1 .5   m
3

 2m
In the figure, the height of the room is about
twice that of Jacky.

Estimated height of the room
 (1.5  2) m
 3m
(0.5)(1.2  2.8)  (0.5)(4)
 (0.5  4)
2
29.
(a)
(c)

height of the building 100 m

height of the floors
3m
 33.33   40
Amount earned in 2007
 $(25 000  9  9000  3)

 $(225 000  27 000)
It is impossible to have 40 floors in the
building.
 $198 000
33.
(b)
divide the measured value by the total number of coins.
Net amount  $200 000  $198 000
 $2000
34.
30.
(a)
We can measure the thickness of all the coins and
47.9  51.5  101.4  131.8  10.3  29.9  72.4
 (47.9  51.5)  101.4  (131.8  72.4)
x x
 1
2 3
x x
    6  1 6
2 3
3x  2 x  6
 (10.3  29.9)
 100  100  200  40
5x  6
 440
x
6
5
4.1  4.25  6.1  35  5.9
(b)
 4  4.25  6  6  35
35.
 17  35
 52
2.8 y  1  5.2  1.4 y
2.8 y  1.4 y  5.2  1
4.2 y  4.2
4. 2
4. 2
y 1
y
31.
(a)
0.15  0.25  0.35
 0.2  0.25  0.4
 0.02

(b)
The given estimation is unreasonable.
36.
154  62  78  61  77  51
 150  60  80  60  80  50
24 p  32  25  5 p
24 p  5 p  25  32
 220

19 p  57
57
p
19
p3
The given estimation is unreasonable.
52  5  65  8  21
(c)
 50  5  64  8  20
 238
 240

The given estimation is reasonable.
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6p 8 5  p

5
4
4(6 p  8)  5(5  p )
64
1
Stage Test
37.
(a)
Let $x be the amount of money that Tom gave to
5.
B
13  (4  7) 13  (3)

( 5)
5
13  3

5
10

5
 2
6.
B
Sam.
26  x  38  x
x  x  38  26
2 x  12
12
2
x6
x

(b)
Tom gave $6 to Sam.
Let $y be the amount of money that Tom gave to
Greatest difference of temperature
 [15  (3)]C
Sam.
26  y  3(38  y )
26  y  114  3 y
 (15  3)C
 18C
y  3 y  114  26
4 y  88
7.
88
y
4
y  22

38.
Stored value left in Peter’s Octopus Card
 $6  $20  $12
 $26
Tom gave $22 to Sam.
8.
Area of the rectangle  x( x  4) cm 2
(a)
C
A
Let x = 2 and y  3.
Then x + y is negative.
(b)
(i)
For B, 2[2  (3)] is negative.
Perimeter  28
2[ x  ( x  4)]  28
For C, 2  ( 3) is positive.
For D, 3  2 is negative.
28
xx4
2
2 x  4  14
2 x  14  4
2 x  10
10
2
x5
9.
D
12.
A
x
(ii)
10.
C
11.
B
Since all the numbers are close to 25, we can estimate
the value of the expression by clustering.
13.
Area of the rectangle
 [5(5  4)] cm 2
B
16 087  527  15 000  500
 30
 (5  9) cm 2
 45 cm 2
14.
Estimated weight of 3 eggs
 (158  12  3) g
Multiple-choice Questions
1.
B
4.
D
2.
A
D
3.
 160 

 3 g
 12

 40 g
D
Counter example:
For A, 2  4  (2)  4
15.
B
For B, 2  4  (7)  1
For C, 2  4  (1)  1
65
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16.
B
23.
We can assume that the number of books on each shelf
A
4( y  3)  2(3 y  5)  2( y  3)
4 y  12  6 y  10  2 y  6
is about the same. There are 30 books in the third shelf
4 y  6 y  2 y  6  12  10
 4 y  28
and there are 5 shelves.
Estimated number of books  30 5

28
4
y  7
 150
17.
y
A
Since the product of y and z = yz,
24.
the required result = x + yz
18.
Let $x be the amount that Andy gets.
x
Then the amount that Ben gets  $ .
3
x
x   300
3
4x
 300
3
3
x  300 
4
x  225
C
Let x be the number.
3x  2 x  5
x5
19.
D
B
Let x be the smallest number.
x  ( x  2)  ( x  4)  123

x  x  2  x  4  123
Andy gets $225.
3x  123  2  4
3x  117
117
x
3
x  39

20.
25.
The smallest number is 39.
A
The bus fare of each adult is $t.
t
Then the bus fare of each children  $ .
2
t

Total bus fare  $ 2t  3  

2

 $3.5t
21.
B
Since 30 minutes = 0.5 hour,
from the given information, we have
22.
d
 50.
0.5
D
x 1
2
5 x
x  1  2 (5  x )
x  1  10  2 x
x  2 x  10  1
3 x  11
x
11
3
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66
C
5a  1  3
5a  3  1
5a  2
2
a
5
a  0 .4