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4. (a) x  x  y  y  2 x  2 y
(b) 2  3  a  2  3a
(c) 4  5  b  20  b
 20b
(d) 10  2  c  5  c
 5c
B uild-up Exercise 2A
(page 2.13)
5. (a) 3a  5a  8a
1. There are 6 squares in the figure.
 a6
There are 5 rectangles in the figure.
 b5
There are 4 circles in the figure.
 c4
There is 1 hexagon in the figure.
 d 1
There are 3 pentagons in the figure.
 e3
There are 2 triangles in the figure.
 f 2
(b) 7b  2b  5b
(c) c  7c  4c  4c
(d) 5  3d  3  2d  3d  2d  5  3
 d 8
6. (a) Daily wage  $a  9
 $9a
 
(b) Height of Jerry  (2  b  5) cm
 
(c) Selling price of a carton of drinks
 $2  12  c
 $24c
 
2. (a) There are 24 hours in a day.
 a  24
(b) 1 kilometre equals 1 000 metres.
 b  1 000
(c) In general, a Hong Kong residential
telephone number consists of 8 digits.
 c 8
(d) 11-year-old children in Hong Kong have to
apply for identity cards.
 d  11
5 plus 3 times m 
3.
Subtract 3 from

the product of m and 5
Divide the sum of 3 and m

by 5
 (2b  5) cm

5m
3
(d) Selling price of each pencil  $e
Selling price of 10 pencils  $10  e
 $10e
Amount of the change  $(50  10  e)
 
 $(50  10e)
7. Selling price of p mobile phones  $2 750  p
 $2 750 p
 3m  5
3 m

5
Subtract 5 from 3

times m
 5  3m
Add 3 to the product of 5
and m 
 5m  3
Divide 5 times m by 3 
 5m  3
8
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8. Selling price of three sausage buns  $ y  3
 $3 y
Selling price of two cartons of milk  $6  2
 $12
 Amount required  $ y  3  $6  2
 $3 y  $12
 $(3 y  12 )
9. (a) Area of the square  a  a cm2
When p  9, q  18  2(9)
 18  18
 a 2 cm2
(b) Perimeter of the square  4  a cm
 4a cm
10. (a) Cost of a student ticket  $
m
2
(b) Total amount spent on the tickets
m
 $m  p  $  20 p
2
 $mp  $10 mp
0
When p  10, q  18  2(10 )
 18  20
 2
14. (a) a  2  6  2
4
(b) 6a  1  6(6)  1
 36  1
 $11mp
 37
B uild-up Exercise 2B
(page 2.15)
11. Algebraic expressions: 3a  4b, 2(  b), r 2
Formulae: c  d, v  u  at, A  b
(c) 20  2a  20  2(6)
 20  12
8
(d) 4(a  1)  4(6  1)
 4(5)
12. When x  1, y  8  1
9
When x  2, y  8  2
 10
 20
(e)
When x  3, y  8  3
 11
When x  4, y  8  4
 12
When x  5, y  8  5
 13
13. When p  6, q  18  2(6)
 18  12
6
When p  7, q  18  2(7)
 18  14
4
3a  4 3(6)  4

2
2
18  4

2
22

2
 11
2
2
(f) a  a  6  6
 36  6
 42
( a  b) h
2
(5  7)(4)

2
(12)(4)

2
 24
15. A 
When p  8, q  18  2(8)
 18  16
2
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16. r  (m 2  1)(n  p )
 ( 2 2  1)(3  11)
 ( 4  1)(3  11)
 (3)(14)
  42
1 2
at
2
1
 (11)(6)  (10)(6) 2
2
1
 66  (10)(36)
2
 66  180
17. s  ut 
 246
18. h 
v2  u 2
2g
8 2  ( 4 ) 2
2(10)
64  16

20
48

20
12

5

19. (a) When m  2,
2  ( 2  1)
n
1
2
23

1
2
 3 1
4
 4 pieces of cakes can be obtained after
cutting the cake 2 times.
(b) When m  7,
7  (7  1)
n
1
2
78

1
2
 28  1
 29
 29 pieces of cakes can be obtained after
cutting the cake 7 times.
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1 1 1
  ) 1
2 3 4
1 1
 12  (1   )  1
2 12
12 6
1
 12  ( 
 ) 1
12 12 12
12  6  1
 12 
1
12
7
 12   1
12
 7 1
20. (a) a  12  (1 
6
a
1
3
6
 1
3
 2 1
(b) b 
3
5( a  1)(b  1)
2
5(6  1)(3  1)

2
5(5)(2)

2
 25
(c) c 
(d) d  2(a 2  b 2 )  2c
 2(62  32 )  2(25)
 2(36  9)  50
 2(45)  50
 90  50
 40
(e) e  10( a  b)  2(c  d )
 10(6  3)  2( 25  40)
 10(9)  2( 15)
 90  30
 120
2(45  d )(c  10)(a  2b)
e
2(45  40)(25  10)[6  2(3)]

120
2(5)(15)(6  6)

120
2(5)(15)(12)

120
 15
(f) f 
f 2
(g) g  ( )  (e  3d  c  3b  3a)
5
15
 ( ) 2  [120  3(40)  25  3(3)  3(6)]
5
 32  (120  120  25  9  18)
(d) The pattern of the sequence:
10, 10, 10, 10, 
(1)
(1)
(1)
 It is a geometric sequence.
24. (a) 2,
5,
3
3
(b) 4,
3
12,
3
(c) 100,
97,
3
108 , 
36,
3
 9  (2)
11, 
8,
3
91, 
94,
3
3
 11
25. (a)
21. (a) $C  $1.4  p  $2.4  q
C  1.4 p  2.4q
The 1st figure The 2nd figure The 3rd figure
(b) C  1.4(10)  2.4(5)
 14  12
The 4th figure
 26
The 5th figure
(b)
(c) C  1.4(15)  2.4(11)
 21  26.4
 47.4
The 1st figure The 2nd figure The 3rd figure
B uild-up Exercise 2C
(page 2.18)
22. (a) 1, 3, 6, 10, 15 and 21 are triangular numbers.
(b) 1, 4, 9, 16 and 25 are square numbers.
23. (a) The pattern of the sequence:
5,
10,
5
20, 
15,
5
The 4th figure
The 5th figure
(c)
The 1st figure The 2nd figure
The 3rd figure
5
 It is an arithmetic sequence.
(b) The pattern of the sequence:
3, 6, 12, 24, 
(2) (2) (2)
 It is a geometric sequence.
(c) Neither
The 4th figure
The 5th figure
26. Number of points of intersection in the 1st figure
 2 2
Number of points of intersection in the 2nd figure
 3 3
Number of points of intersection in the 3rd figure
 4 4
11
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Number of points of intersection in the 4th figure
 55
Number of points of intersection in the 5th figure
 66
 36
28. Suggested answer:
1 and 36 are both triangular numbers and square
numbers.
29. (a) 9  3  6
 9 is obtained by adding the consecutive
27. (a) The pattern of the sequence:
3,
7,
11,
15,
triangular numbers 3 and 6.
,
4 4 4
4
The 5th term  15  4
(b) 36  15  21
 36 is obtained by adding the consecutive
4
triangular numbers 15 and 21.
 19
(c) 81  36  45
 81 is obtained by adding the consecutive
The 6th term  19  4
 23
triangular numbers 36 and 45.
It is an arithmetic sequence.
(b) The pattern of the sequence:
2,
10,
5
50,
5
250,
5
30. (a)
,
5
5
The 4th figure
The 5th figure
The 5th term  250  5
 1 250
The 6th term  1 250  5
 6 250
The 6th figure
It is a geometric sequence.
(c) The pattern of the sequence:
2,
8,
14,
20,
,
6
6
6
6
The 5th term  20  6




6
  26
The 6th term  26  6
 32
(b) Number of lines in the 1st figure  6
Number of lines in the 2nd figure  6  5
Number of lines in the 3rd figure  6  5  5
Number of lines in the 4th figure
6555
Number of lines in the 5th figure
 65555
Number of lines in the 6th figure
655555
 The number of lines in each figure form
an arithmetic sequence.
It is an arithmetic sequence.
(d) The pattern of the sequence:
1,
3,
9,
27,
,
(3) (3) (3) (3) (3)
The 5th term  27  (3)
31. The difference between the fifth term and the
eighth term of the Fibonacci sequence
 21  5
 16
 81
The 6th term  81  (3)
 243
It is a geometric sequence.
12
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32. (a) Number of logs in 8 layers
1 2  3  4  5  6  7  8
 36
(b) Number of logs added  9  10
 19
(c) (i) Number of logs in the upper 6 layers
1 2  3  4  5  6
 21
 Selling price of the logs  $350  21
 $7 350
(ii) Number of logs remained  55  21
 34
 Unit price of the logs exported to
Singapore
14 280
$
34
 $420
B uild-up Exercise 2D
33.
Input
(page 2.21)
Process
(c) The 1st term  4  1  1
The 2nd term  4  2  1
The 3rd term  4  3  1
The 4th term  4  4  1
According to the above pattern,
the nth term  4  n  1
4n
1
2
2
The 2nd term 
2
3
The 3rd term 
2
4
The 4th term 
2
According to the above pattern,
n
the nth term 
2
(d) The 1st term 
Output
36. (a) The 1st term  3  1
34.
The nth term of
sequence
The first term
The second term
2  3n
2  3(1)  5
2  3(2)  8
2n  1
2(1)  1  1
2(2)  1  3
n(n  1)
1(1  1)  0
2(2  1)  2
1st term  1 1
2nd term  2  1
3rd term  3  1
4th term  4  1
According to the above pattern,
the nth term  n  1
n
35. (a) The
The
The
The
(b) The 1st term  2  1
The 2nd term  2  2
The 3rd term  2  3
The 4th term  2  4
According to the above pattern,
the nth term  2  n
 2n
4
The 2nd term  3  2
5
The 3rd term  3  3
6
The 4th term  3  4
7
(b) The 1st term  1  2(1)
1 2
3
The 2nd term  1  2(2)
1 4
5
The 3rd term  1  2(3)
1 6
7
The 4th term  1  2(4)
1 8
9
13
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(c) The 1st term  (1)(1  3)
 (1)(4)
4
3
3

4 3 1
4
4
The 4th term  
5 4 1
5
5
The 5th term  
6 5 1
According to the above pattern,
n
the nth term 
n 1
The 3rd term 
The 2nd term  (2)(2  3)
 (2)(5)
 10
The 3rd term  (3)(3  3)
 (3)(6)
 18
The 4th term  (4)(4  3)
 (4)(7)
 28
1
5
(d) The 1st term 
The 2nd term 
2
5
The 3rd term 
3
5
The 4th term 
4
5
14, 21,
7
7
The 4th figure
28,
7
7
The 5th term  28  7
 35
(b) The
The
The
The
The
1st term  7  7  1
2nd term  14  7  2
3rd term  21  7  3
4th term  28  7  4
5th term  35  7  5
According to the above pattern,
the nth term  7  n
 7n
38. (a) The 5th term 
(b) The 7th term  7 2  7
 49  7
 56
40. (a)
37. (a) The pattern of the sequence:
7,
39. (a) The nth term  n 2  n
5
6
1
1

2 11
2
2
The 2nd term  
3 2 1
(b) The 1st term 
14
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(b)
The 5th figure
Order of
figures
1
2
3
4
5
Number of
lines
31
3
32
6
33
9
34
 12
35
 15
(c) According to the above pattern,
number of lines in the nth figure
 3 n
 3n
(d) Number of lines in the 9th figure
 3(9)
 27
41. (a) The pattern of the sequence:
10, 14, 18,
4
4
4
,
4
Number of seats in the 4th row  18  4
 22
Number of seats in the 5th row  22  4
 26
(b) It is an arithmetic sequence.
(c) Number of seats in the 1st row
 10  6  4  1
Number of seats in the 2nd row
 14  6  4  2
Number of seats in the 3rd row
 18  6  4  3
Number of seats in the 4th row
 22  6  4  4
Number of seats in the 5th row
 26  6  4  5
According to the above pattern,
number of seats in the nth row
 6  4 n
 6  4n
(d) Number of seats in the 10th row  6  4(10)
 6  40
 46
 There are 46 seats in the last row.
15
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