1. Simplify the following expressions.
(a)
2
8a
(c)
c2
c 3d
(b)
7x
x2
(b)
12 xy 2
3x 2 y
(b)
a 2 (b  c)
a (b  c)3
(b)
3n 2  15 n
9n
(b)
nm
2m  2n
2. Simplify the following expressions.
(a)
2a
6ab
(c)
5 pq3
20 q 2 r 2
3. Simplify the following expressions.
(a)
x y
3( x  y ) 2
(c)
2q ( m  n)3
6q 2 ( m  n) 2
4. Simplify the following expressions.
(a)
4
2 p  8q
(c)
12 ab
18a 2  6ab
5. Simplify the following expressions.
(a)
6b  2a
4a  6b
(c)
6 xz  4 yz
15 x  10 y
9.9
 2009 Chung Tai Educational Press. All rights reserved.
6. Simplify the following expressions.
(a)
a 2  ab
ab  b 2
(c)
1  x2
4  4x
(b)
p2  p
2 p  2
(b)
a 2b 3ab2
 3
6b3
a
(b)
9 y 2 3xy
 2
xy
x
(b)
p  4q
1 3p

8q  2 p 5  15 p
(b)
c  2d 4c  8d

4b  6a 3a  2b
(b)
9
6 p 2 8 p 2  2 pq
 2 
4p  q p q
pq2
7. Simplify the following expressions.
(a)
y 2 5x

2x y
(c)
10 pq 12 pr3

8 p 2 r 2 15q 4 r
8. Simplify the following expressions.
(a)
2a a 3

b 2 4b
(c)
12c 2 d 4 6c3d
 2
2cd 2
3c d
9. Simplify the following expressions.
(a)
6b
a 1
 2
3  3a
b
(c)
9 x  12 y x 2  xy

y 2  xy 6 x  8 y
10. Simplify the following expressions.
(a)
12 y 2
8y
 2
3x  3 x  x
(c)
2a  2b a 2  b 2

4ab
ba
11. Simplify the following expressions.
(a)
10a 12c 2
c


2
8b 15a
ab
(c)
3xy  6 x 2 4 xy  2 y 2

 (4 x 2  y 2 )
2y
9 xy 2
9.10
 2009 Chung Tai Educational Press. All rights reserved.
12. (a) Factorize ax  bx  ay  by .
(b) From the result of (a), simplify
ax  bx  ay  by
a

.
ab
3x  3 y
13. (a) Factorize 1  a  b  ab .
(b) From the result of (a), simplify
1  a  b  ab a 2  a b 2  b
.


a  ab
ab
1  a2
14. Fill in the blanks with suitable numbers.
(a)
3 4
 
x x
2 3
(c)   
z z
(b)
x
z
7 6
 
y y
(d) 
5 2
 
p p
y
p
15. Simplify the following expressions.
4 2
(a)  
x x
(c)
6 27

7z 7z
(b)
8
7

3y 3y
(d)
a 13a

b
b
2x
3

x y x y
16. Simplify the following expressions.
(a)
4
5

ab ab
(b)
(c)
2a
2b

ab ab
(d) 
2x
y

2x  y 2x  y
9.11
 2009 Chung Tai Educational Press. All rights reserved.
17. Simplify the following expressions.
(a)
1 1

h 2h
(b)
1
3

4a 2 a
(c)
3b 2

c 3c
(d)
k 2k

3h h
18. Simplify the following expressions.
(a)
5
1

4c 5c
(b)
7
5

2a 3a
(c)
5x 5

8a 6a
(d)
u 2u

3v 5v
(b)
3b (

5c
19. Fill in the brackets with suitable expressions.
(a) 
(c)
2
10
(


a 1 a 1
(
)
2d  e

)
a 1
2d
1

2d  e
2d  e
(d)
(
)
5c
)
f g

(a)
8
1

7m  n n  7m
(b)
p
6

p6 6 p
(c)
w
w

w  1 1  w
(d)
2x
x y

3x  y  y  3x
(a)
1
7

3  x 4(3  x)
(b)
3
5

2(a  b) a  b
(c)
3x
x

x  6 5( x  6)
(d)
3b  1
2b

2(a  b) a  b
9.12
 2009 Chung Tai Educational Press. All rights reserved.
b
5c
f
2g

f g
f g
20. Simplify the following expressions.
21. Simplify the following expressions.

22. Simplify the following expressions.
(a)
1
2

2( x  y ) 3( x  y )
(b)
1
2h

4(h  11) 3(h  11)
(c)
m
1

4(m  5) 5(m  5)
(d)
2y
x

3( x  2 y ) 8(2 y  x)
(b)
2  3y
2
6y
23. Simplify the following expressions.
(a) 1 
(c)
x 1
2x
5 z
1
3(2 z  1)
(d) 2a 
4ab
5  3b
1
into an algebraic fraction with the denominator x( x  8) .
x
1
(ii) Convert
into an algebraic fraction with the denominator x( x  8) .
x8
1
1
(b) From the result of (a), simplify 
.
x x8
24. (a) (i) Convert
25. Given that x  3 and y  4 , find the value of z in each of the following expressions.
(a) z  x  3 y
(c) z 
2x
y
(b) z  x 2 y
(d) z 
1 1

x y
26. Given that a  2 , b  5 and c  3 , find the value of d in each of the following expressions.
2a
bc
(a) d 
(b) d 
bc
a
(c) d  2(a  b  c)
(d) d 
2a  5b  3c
5
9.13
 2009 Chung Tai Educational Press. All rights reserved.
27. Given that a 
1 1
 , find the value of a if b  4 and c  2 .
b c
28. Given that P 
30T
, find the value of P if T  5 and V  12 .
V
29. Given that E 
1 2
mv , find the value of E if m  20 and v  3 .
2
30. Given that N  k (2t ) , find the value of N if k  0.25 and t  6 .
31. Given that P  Q (1  0.1n ) , find the value of P if Q  80 and n  3 .
32. Given that a 
1
T2
1

, find the value of a if P  , T  3 and U  6 .
4P U
2
33. Given that S 
n
( A  Fn) , find the value of S if n  3 , A  4 and F  6 .
2
34. Given that P  4 , find the value of  if P  32 .
35. Given that a  b  c  360 , find the value of c if a  100 and b  160 .
36. Given that M 
V
, find the value of n if M  10 and V  8 .
n 1
37. Given that A  4 x( x  y) , find the value of y if A  96 and x  3 .
9.14
 2009 Chung Tai Educational Press. All rights reserved.
38. Given that s  ut 
39. Given that y 
1 2
at , find the value of a if s  122 .5 , u  0 and t  5 .
2
3x  4 z
, find the value of z if y  10 and x  4 .
2
40. Given that M  3ab2  4ac , find the value of a if M  10 , b  2 and c  6 .
41. Given that
1 x 1

, find the value of x if y  5 .
y x 1
42. (a) Simplify
1
1
.

3a 4a
(b) It is given that d  bc(
1
1
 ) . From the result of (a), if d  5, a  2 and b  6, find the value
3a 4a
of c.
43. It is given that the surface area of a cylinder is A  2rh  2r 2 .
r
(a) If   3.14 , r  5 and h  10 , find the value of A.
(b) If A  165 ,  
22
and r  3.5 , find the value of A.
7
h
44. A string of (5w  4) cm long is evenly divided into several parts, the length  cm of each part can be
5w  4
found by the formula  
where w is an integer greater than 3.
w2
(a) If a string is 24 cm long originally,
(i) find the value of w.
(ii) find the length of each part.
(b) If each part of a string is 7 cm long,
(i) find the value of w.
(ii) find the original length of the string.
9.15
 2009 Chung Tai Educational Press. All rights reserved.
45. Given that 1  2  3    (n  1)  n  (n  1)    3  2  1  n 2 , where n is a positive integer.
(a) Find the value of 1  2  3    19  20  19    3  2  1 .
(b) Find the value of 1  2  3    39  40  39    3  2  1.
(c) From the results of (a) and (b), find the value of 20  21  22    39  40  39    22  21  20.
46. The degree Celsius (C) and degree Fahrenheit (F) are two units of temperature commonly used. The
conversion between the two units can be expressed in the following formula:
f  1.8c  k
where f F is the degree Fahrenheit, cC is the degree Celsius and k is a constant.
(a) Given that 0C corresponds to 32F, find the value of k.
(b) (i) Given that the boiling point of water is 100C, express it in degree Fahrenheit.
(ii) Given that the boiling point of alcohol is 173.3F, express it in degree Celsius.
(c) Suppose a person with the body temperature higher than 37.2C is regarded as having a fever, is
Jade having a fever if her body temperature is 100F? Explain briefly.
47. Determine whether each of the following sentences is correct. If yes, put a ‘  ’ in the box; otherwise
put a ‘  ’.
(a) Make x the subject of the formula y  4  x, we can obtain the formula x  4  y .
(b) Make x the subject of the formula y  2 x , we can obtain the formula x 
y
.
2
1
(c) Make x the subject of the formula y   x, we can obtain the formula x  3  y .
3
1
(d) Make x the subject of the formula y  5 x  1, we can obtain the formula x  y  1 .
5
48. Make each of the following letters the subject of the formula d  a  bc .
(a) a
(b) b
(c) c
9.16
 2009 Chung Tai Educational Press. All rights reserved.
□
□
□
□
49. Make the letters in brackets the subjects of the corresponding formulae.
(a) x  y  z  360
[z]
(b) 2 y  5 x
[x]
50. Make the letters in brackets the subjects of the corresponding formulae.
(a) y  3x  2
[x]
(b) 3 y  6 x  8
[x]
51. Make the letters in brackets the subjects of the corresponding formulae.
(a) a 
b7
4
[b]
(b) p 
6  3q
4
[q]
52. Make the letters in brackets the subjects of the corresponding formulae.
(a) 9 
n
4m
[m]
(b)
4p
6
q
[q]
53. Make the letters in brackets the subjects of the corresponding formulae.
(a)
a
b
bc
[c]
(b) t 
2s
uv
[v]
54. Make the letters in brackets the subjects of the corresponding formulae.
(a)
y
8
x2
[x]
(b) x 
y
1  3z
[z]
55. Make the letters in brackets the subjects of the corresponding formulae.
(a) P  mu  mv
[m]
(b) 9 f  11e  3ef
[e]
56. Make the letters in brackets the subjects of the corresponding formulae.
(a) a  b(c  de)
[d]
(b)
p
q
 11  4(  1)
3
2
[q]
57. Make the letters in brackets the subjects of the corresponding formulae.
(a) y 
1
1

 2y
3x 4 x
[x]
(b)
1
1
1


b
2a 4b 3a
[a]
9.17
 2009 Chung Tai Educational Press. All rights reserved.
58. Make the letters in brackets the subjects of the corresponding formulae.
(a) T 
ad f b

ce ec
[a]
(b) S  (a  c)(b  e)
[e]
59. Make the letters in brackets the subjects of the corresponding formulae.
(a) w 
1  2r
r2
[r]
(b)  
m 1

n m
[n]
60. It is given that xt  4(1  t ) and y  4t 2 .
(a) Express t in terms of x.
(b) From the result of (a), express y in terms of x.
2a  1
2a  1
and y 
.
a 1
a 1
(a) (i) Express a in terms of x.
61. It is given that x 
(ii) Express a in terms of y.
(b) From the result of (a), express y in terms of x.
(c) Express x in terms of y.
62. (a) Simplify
y
x

x
y
x y
.
(b) It is given that A 
y
x

x
y
x y
.
(i) From the result of (a), make y the subject of the above formula.
1
(ii) If x  and A  12 , find the value of y.
4
63. Miss Cheung deposits a sum of money $P in a bank. The amount $A received after T years is given by
the following formula:
A  P(1  0.02T )
(a) If Miss Cheung deposits $5 000 in a bank, find the amount received after 4 years.
(b) Make T the subject of the formula.
(c) If Miss Cheung deposits $12 000 in the bank, how long does it take for her to receive an amount
of $14 400?
9.18
 2009 Chung Tai Educational Press. All rights reserved.