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1. ‘There are a squares, b rectangles, c circles, d hexagon, e pentagons and f triangles in the following figure.’
What number does each italic letter represent in the sentence?
2. In the following sentences, write down the numbers represented by the italic letters.
(a) There are a hours in a day.
(b) 1 kilometre equals b metres.
(c) In general, a Hong Kong residential telephone number consists of c digits.
(d) d-year-old children in Hong Kong have to apply for identity cards.
3. Match the following sentences with appropriate algebraic expressions.
5 plus 3 times m 
Subtract 3 from the product of m and 5 
Divide the sum of 3 and m by 5 

5m
3
 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
2.13
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4. Simplify the following expressions.
(a) x  x  y  y
(b) 2  3  a
(c) 4  5  b
(d) 10  2  c
5. Simplify the following expressions.
(a) 3a  5a
(b) 7b  2b
(c) c  7c  4c
(d) 5  3d  3  2d
6. Determine whether each of the following sentences is correct. If yes, put a ‘  ’ in the box; otherwise put
a ‘  ’.
9
(a) With an hourly wage of $a and 9-hour work a day, the daily wage is $ .
a
□
(b) The height of Jerry is 5 cm more than 2 times the height of Harry. If the height of
Harry is b cm, the height of Jerry is (2b + 5) cm.
□
(c) There are two dozen cans of drinks in a carton. If the selling price of each can of
drink is $c, the selling price of a carton of drinks is $2c.
□
□
(d) A pencil costs $e. Paying $50 for 10 pencils will receive a change of $(10e  50).
7. The selling price of a mobile phone is $2 750. Express the selling price of p mobile phones by using the
simplest algebraic expression.
8. The selling price of a sausage bun is $y and that of a carton of milk is $6. Express the amount required
for buying three sausage buns and two cartons of milk by using the simplest algebraic expression.
9. If the length of a side of a square is a cm,
(a) find the area of the square.
(b) find the perimeter of the square.
2.14
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10. There are p teachers and 20p students visiting a museum. The cost of an adult ticket is $m and the cost
of a student ticket is half of that of an adult ticket.
(a) Find the cost of a student ticket.
(b) Find the total amount spent on the tickets.
11. In the following, which of them are algebraic expressions? Which of them are formulae? Write them down
on appropriate books.
c  d
3a  4b
v  u  at
2(  b)
r
A  b
pressio
Algebraic ex
2
ns
Formulae
12. Given that y  8  x, complete the following table.
x
1
2
3
4
5
y
13. Given that q  18  2p, complete the following table.
p
6
7
8
9
10
q
2.15
 2008 Chung Tai Educational Press. All rights reserved.
14. If a  6, find the value of each of the following expressions.
(a) a  2
(b) 6a  1
(c) 20  2a
(d) 4(a  1)
(e)
3a  4
2
15. Given that A 
(f) a 2  a
(a  b)h
, let a  5, b  7 and h  4, find the value of A.
2
16. Given that r  (m 2  1)(n  p), let m  2, n  3 and p  11, find the value of r.
17. Given that s  ut 
18. Given that h 
1 2
at , let a  10, u  11 and t  6, find the value of s.
2
v2  u 2
, let v  8, u  4 and g  10, find the value of h.
2g
19. When a cake is cut from the top to the bottom m times, at most n pieces of cakes can be obtained. It
m  (m  1)
is known that n can be found by the formula n 
 1.
2
(a) At most how many pieces of cakes can be obtained after cutting the cake 2 times?
(b) At most how many pieces of cakes can be obtained after cutting the cake 7 times?
2.16
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20. In the following expressions, values represented by the same letters are the same. Find the value
represented by each letter.
(a) a  12  (1 
1 1 1
  ) 1
2 3 4

a
1
3
(b) b 

(c) c 
5(a  1)(b  1)
2

2
2
(d) d  2(a  b )  2c

(e) e  10(a  b)  2(c  d )

(f) f 
2(45  d )(c  10)(a  2b)
e

f 2
(g) g  ( )  (e  3d  c  3b  3a)
5

21. Betty used $C to buy p stamps of $1.4 and q stamps of $2.4.
(a) Write down a formula about C.
(b) If p  10 and q  5, find the value of C.
(c) If p  15 and q  11, find the value of C.
2.17
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22. Consider the following numbers.
1, 3, 4, 6, 9, 10, 15, 16, 21, 25
(a) Which of them are triangular numbers?
(b) Which of them are square numbers?
23. Is each of the following an arithmetic sequence, a geometric sequence or neither one of the two types of
sequences? Put a ‘  ’ in the appropriate box.
(a) 5, 10, 15, 20, 
(b) 3, 6, 12, 24, 
(c) 1,
1 1 1
, , ,
2 3 4
(d) 10, 10, 10, 10, 
Arithmetic sequence
Geometric sequence
Neither
□
□
□
□
□
□
□
□
□
□
□
□
24. According to each of the following sequences, fill in the boxes.
(a) 2,
5,
3
(b) 4,
11, 
8,
3
12,
36,
3
3
(c) 100,
97,
,
3
94,
91, 
2.18
 2008 Chung Tai Educational Press. All rights reserved.
25. Each of the following is a sequence of figures, fill in the blank with appropriate figure.
(a)
The 1st figure
The 2nd figure
The 3rd figure
The 4th figure
The 5th figure
(b)
The 1st figure The 2nd figure
The 3rd figure
The 1st figure The 2nd figure
The 3rd figure
The 4th figure
The 5th figure
(c)
The 4th figure
The 5th figure
26. The following is a sequence of figures. How many points of intersection are there in the fifth one?

The 1st figure
The 2nd figure
The 3rd figure
The 4th figure
27. Observe the pattern of each of the following sequences, write down the next two terms of the seq uence
and determine what kind of sequence it is.
(a) 3, 7, 11, 15, 
(b) 2, 10, 50, 250, 
(c) 2, 8, 14, 20, 
(d) 1, 3, 9, 27, 
28. Write down two numbers which are both triangular numbers and square numbers.
2.19
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29. Adding which two consecutive triangular numbers will result in each of the following square numbers?
(a) 9
(b) 36
(c) 81
30. The following is a sequence of figures.

The 1st figure
The 2nd figure
The 3rd figure
(a) Draw the next three figures.
(b) Which type of sequence is formed by the number of lines () in each figure?
31. Find the difference between the fifth term and the eighth term of the Fibonacci sequence.
32. The following shows the logs piling up in a timber factory where the number of logs in each layer are
1, 2, 3,  counting from the top to the bottom.
(a) If there are 8 layers of logs piled up as shown in the figure, how many logs are there in total?
(b) If two more layers of logs are added now, how many logs are added?
(c) Among these 10 layers of logs, the upper 6 layers will be exported to Japan and the remaining will
be exported to Singapore.
(i) If the logs exported to Japan are sold at $350 each, how much can be obtained from the sale of
the logs to Japan?
(ii) It is given that $14 280 is obtained from the sale of the logs exported to Singapore, find the unit
price of the logs exported to Singapore.
2.20
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33. Write down ‘Input’, ‘Output’ and ‘Process’ in appropriate boxes.
34. Complete the following table.
The nth term of
sequence
The first term
The second term
2  3n
2n  1
n(n  1)
35. According to the first 4 terms of each of the following sequences, write down the nth term of the
sequence.
(a) 1  1, 2  1, 3  1, 4  1, 
(c) 4  1  1, 4  2  1, 4  3  1, 4  4  1, 
(b) 2  1, 2  2, 2  3, 2  4, 
1 2 3 4
(d)
, , , ,
2 2 2 2
36. Each of the following represents the nth term of a sequence. Find the first 4 terms of the sequence.
(a) 3  n
(c) n(n  3)
(b) 1  2n
n
(d)
5
37. A sequence 7, 14, 21, 28,  is given.
(a) Write down the 5th term of the sequence.
(b) Find an algebraic expression to represent the nth term of the sequence.
2.21
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1 2 3 4
, , , ,  is given.
2 3 4 5
(a) Write down the 5th term of the sequence.
(b) Find an algebraic expression to represent the nth term of the sequence.
38. A sequence
39. A sequence 2, 6, 12, 20,  is given, where
the first term  1 2  1  2,
the second term  2 2  2  6,
the third term  3 2  3  12,
the fourth term  4 2  4  20.
(a) According to the above expressions, find an algebraic expression to represent the nth term of the
sequence.
(b) Using the result of (a), find the 7th term of the sequence.
40. The following is a sequence of figures.

The 1st figure
The 2nd figure
The 3rd figure
(a) Draw the 4th and 5th figures.
(b) Complete the following table.
Order of figures
1
2
3
4
5
Number of lines
(c) Find the number of lines in the nth figure.
(d) Find the number of lines in the 9th figure.
41. There are 10 seats, 14 seats and 18 seats in the first, second and third rows of a theatre respectively. The
number of seats in each of the succeeding rows increases according to this pattern.
(a) Find the respective number of seats in the fourth row and the fifth row.
(b) What type of sequence is formed by the number of seats in each row?
(c) Find the number of seats in the nth row.
[ Hint : 10  6  4  1, 14  6  4  2, 18  6  4  3 ]
(d) If there are 10 rows in the theatre, how many seats are there in the last row?
2.22
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