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15 More about Probability
60
$
6
10
$
=
´
Mathematics in Action (3rd Edition) 1A Full Solutions
c
b
a
-
+
2 Introduction to Algebra
2 Introduction to Algebra
Activity
Warm-Up Activity (p. 2.3)
1.
2.
n
n
10
$
10
$
=
´
Activity 2.1 (p. 2.23)
1.
Figure
Number of dots
1
1 ( 1 = 12 = (1)
2
2 ( 2 = (2)2 = (4)
3
(3) ( (3) = (3)2 = (9)
4
(4) ( (4) = (4)2 = (16)
2.(a)Figure 5 is made of (5)2 dots, i.e. (25) dots.
(b)Figure 6 is made of (6)2 dots, i.e. (36) dots.
Activity 2.2 (p. 2.24)
1.
Figure
Number of dots
1
1
2
1 + 2 = (3)
3
1 + 2 + (3) = (6)
4
(1) + (2) + (3) + (4) = (10)
2.(a)1 + 2 + 3 + 4 + 5 = 15
(b)1 + 2 + 3 + 4 + 5 + 6 = 21
Maths Dialogue
Maths Dialogue (p. 2.31)
1.For Harry’s general term:
The 1st term
0
)
1
1
(
4
=
-
=
The 2nd term
4
)
1
2
(
4
=
-
=
The 3rd term
8
)
1
3
(
4
=
-
=
The 4th term
12
)
1
4
(
4
=
-
=
∴Harry’s general term is correct.
For Amy’s general term:
The 1st term
0
)
1
(
4
4
=
+
-
=
The 2nd term
4
)
2
(
4
4
=
+
-
=
The 3rd term
8
)
3
(
4
4
=
+
-
=
The 4th term
12
)
4
(
4
4
=
+
-
=
∴Amy’s general term is correct.
∴Both general terms are correct.
2.Let Tn be the nth term of the sequence.
∵T1 =
2
-
]
2
)
1
[(
2
-
=
T2 = 0
]
2
)
2
[(
2
-
=
T3 = 2
]
2
)
3
[(
2
-
=
T4 = 4
]
2
)
4
[(
2
-
=
M
∴Tn
)
2
(
2
-
=
n
∴The general term of the sequence is
)
2
(
2
-
n
(or – 4 + 2n).
To Learn More
To Learn More (p. 2.27)
1.∵52 = 1 + 3 + 5 + 7 + 9
∴52 is the sum of the first 5 consecutive positive odd numbers.
2.The sum of the first 20 consecutive positive odd numbers
400
20
2
=
=
Classwork
Classwork (p. 2.5)
1.(a)
1
+
m
(b)
x
5
(c)
q
p
-
3
(d)
z
y
6
2.xy, yx; –y + x, x – y
3.(a)Wrong
(b)Correct
(c)Wrong
Classwork (p. 2.7)
1.(a)
3
4
4
4
4
=
´
´
(b)
4
w
w
w
w
w
=
´
´
´
(c)
10
times
10
...
m
m
m
m
m
=
´
´
´
´
4
4
4
3
4
4
4
2
1
(d)
r
r
q
q
q
q
q
=
´
´
´
´
4
4
3
4
4
2
1
times
...
2.(a)
b
b
b
b
´
´
=
3
(b)
k
k
k
k
k
k
k
´
´
´
´
´
=
6
Classwork (p. 2.16)
(a)Formula
(b)Algebraic expression
(c)Formula
(d)Formula
(e)Algebraic expression
Classwork (p. 2.25)
1.1, 4, 9, 16, 25, 36, 49, 64, …
2.1, 3, 6, 10, 15, 21, 28, 36, …
Classwork (p. 2.26)
1.(a)1, 5, 9, 13, 17, 21, …
(b)7, 5, 3, 1, −1, −3, …
2.(a)1, 3, 9, 27, 81, 243, …
(b)64, 32, 16, 8, 4, 2, …
3.1, 1, 2, 3, 5, 8, 13, 21, …
Classwork (p. 2.28)
1.T3 = 15 = 5(3)
T4 = 20 = 5(4)
Tn = 5n
2.T3 = 16 = 5(3) +1
T4 = 21 = 5(4) + 1
Tn = 5n + 1
3.T3 = 103 = 100 + 3
T4 = 104 = 100 + 4
Tn = 100 + n
Quick Practice
Quick Practice 2.1 (p. 2.7)
(a)The required expression is:
4x + 2
(b)The required expression is:
3
z
y
-
Quick Practice 2.2 (p. 2.8)
(a)Multiply 4 to the sum of x and 2. (or any other reasonable answers)
(b)Subtract d from c and then divide the difference by 8. (or any other reasonable answers)
Quick Practice 2.3 (p. 2.9)
(a)
p
p
p
p
2
4
=
-
-
(b)
q
p
q
q
p
p
q
p
q
p
+
=
-
+
-
=
-
-
+
2
2
3
2
2
3
(c)
x
x
x
x
x
x
x
4
5
2
10
2
10
=
-
=
-
=
-
¸
(d)
b
b
b
b
b
b
b
6
4
2
4
3
6
4
3
6
=
+
=
+
=
´
+
¸
Quick Practice 2.4 (p. 2.10)
(a)
3
3
8
8
)
(
)
2
4
(
2
4
d
d
d
d
d
d
d
d
=
´
=
´
´
´
´
=
´
´
´
´
(b)
z
y
z
y
y
y
y
z
y
y
y
y
4
)
(
=
´
´
´
´
=
´
´
´
´
(c)
2
2
3
)
(
)
(
)
2
3
2
(
2
3
2
2
3
2
n
m
n
n
m
m
n
m
n
m
n
m
n
m
=
´
´
´
´
¸
´
=
¸
´
´
´
´
´
=
¸
´
´
´
Quick Practice 2.5 (p. 2.10)
(a)Weight of Peter
kg
2
x
=
(b)Weight of Kitty
kg
)
2
(
y
x
-
=
Quick Practice 2.6 (p. 2.11)
The price of 5 skirts
p
p
5
$
5
$
=
´
=
The price of a pair of trousers
200
$
=
∴The change
)
5
800
$(
)
200
5
1000
$(
p
p
-
=
-
-
=
Quick Practice 2.7 (p. 2.17)
(a)When
4
=
u
, EQ
4
8
12
8
)
4
(
3
8
3
=
-
=
-
=
-
=
u
v
(b)When
4
-
=
u
,
20
8
12
8
)
4
(
3
8
3
-
=
-
-
=
-
-
=
-
=
u
v
Quick Practice 2.8 (p. 2.17)
(a)When u = −3 and v = −9,
4
3
12
9
)
9
(
)
3
(
9
=
-
-
=
-
+
-
-
=
+
=
v
u
v
f
(b)When
2
1
=
u
and
2
1
=
v
,
2
1
1
2
1
2
1
2
1
2
1
=
=
+
=
+
=
v
u
v
f
Quick Practice 2.9 (p. 2.18)
When
38
=
m
,
800
19
300
13
6500
)
38
(
350
6500
=
+
=
+
=
S
∴The salesman’s salary in that month is $19 800.
Quick Practice 2.10 (p. 2.30)
13
)
5
(
3
2
5
-
=
-
=
T
EQ
16
)
6
(
3
2
6
-
=
-
=
T
Quick Practice 2.11 (p. 2.31)
(a)∵T1 = 3 = 1 + 2
T2 = 4 = 2 + 2
T3 = 5 = 3 + 2
T4 = 6 = 4 + 2
M
∴Tn = n + 2
(b)By substituting n = 99 into
2
+
=
n
T
n
, we have
101
2
99
99
=
+
=
T
∴The number of dots in the 99th figure is 101.
Consolidation Corner
Consolidation Corner (p. 2.11)
1.
Word phrase
Algebraic expression
(a)
Add 3 to the square of x.
3
2
+
x
(b)
Subtract the cube of b from a.
3
b
a
-
(c)
Multiply 4 by the sum of p and q.
)
(
4
q
p
+
(d)
Divide the product of c and d by 2.
2
cd
2.
bc
a
2
)
(
c
b
a
+
q
p
´
¸
2
2
q
p
-
ab
c
-
2
¸
-
q
p
2
pq
bc
a
2
)
2
(
q
p
´
¸
2
q
p
-
2
)
(
¸
-
q
p
q
p
2
3.(a)
z
y
z
y
y
y
+
=
+
+
+
3
(b)
yz
z
y
y
y
3
)
(
=
´
+
+
(c)
a
a
a
a
6
2
3
=
+
+
(d)
3
6
2
3
a
a
a
a
=
´
´
Consolidation Corner (p. 2.18)
1.(a)
45
9
5
))
5
(
4
)(
2
3
(
)
4
)(
3
(
=
´
=
-
-
+
=
-
+
b
a
(b)
2
1
6
3
1
5
1
2
1
1
-
=
-
=
-
-
+
=
-
+
b
a
2.When
2
=
x
and
1
=
y
,
780
180
600
)
1
(
180
)
2
(
300
180
300
=
+
=
+
=
+
=
y
x
C
When
1
=
x
and
3
=
y
,
840
540
300
)
3
(
180
)
1
(
300
180
300
=
+
=
+
=
+
=
y
x
C
When
3
=
x
and
2
=
y
,
1260
360
900
)
2
(
180
)
3
(
300
180
300
=
+
=
+
=
+
=
y
x
C
Number of adults (x)
Number of children (y)
Total cost ($C)
2
1
780
1
3
840
3
2
1260
Consolidation Corner (p. 2.32)
1.(a)In the sequence, each term is larger than its
preceding term by 2.
∴It is an arithmetic sequence.
(b)Neither
(c)In the sequence, the division of any term (except the first term) by its preceding term is 2.
∴It is a geometric sequence.
(d)In the sequence, each term is smaller than its
preceding term by 9.
∴It is an arithmetic sequence.
(e)Neither
2.
0
)
1
1
)(
1
(
1
=
-
=
T
2
)
1
2
)(
2
(
2
=
-
=
T
6
)
1
3
)(
3
(
3
=
-
=
T
12
)
1
4
)(
4
(
4
=
-
=
T
∴The first 4 terms of the sequence are 0, 2, 6 and 12.
3.(a)∵T1 = 1
T2 = 2
T3 = 3
T4 = 4
∴Tn
n
=
(b)∵T1 =
5
1
T2 =
5
2
T3 =
5
3
T4 =
5
4
∴Tn
5
n
=
(c)∵T1 = −4 = −4(1)
T2 = −8 = −4(2)
T3 = −12 = −4(3)
T4 = −16 = −4(4)
∴Tn
n
4
-
=
Exercise
Exercise 2A (p. 2.12)
Level 1
1.(a)The required expression is 2a + b.
(b)The required expression is
y
x
2
5
-
.
(c)The required expression is
pq
4
.
(d)The required expression is
h
k
2
3
.
2.(a)The required expression is
3
+
xy
.
(b)The required expression is
2
2
q
p
-
.
(c)The required expression is
)
(
8
d
c
+
.
(d)The required expression is
b
a
3
3
.
3.(a)Add y to x. (or any other reasonable answers)
(b)Subtract 2 from the product of 3 and x.
(or any other reasonable answers)
(c)Divide r by the product of 4 and s.
(or any other reasonable answers)
(d)The product of p and the square of q.
(or any other reasonable answers)
4.(a)
3
8
3
8
+
=
+
´
u
u
(b)
5
5
1
-
=
-
¸
d
d
(c)
b
a
b
a
3
3
-
=
´
-
(d)
8
8
c
z
c
z
+
=
¸
+
5.(a)
y
x
y
x
4
4
=
¸
´
(b)
q
p
q
p
2
)
2
(
+
=
¸
+
(c)
p
p
p
4
2
8
2
8
=
´
=
¸
´
(d)
st
t
s
t
s
12
3
4
3
4
=
´
´
´
=
´
6.(a)
b
a
b
a
a
a
-
=
-
+
+
3
(b)
q
q
q
p
p
2
=
+
+
-
(c)
5
3
5
4
+
=
+
-
x
x
x
(d)
2
5
4
2
3
2
-
=
-
+
+
s
s
s
7.(a)
z
z
z
z
2
2
3
=
-
+
(b)
y
y
y
y
3
3
5
=
+
-
(c)
p
p
p
p
-
=
-
+
4
2
(d)
q
q
q
q
5
6
2
-
=
-
-
8.(a)
x
x
x
x
x
9
8
4
2
=
+
=
´
+
(b)
m
m
m
m
m
m
m
=
-
=
-
=
-
¸
2
3
2
5
15
2
5
15
(c)
y
y
y
y
y
y
y
-
=
-
=
-
=
¸
-
2
3
6
3
6
(d)
k
k
k
k
k
7
10
3
2
5
3
-
=
-
=
´
-
9.(a)
2
2
8
8
)
(
2)
4
(
2
4
a
a
a
a
a
a
=
´
=
´
´
´
=
´
´
´
(b)
2
2
)
(
)
(
n
m
n
n
m
m
n
n
m
m
=
´
´
´
=
´
´
´
(c)
2
2
30
30
)
(
)
5
3
2
(
5
3
2
b
b
b
b
b
b
=
´
=
´
´
´
´
=
´
´
(d)
3
3
12
12
)
(
)
6
2
(
6
2
z
z
z
z
z
z
z
z
=
´
=
´
´
´
´
=
´
´
10.The amount the man needs to pay
)
$(
y
x
+
=
11.Total volume of 8 cans of soft drink
mL
8
mL
8
V
V
=
´
=
12.Number of dolls Katie has now
b
a
-
=
13.Fred’s monthly salary
12
$
12
$
S
S
=
¸
=
14.(a)Price of x correction pens
x
x
15
$
15
$
=
´
=
(b)Amount that Alan originally has
)
20
15
$(
+
=
x
15.(a)Age of John’s father now
old
years
30)
(
+
=
x
(b)Age of John’s father y years ago
old
years
)
30
(
+
-
=
y
x
16.Number of passengers a bus can carry
y
x
+
=
Number of passengers 5 buses can carry
)
(
5
y
x
+
=
Level 2
17.(a)The required expression is
y
x
3
2
.
(b)The required expression is
2
3
y
x
-
.
(c)The required expression is
pq
r
+
4
.
(d)The required expression is
1
2
+
+
b
a
.
18.(a)The required expression is
t
m
2
5
-
+
.
(b)The required expression is
b
a
5
2
+
.
(c)The required expression is
3
)
8
(
z
y
x
-
.
(d)The required expression is
3
)
(
2
v
u
+
.
19.(a)Divide p by q and then subtract r from the quotient.
(or any other reasonable answers)
(b)The product of 8, p, q and the square of r
(or any other reasonable answers)
(c)Divide 9 by the product of 4 and the cube of m.
(or any other reasonable answers)
(d)Add y to the product of 2 and x and then multiply the sum by z. (or any other reasonable answers)
20.(a)
4
4
5
3
2
5
4
3
2
=
+
-
+
=
-
+
+
y
y
y
y
y
y
(b)
2
5
5
3
2
7
5
2
3
7
-
=
-
+
-
=
-
-
+
a
a
a
a
a
(c)
3
5
2
5
2
4
2
2
5
4
-
-
=
+
-
-
-
=
+
-
-
-
x
x
x
x
x
x
x
(d)
4
2
4
8
3
2
4
3
2
8
+
-
=
-
+
-
+
-
=
-
-
+
+
-
c
c
c
c
c
c
c
21.(a)
y
x
y
y
x
x
3
2
3
4
+
=
+
+
-
(b)
q
p
q
q
p
p
q
p
q
p
5
2
4
3
5
4
3
5
+
=
+
+
-
=
+
-
+
(c)
n
m
n
n
m
m
2
4
)
2
4
(
6
2
-
-
=
-
-
-
(d)
y
x
y
y
x
y
y
x
x
y
y
x
y
x
6
4
3
3
4
)
3
(
3
2
2
)
4
(
2
3
2
+
-
=
+
+
-
=
-
-
+
-
-
=
-
-
-
+
-
22.(a)
3
24
)
(
)
3
2
4
(
3
2
4
3
2
4
p
p
p
p
p
p
p
p
p
p
=
´
´
´
´
´
=
´
´
´
´
´
=
´
´
´
(b)
3
6
)
(
)]
2
(
4
3
[
)
2
(
4
3
)
2
(
4
3
r
r
r
r
r
r
r
r
r
r
-
=
´
´
´
-
¸
´
=
-
¸
´
´
´
´
=
-
¸
´
´
(c)
2
3
)
(
]
4
)
6
(
2
)
1
[(
4
)
6
(
2
1
4
)
6
(
2
rs
s
s
r
s
r
s
s
r
s
=
´
´
´
¸
-
´
´
-
=
¸
´
-
´
´
´
´
-
=
¸
-
´
´
-
(d)
2
2
2
)
(
)
(
)
3
6
4
(
3
6
4
3
6
4
q
p
q
q
p
p
p
q
q
p
p
q
q
p
=
´
´
´
´
´
¸
=
´
´
¸
´
´
´
=
´
¸
´
´
23.(a)
a
a
a
a
a
2
8
10
8
2
5
=
-
=
´
-
´
(b)
x
x
x
x
x
x
x
12
6
6
6
2
12
2
3
2
12
=
+
=
+
=
´
+
¸
(c)
2
7
2
3
2
2
2
3
2
4
8
3
2
2
4
8
+
-
=
+
-
-
-
=
+
-
-
-
=
-
+
-
¸
-
p
p
p
p
p
p
p
p
p
p
(d)
5
7
5
3
8
2
3
5
2
4
2
-
=
-
-
+
=
-
-
´
+
c
c
c
c
c
c
c
24.(a)
ab
b
a
b
b
a
3
)
3
(
)
4
(
-
=
-
´
=
-
´
(b)
n
m
n
m
n
m
n
n
n
n
m
m
-
=
-
=
-
¸
=
-
-
-
¸
+
2
2
)
2
(
)
2
(
)
(
)
(
(c)
2
6
)
2
(
3
)
(
3
a
a
a
a
a
a
=
´
=
+
´
(d)
3
3
3
)
2
(
)
2
(
k
k
k
k
k
k
k
k
k
=
´
´
=
-
´
+
´
25.(a)There are x + y animals in the farm.
(b)Total number of legs that chickens have
x
x
2
2
=
´
=
Total number of legs that cows have
y
y
4
4
=
´
=
∴Total number of legs that all animals have
y
x
4
2
+
=
26.Cost of x cash vouchers
x
x
100
$
100
$
=
´
=
Amount David owes
)
80
100
$(
-
=
x
27.Total number of cookies Kenny, Steven and Daniel have
x
x
3
3
=
´
=
∴Original number of cookies in the box
1
3
+
=
x
28.Capacity of milk in all the cups
mL
)
200
(
-
=
V
∴Capacity of a glass cup
mL
4
200
-
=
V
29.Total amount of $10 coins
m
m
20
$
)
2
(
10
$
=
´
=
Total amount of $5 coins
n
n
15
$
)
3
(
5
$
=
´
=
∴Total amount that Nancy has
)
15
20
$(
n
m
+
=
30.Perimeter of the triangle
cm
9
cm
)
4
3
2
(
x
x
x
x
=
+
+
=
31.(a)Price of a bottle of coffee
C
C
3
$
3
$
=
´
=
(b)Difference between their prices
C
C
C
2
$
)
3
$(
=
-
=
32.(a)Weight of Martin
kg
18)
(6
kg
18)
3
2
(
+
=
+
´
=
x
x
(b)The weight of Martin heavier than Linda
kg
18)
(4
kg
]
2
18)
6
[(
+
=
-
+
=
x
x
x
Exercise 2B (p. 2.19)
Level 1
1.(a)yes
(b)no
(c)no
(d)yes
2.When
4
=
v
, EQ
100
)
4
(
25
25
=
=
=
v
d
3.When
3
=
T
, EQ
21
24
3
)
3
(
8
3
8
3
-
=
-
=
-
=
-
=
T
R
4.When
11
=
f
, EQ
118
3
121
3
)
11
(
3
2
2
=
-
=
-
=
-
=
f
e
5.When
6
=
c
,
7
5
35
5
1
)
6
(
6
5
1
6
=
=
-
=
-
=
c
H
6.When
5
=
w
,
5
6
5
1
5
1
=
+
=
+
=
w
w
Q
7.When
9
=
a
,
36
2
)
8
(
9
2
)
1
9
(
9
2
)
1
(
=
=
-
=
-
=
a
a
M
8.When
8
=
a
and
12
=
t
,
78
18
96
18
)
12
)(
8
(
18
=
-
=
-
=
-
=
at
v
9.When
11
=
b
and
2
=
n
,
81
9
)
2
11
(
)
(
2
2
2
=
=
-
=
-
=
n
b
A
10.When
4
=
I
and
250
=
R
,
4000
)
250
)(
16
(
)
250
(
)
4
(
2
2
=
=
=
=
R
I
P
11.When
14
=
r
,
88
)
14
(
7
22
2
2
=
÷
ø
ö
ç
è
æ
=
=
r
C
p
12.When
200
=
n
,
2500
500
3000
500
)
200
(
15
500
15
=
-
=
-
=
-
=
n
P
13.When
45
=
n
,
2550
2250
300
)
45
(
50
300
50
300
=
+
=
+
=
+
=
n
C
Level 2
14.When
3
=
a
and
2
1
=
r
,
6
2
1
3
2
1
1
3
1
=
=
-
=
-
=
r
a
S
15.When
23
=
p
and
9
=
q
,
7
16
14
32
9
23
9
23
=
=
-
+
=
-
+
=
q
p
q
p
M
16.When
2
-
=
u
,
10
=
a
and
1
=
t
,
8
10
2
)
1
)(
10
(
2
=
+
-
=
+
-
=
+
=
at
u
v
17.When
6
=
c
,
1
-
=
d
and
13
=
e
,
2
1
12
6
13
1
6
=
=
+
-
=
+
=
e
d
c
P
18.When
8
=
n
,
3
=
a
and
17
=
l
,
80
2
)
20
(
8
2
)
17
3
(
8
2
)
(
=
=
+
=
+
=
l
a
n
S
19.When
1
=
x
,
2
-
=
y
and
3
=
z
,
6
5
3
1
2
1
1
3
1
2
1
1
1
1
1
1
=
+
-
=
+
-
+
=
+
+
=
z
y
x
T
20.When
3
2
=
a
,
2
1
=
b
and
4
1
=
c
,
8
1
4
1
6
1
3
4
1
2
1
2
1
3
2
3
)
)(
(
3
=
÷
ø
ö
ç
è
æ
÷
ø
ö
ç
è
æ
=
÷
ø
ö
ç
è
æ
-
÷
ø
ö
ç
è
æ
-
=
-
-
=
c
b
b
a
m
21.(a)When
1000
=
P
,
05
.
0
=
r
and
10
=
t
,
500
)
10
)(
05
.
0
)(
1000
(
=
=
=
Prt
I
(b)When
5000
=
P
,
25
1
=
r
and
4
=
t
,
800
)
4
(
25
1
)
5000
(
=
÷
ø
ö
ç
è
æ
=
=
Prt
I
22.(a)When
2
-
=
a
,
5
=
b
and
3
-
=
c
,
1
24
25
)
3
)(
2
(
4
5
4
2
2
=
-
=
-
-
-
=
-
=
ac
b
D
(b)When
0
=
a
,
2
-
=
b
and
7
=
c
,
4
)
7
)(
0
(
4
)
2
(
4
2
2
=
-
-
=
-
=
ac
b
D
23.(a)In August,
20
=
v
,
53
5
48
5
)
20
(
4
.
2
5
4
.
2
=
+
=
+
=
+
=
v
C
∴The monthly water charge paid by the Chan family in August is $53.
(b)In September,
31
=
v
,
4
.
79
5
4
.
74
5
)
31
(
4
.
2
5
4
.
2
=
+
=
+
=
+
=
v
C
∴The monthly water charge paid by the Chan family in September is $79.4.
(c)In October,
28
=
v
,
2
.
72
5
2
.
67
5
)
28
(
4
.
2
5
4
.
2
=
+
=
+
=
+
=
v
C
∴The monthly water charge paid by the Chan family in October is $72.2.
24.When
100
=
x
and
150
=
y
,
000
60
000
42
000
18
)
150
(
280
)
100
(
180
280
180
=
+
=
+
=
+
=
y
x
I
∴The total income is $60 000.
25.(a)
a
P
3
=
(b)When
8
=
a
,
24
)
8
(
3
3
=
=
=
a
P
∴The perimeter of the triangle is 24 cm.
26.(a)(i)
)
(
2
y
x
P
+
=
(ii)
xh
A
=
(b)When
4
=
x
, y = 5 and h = 3,
18
)
9
(
2
)
5
4
(
2
)
(
2
=
=
+
=
+
=
y
x
P
12
)
3
)(
4
(
=
=
=
xh
A
∴The perimeter and the area of the parallelogram are 18 cm and 12 cm2 respectively.
27.(a)
64
8
2
2
2
-
=
-
=
x
x
A
(b)When
10
=
x
,
36
64
100
64
)
10
(
64
2
2
=
-
=
-
=
-
=
x
A
∴The area of the frame is 36 cm2.
28.For team A, m = 8 and n = 7,
290
70
160
200
)
7
(
10
)
8
(
20
200
10
20
200
=
-
+
=
-
+
=
-
+
=
n
m
S
∴Team A got a score of 290.
For team B, m = 6 and n = 2,
300
20
120
200
)
2
(
10
)
6
(
20
200
10
20
200
=
-
+
=
-
+
=
-
+
=
n
m
S
∴Team B got a score of 300.
∴Team B got a higher score.
29.(a)
y
x
C
4
5
+
=
(b)When x = 12 and y = 8,
92
32
60
)
8
(
4
)
12
(
5
4
5
=
+
=
+
=
+
=
y
x
C
∴The cost of the oranges and apples is $92.
As Nancy gets $100, she has enough money to buy the fruits.
30.(a)(i)When n = 50,
1275
)
51
(
2
50
)
1
50
(
2
50
)
1
(
2
=
=
+
=
+
=
n
n
S
(ii)When n = 100,
5050
)
101
(
2
100
)
1
100
(
2
100
)
1
(
2
=
=
+
=
+
=
n
n
S
(b)
3775
1275
5050
)
50
...
2
1
(
)
100
...
2
1
(
100
...
53
52
51
=
-
=
+
+
+
-
+
+
+
=
+
+
+
+
Exercise 2C (p. 2.32)
Level 1
1.The 5th term = 12 + 3 = 15
The 6th term = 15 + 3 = 18
∴The next two terms of the sequence are 15 and 18.
2.The 5th term = −1 − 2 = −3
The 6th term = −3 − 2 = −5
∴The next two terms of the sequence are −3 and −5.
3.The 5th term
5
1
1
4
1
=
+
=
The 6th term
6
1
1
5
1
=
+
=
∴The next two terms of the sequence are
5
1
and
6
1
.
4.The 5th term
000
10
10
1000
=
´
=
The 6th term
000
100
10
000
10
=
´
=
∴The next two terms of the sequence are 10 000 and
100 000.
5.
6
)
1
(
6
1
=
=
T
12
)
2
(
6
2
=
=
T
18
)
3
(
6
3
=
=
T
24
)
4
(
6
4
=
=
T
∴The first 4 terms of the sequence are 6, 12, 18 and 24.
6.
1
)
1
(
2
1
1
-
=
-
=
T
3
)
2
(
2
1
2
-
=
-
=
T
5
)
3
(
2
1
3
-
=
-
=
T
7
)
4
(
2
1
4
-
=
-
=
T
∴The first 4 terms of the sequence are –1, –3, –5 and
–7.
7.
3
1
2
1
1
1
=
+
=
T
4
1
2
2
1
2
=
+
=
T
5
1
2
3
1
3
=
+
=
T
6
1
2
4
1
4
=
+
=
T
∴The first 4 terms of the sequence are
3
1
,
4
1
,
5
1
and
6
1
.
8.
1
)
1
(
3
1
=
=
T
8
)
2
(
3
2
=
=
T
27
)
3
(
3
3
=
=
T
64
)
4
(
3
4
=
=
T
∴The first 4 terms of the sequence are 1, 8, 27 and 64.
9.
6
3
)
3
(
2
3
=
-
=
T
30
6
)
6
(
2
6
=
-
=
T
10.T1
4
1
5
+
=
=
T2
4
2
6
+
=
=
T3
4
3
7
+
=
=
T4
4
4
8
+
=
=
∴Tn
4
+
=
n
11.T1
)
1
(
10
10
=
=
T2
)
2
(
10
20
=
=
T3
)
3
(
10
30
=
=
T4
)
4
(
10
40
=
=
∴Tn
n
10
=
12.T1
)
1
(
2
1
2
1
=
=
T2
)
2
(
2
1
4
1
=
=
T3
)
3
(
2
1
6
1
=
=
T4
)
4
(
2
1
8
1
=
=
∴Tn
n
2
1
=
Level 2
13.The 5th term =
3
2
6
=
The 6th term =
2
3
∴The next two terms of the sequence are 3 and
2
3
.
14.The 5th term =
25
1
5
1
2
=
The 6th term =
36
1
6
1
2
=
∴The next two terms of the sequence are
25
1
and
36
1
.
15.The 5th term =
26
9
17
=
+
The 6th term =
37
11
26
=
+
∴The next two terms of the sequence are 26 and 37.
16.The 5th term =
160
)
2
)(
80
(
=
-
-
The 6th term =
320
)
2
)(
160
(
-
=
-
∴The next two terms of the sequence are 160 and
–320.
17.(a)
1
2
)
1
1
)(
1
(
1
=
+
=
T
3
2
)
1
2
)(
2
(
2
=
+
=
T
6
2
)
1
3
)(
3
(
3
=
+
=
T
10
2
)
1
4
)(
4
(
4
=
+
=
T
∴The first 4 terms of the sequence are 1, 3, 6 and
10.
(b)It is a sequence of triangular numbers.
18.(a)It is an arithmetic sequence.
(b)
46
8
38
=
+
=
a
54
8
46
=
+
=
b
19.(a)It is a geometric sequence.
(b)
48
2
24
=
´
=
x
96
2
48
=
´
=
y
20.(a)T1
)
1
1
(
4
8
+
=
=
T2
)
1
2
(
4
12
+
=
=
T3
)
1
3
(
4
16
+
=
=
T4
)
1
4
(
4
20
+
=
=
∴Tn
)
1
(
4
+
=
n
(or
4
4
+
n
)
(b)The 14th term of the sequence
60
)
1
14
(
4
=
+
=
21.(a)T1
)
1
(
2
1
-
=
=
T2
)
2
(
2
0
-
=
=
T3
)
3
(
2
1
-
=
-
=
T4
)
4
(
2
2
-
=
-
=
∴Tn
n
-
=
2
(b)The 10th term of the sequence
8
10
2
-
=
-
=
22.Denote the number of dots in the nth figure by Tn.
(a)∵T1
1
)
1
(
2
1
-
=
=
T2
1
)
2
(
2
3
-
=
=
T3
1
)
3
(
2
5
-
=
=
T4
1
)
4
(
2
7
-
=
=
∴Tn
1
2
-
=
n
∴The number of dots in the nth figure is 2n – 1.
(b)By substituting n = 28 into
1
2
-
=
n
T
n
, we have
55
1
)
28
(
2
28
=
-
=
T
∴The number of dots in the 28th figure is 55.
23.(a)(i)T1
1
=
T2
5
=
T3
9
=
T4
13
=
(ii)T1
3
)
1
(
4
1
-
=
=
T2
3
)
2
(
4
5
-
=
=
T3
3
)
3
(
4
9
-
=
=
T4
3
)
4
(
4
13
-
=
=
∴Tn
3
4
-
=
n
(b)By substituting n = 12 into
3
4
-
=
n
T
n
, we have
45
3
)
12
(
4
12
=
-
=
T
∴The number of dots in the 12th figure is 45.
(c)Let the kth figure be the figure consists of 77 dots,
then
20
80
4
77
3
4
77
=
=
=
-
=
k
k
k
T
k
∴The 20th figure consists of 77 dots.
24.(a)
(b)
Figure
1st
2nd
3rd
4th
5th
Number of dots
2
6
12
20
30
(c)Denote the number of dots in the nth figure be Tn.
∵T1 = 2 = 1 ( 2 = 1(1 + 1)
T2 = 6 = 2 ( 3 = 2(2 + 1)
T3 = 12 = 3 ( 4 = 3(3 + 1)
T4 = 20 = 4 ( 5 = 4(4 + 1)
∴Tn = n(n + 1)
∴The number of dots in the nth figure is n(n + 1).
Check Yourself (p. 2.37)
1.
)
(
c
b
a
+
ab
c
-
(a)a times the sum of b and c.
c
ab
+
c
b
a
-
+
(b)Subtract the product of
a and b from c.
(c)Multiply a by b and then
add c to the result.
(d)Divide the square of a by
the product of b and c.
(e)Add b to a and then subtract
c from the sum.
2.(a)
a
a
a
a
4
2
3
3
=
-
+
(b)
2
)
6
3
(
6
3
xy
y
x
y
x
=
´
´
¸
=
´
¸
(c)
q
p
q
p
p
p
p
p
q
p
3
35
)
(
)
7
5
(
7
5
=
´
´
´
´
´
=
´
´
´
´
´
3.Age of Andrew’s father now
x
x
4
4
=
´
=
Age of Andrew’s father after 5 years
5
4
+
=
x
4.Amount of money David has left
)
3
450
$(
)
3
50
500
$(
x
x
-
=
-
-
=
5.When F = 50,
10
)
18
(
9
5
)
32
50
(
9
5
)
32
(
9
5
=
=
-
=
-
=
F
C
6.When b = 10 and h = 8,
40
)
80
(
2
1
)
8
)(
10
(
2
1
2
1
=
=
=
=
bh
A
∴The area of the triangle is 40 cm2.
7.
16
6
10
sequence
the
of
term
3rd
=
+
=
=
a
46
6
40
sequence
the
of
8th term
=
+
=
=
b
8.The 5th term of the sequence
13
)
5
(
4
7
-
=
-
=
9.Number of dots in the 1st figure
)
1
(
2
2
=
=
Number of dots in the 2nd figure
)
2
(
2
4
=
=
Number of dots in the 3rd figure
)
3
(
2
6
=
=
Number of dots in the 4th figure
)
4
(
2
8
=
=
∴Number of dots required to form the nth figure
n
2
=
10.The 1st term of the sequence
1
)
1
(
3
2
-
=
=
The 2nd term of the sequence
1
)
2
(
3
5
-
=
=
The 3rd term of the sequence
1
)
3
(
3
8
-
=
=
The 4th term of the sequence
1
)
4
(
3
11
-
=
=
∴The nth term of the sequence
1
3
-
=
n
Revision Exercise 2 (p. 2.38)
Level 1
1.(a)The required expression is 2a + 5.
(b)The required expression is
3
cd
.
(c)The required expression is
6
q
p
.
(d)The required expression is
2
x
z
y
-
+
.
2.(a)Add the product of 5 and y to the product of 4 and x.
(or any other reasonable answers)
(b)Divide t by the sum of s and t. (or any other
reasonable answers)
(c)Subtract b from a and then multiply the difference by 3. (or any other reasonable answers)
(d)Multiply the square of p by q and then divide the product by r. (or any other reasonable answers)
3.(a)
5
3
8
3
3
+
=
+
´
+
-
a
a
(b)
b
a
b
a
8
6
4
2
2
3
-
=
´
-
´
(c)
q
q
4
5
6
12
2
5
+
=
¸
´
+
4.(a)
y
y
y
y
2
3
2
=
+
-
(b)
c
c
c
c
c
3
2
2
8
10
8
2
10
+
=
+
+
-
=
-
+
+
(c)
b
b
b
b
b
4
3
)
1
(
3
=
+
=
-
´
-
5.(a)
2
2
)
(
)]
2
(
)
1
[(
)
2
(
)
1
(
)
2
(
)
(
a
a
a
a
a
a
a
=
´
´
-
´
-
=
´
-
´
´
-
=
-
´
-
(b)
3
24
)
(
)
2
4
3
(
2
4
3
2
4
3
k
k
k
k
k
k
k
k
k
k
=
´
´
´
´
´
=
´
´
´
´
´
=
´
´
´
(c)
z
y
z
y
y
y
z
y
y
y
z
y
y
y
2
)
(
)
4
2
(
4
2
4
2
3
=
¸
´
´
´
¸
=
¸
¸
´
´
´
=
¸
´
´
6.Price of an egg
12
$
x
=
7.Distance between the two towns
km
2
km
2
y
y
=
´
=
8.Price for x pens
x
x
8
$
8
$
=
´
=
The change Chris should get back from the shopkeeper
)
8
500
$(
x
-
=
9.(a)Perimeter of the rectangle
cm
2
cm
]
1
)
1
[(
2
y
y
=
+
-
=
(b)Area of the rectangle
2
2
cm
)
1
(
cm
]
1
)
1
[(
-
=
´
-
=
y
y
10.When
10
-
=
a
and
6
=
t
,
180
)
6
)(
10
(
2
1
2
1
2
2
-
=
-
=
=
at
s
11.When
8
=
m
and
15
=
n
,
56
120
64
)
15
)(
8
(
2
)
1
15
)(
8
(
2
)
1
(
-
=
-
=
-
+
=
-
+
=
mn
n
m
L
12.When
7
=
r
,
154
)
7
(
7
22
2
2
=
=
=
r
A
p
∴The area of the circle is 154 cm2.
13.When
1
=
n
,
320
1
240
80
240
80
=
+
=
+
=
n
C
When
2
=
n
,
200
2
240
80
240
80
=
+
=
+
=
n
C
When
3
=
n
,
160
3
240
80
240
80
=
+
=
+
=
n
C
When
4
=
n
,
140
4
240
80
240
80
=
+
=
+
=
n
C
Total number of toy cars produced
1
2
3
4
Unit cost of a toy car ($)
320
200
160
140
14.The polygon shown has 8 sides, so
8
=
n
.
When
8
=
n
,
20
2
)
3
8
(
8
2
)
3
(
=
-
=
-
=
n
n
N
∴The polygon shown has 20 diagonals.
15.The 5th term
9
=
The 6th term
10
-
=
∴The next two terms of the sequence are 9 and −10.
16.The 5th term
15
1
3
12
1
-
=
+
-
=
The 6th term
18
1
3
15
1
-
=
+
-
=
∴The next two terms of the sequence are
15
1
-
and
18
1
-
.
17.
2
)
1
(
5
3
1
-
=
-
=
T
7
)
2
(
5
3
2
-
=
-
=
T
12
)
3
(
5
3
3
-
=
-
=
T
17
)
4
(
5
3
4
-
=
-
=
T
∴The first 4 terms of the sequence are –2, –7, –12
and –17.
18.The 10th term of the sequence
96
4
)
10
(
2
=
-
=
19.
3
)
2
1
)(
1
(
1
=
+
=
T
8
)
2
2
)(
2
(
2
=
+
=
T
∴
11
8
3
2
1
=
+
=
+
T
T
20.(a)
11
1
12
1
+
=
=
T
11
2
13
2
+
=
=
T
11
3
14
3
+
=
=
T
11
4
15
4
+
=
=
T
∴
11
+
=
n
T
n
(b)
1
1
5
5
=
=
T
2
2
5
25
=
=
T
3
3
5
125
=
=
T
4
4
5
625
=
=
T
∴
n
n
T
5
=
(c)
2
)
1
(
3
1
1
-
=
=
T
2
)
2
(
3
4
2
-
=
=
T
2
)
3
(
3
7
3
-
=
=
T
2
)
4
(
3
10
4
-
=
=
T
∴
2
3
-
=
n
T
n
21.Sticks used to form the 1st figure
5
=
Sticks used to form the 2nd figure
8
3
5
=
+
=
Sticks used to form the 3rd figure
11
3
8
=
+
=
Sticks used to form the 4th figure
14
3
11
=
+
=
∴Sticks used to form the 5th figure
17
3
14
=
+
=
Sticks used to form the 6th figure
20
3
17
=
+
=
22.(a)
Figure
1st
2nd
3rd
4th
Number of dots
3
6
9
12
(b)The number of dots in the 1st figure
1
3
3
´
=
=
The number of dots in the 2nd figure
2
3
6
´
=
=
The number of dots in the 3rd figure
3
3
9
´
=
=
The number of dots in the 4th figure
4
3
12
´
=
=
∴The number of dots in the nth figure
n
3
=
∴The number of dots in the 8th figure
24
)
8
(
3
=
=
Level 2
23.(a)
2
6
)
3
)(
2
(
)
)(
(
a
a
a
a
a
a
a
a
=
=
+
+
+
(b)
w
w
w
w
w
w
w
w
4
5
)
(
5
2
)
2
(
5
2
)
4
2
(
=
+
-
=
+
¸
-
=
+
¸
-
(c)
x
x
x
x
x
x
x
8
6
2
)
6
(
2
)
2
(
3
3
6
=
+
=
-
-
=
-
´
-
¸
24.(a)
6
8
14
8
14
8
3
3
14
=
-
+
-
=
-
-
+
=
-
-
¸
+
a
a
a
a
a
a
(b)
3
3
3
6
4
3
6
2
2
-
=
-
+
-
=
-
+
´
-
y
y
y
y
y
y
y
(c)
b
a
b
b
a
a
b
a
b
a
b
a
b
a
+
-
=
+
-
-
=
+
-
-
=
+
´
-
-
3
3
2
8
5
3
8
2
5
3
4
2
2
5
25.Price for 4 packs of rubber bands
)
50
$(
x
-
=
∴Price for a pack of rubber band
÷
ø
ö
ç
è
æ
-
=
4
50
$
x
26.(a)Number of $5 coins
x
x
2
2
=
´
=
Number of $1 coins = 2x – 3
Total number of coins in the purse
3
5
)
3
2
(
2
-
=
-
+
+
=
x
x
x
x
(b)Amount of $2 coins
x
x
2
$
2
$
=
´
=
Amount of $5 coins
x
x
10
$
2
5
$
=
´
=
Amount of $1 coins
)
3
2
$(
)
3
2
(
1
$
-
=
-
´
=
x
x
Total value of the coins in the purse
)
3
14
$(
)]
3
2
(
10
2
$[
-
=
-
+
+
=
x
x
x
x
27.When
2
-
=
a
,
3
-
=
b
and
4
-
=
c
,
77
48
16
9
4
)
4
)(
3
)(
2
(
2
)
4
(
)
3
(
)
2
(
2
2
2
2
2
2
2
=
+
+
+
=
-
-
-
-
-
+
-
+
-
=
-
+
+
=
abc
c
b
a
S
28.(a)The amount that Jennifer spends on entertainment
3
$
y
=
Total amount that Jennifer spends
÷
ø
ö
ç
è
æ
+
=
÷
ø
ö
ç
è
æ
+
+
=
3
4
$
3
$
y
x
y
y
x
Amount that Jennifer saves
÷
ø
ö
ç
è
æ
-
-
=
ú
û
ù
ê
ë
é
÷
ø
ö
ç
è
æ
+
-
=
3
4
1000
$
3
4
1000
$
y
x
y
x
∴The formula for the amount ($S) that Jennifer saves in a month is
3
4
1000
y
x
S
-
-
=
.
(b)When
200
=
x
and
300
=
y
,
400
3
)
300
(
4
200
1000
3
4
1000
=
-
-
=
-
-
=
y
x
S
∴Jennifer saves $400 in a month.
29.(a)Marks given
x
x
2
2
=
´
=
Marks deducted
y
y
=
´
=
1
The marks scored by the student
y
x
z
y
x
-
=
´
+
-
=
2
0
2
∴The formula for calculating the mark (M) scored
by the student is
y
x
M
-
=
2
.
(b)∵Gigi answered all the questions without leaving
any questions blank and answered 4 questions
correctly.
∴Gigi answered 4 questions correctly and 4 questions wrongly.
i.e.
4
=
x
and
4
=
y
4
4
)
4
(
2
2
=
-
=
-
=
y
x
M
∴Gigi got 4 marks.
∵Leslie left 2 questions blank and answered
4 questions correctly.
∴Leslie answered 4 questions correctly and
2 questions wrongly.
i.e.
4
=
x
and
2
=
y
6
2
)
4
(
2
2
=
-
=
-
=
y
x
M
∴Leslie got 6 marks.
∴Leslie got a higher score in the quiz.
30.The 5th term
14
)
18
22
(
18
=
-
-
=
The 6th term
10
)
18
22
(
14
=
-
-
=
31.The 13th term
233
144
89
=
+
=
The 14th term
377
233
144
=
+
=
32.(a)The 1st term
)
1
(
8
8
=
=
The 2nd term
)
2
(
8
16
=
=
The 3rd term
)
3
(
8
24
=
=
The 4th term
)
4
(
8
32
=
=
∴The general term
n
8
=
(b)(i)Note that each term in the sequence 4, 8, 12,
16, … is half the corresponding term of the
sequence 8, 16, 24, 32, ….
∴The general term of the sequence is 4n.
(ii)Note that each term in the sequence 6, 10, 14,
18, … is 2 more than the corresponding term of
the sequence 4, 8, 12, 16, ….
∴The general term of the sequence is 4n + 2.
33.(a)(i)The 1st term
2
1
1
=
=
The 2nd term
2
2
4
=
=
The 3rd term
2
3
9
=
=
The 4th term
2
4
16
=
=
∴The general term
2
n
=
(ii)The 1st term
)
1
(
3
3
=
=
The 2nd term
)
2
(
3
6
=
=
The 3rd term
)
3
(
3
9
=
=
The 4th term
)
4
(
3
12
=
=
∴The general term
n
3
=
(b)(i)Note that each term in the sequence 4, 10, 18, 28, … is the sum of the corresponding term of the sequence 1, 4, 9, 16, … and the sequence 3,
6, 9, 12, ….
∴The general term of the sequence is
n
n
3
2
+
.
(ii)The 8th term of the sequence
88
)
8
(
3
)
8
(
2
=
+
=
34.(a)
)
1
(
2
1
)
1
(
2
2
1
1
-
=
=
T
)
2
(
2
1
)
2
(
2
4
3
2
-
=
=
T
)
3
(
2
1
)
3
(
2
6
5
3
-
=
=
T
)
4
(
2
1
)
4
(
2
8
7
4
-
=
=
T
∴
n
n
T
n
2
1
2
-
=
(b)∵2n – 1 is smaller than 2n,
i.e.the numerator is always smaller than the
denominator.
∴Tn < 1
∴All the terms are smaller than 1.
∴Frankie’s claim is agreed.
35.(a)The 1st term
)
1
(
20
500
520
+
=
=
The 2nd term
)
2
(
20
500
540
+
=
=
The 3rd term
)
3
(
20
500
560
+
=
=
∴The general term of the sequence
n
20
500
+
=
(b)
n
y
20
500
+
=
(c)When
100
=
n
,
2500
)
100
(
20
500
20
500
=
+
=
+
=
n
y
∴The total cost is $2500.
36.(a)Number of sticks used to form the 1st figure
3
)
1
(
2
5
+
=
=
Number of sticks used to form the 2nd figure
3
)
2
(
2
7
+
=
=
Number of sticks used to form the 3rd figure
3
)
3
(
2
9
+
=
=
∴Number of sticks used to form the nth figure
3
2
+
=
n
(b)Number of sticks used to form the 18th figure
39
3
)
18
(
2
=
+
=
37.(a)(i)
4
1
=
T
7
2
=
T
10
3
=
T
13
4
=
T
(ii)
1
)
1
(
3
4
1
+
=
=
T
1
)
2
(
3
7
2
+
=
=
T
1
)
3
(
3
10
3
+
=
=
T
∴
1
3
+
=
n
T
n
(b)By substituting n = 8 into
1
3
+
=
n
T
n
, we have
25
1
)
8
(
3
8
=
+
=
T
∴The number of dots in the 8th figure is 25.
38.(a)
(b)(i)
Figure
1st
2nd
3rd
4th
Number of squares
5
9
13
17
(ii)The 1st term = 5 = 1 + 4(1)
The 2nd term = 9 = 1 + 4(2)
The 3rd term = 13 = 1 + 4(3)
The 4th term = 17 = 1 + 4(4)
∴Number of squares in the nth figure
n
4
1
+
=
(c)(i)
Figure
1st
2nd
3rd
4th
Length of a side of each smallest square (cm)
2
1
4
1
8
1
16
1
Area of each smallest square (cm2)
4
1
16
1
64
1
256
1
(ii)In the sequence
4
1
,
16
1
,
64
1
,
256
1
, (, the division of any term (except the first term) by its preceding term is
4
1
.
∴The areas of the smallest squares in the figures form a geometric sequence.
39.(a)3 + 6 + 9 + ( + 120
2460
2
41
120
2
)
1
40
(
40
3
)
40
...
3
2
1
(
3
=
´
=
ú
û
ù
ê
ë
é
+
=
+
+
+
+
=
(b)101 + 102 + 103 + ( + 200
050
15
5050
000
10
2
)
1
100
(
100
000
10
)
100
...
3
2
1
(
100
100
)
100
100
(
...
)
3
100
(
)
2
100
(
)
1
100
(
=
+
=
+
+
=
+
+
+
+
+
´
=
+
+
+
+
+
+
+
+
=
Multiple Choice Questions (p. 2.43)
1.Answer: A
I means
2
a
b
-
.
II means
2
b
a
-
.
III means
2
ab
.
∴Only II can represent the given algebraic expression.
∴The answer is A.
2.Answer: D
b
b
b
b
b
3
2
5
2
4
5
=
-
=
¸
-
3.Answer: B
Time taken for the car to travel from town X to town Y
hours
3
v
=
4.Answer: C
When
7
=
a
,
5
=
b
and
10
=
h
,
350
)
10
)(
5
)(
7
(
=
=
=
abh
V
∴The volume of the box of tea is 350 mL.
5.Answer: C
Total number of participants
40
4
36
=
+
=
When
40
=
n
,
3000
)
40
(
50
1000
50
1000
=
+
=
+
=
n
C
∴The cost of organizing a school picnic is $3000.
6.Answer: D
I.In the sequence, each term is the square of the corresponding term of the sequence 1, 2, 3, 4, ….
∴It is the sequence of square numbers.
II.In the sequence, each term is larger than its following term by 3.
∴It is an arithmetic sequence.
III.In the sequence, the division of any term (except the first term) by its preceding term is 3.
∴It is a geometric sequence.
7.Answer: D
34
21
13
=
+
=
x
144
89
55
=
+
=
y
8.Answer: A
13
5
26
10
1
5
)
5
(
2
2
5
=
=
+
=
T
9.Answer: C
)
1
(
7
25
18
1
-
=
=
T
)
2
(
7
25
11
2
-
=
=
T
)
3
(
7
25
4
3
-
=
=
T
∴
n
T
n
7
25
-
=
10.Answer: D
Number of dot used to form the 1st figure
2
)
1
(
3
1
-
=
=
Number of dots used to form the 2nd figure
2
)
2
(
3
4
-
=
=
Number of dots used to form the 3rd figure
2
)
3
(
3
7
-
=
=
∴Number of dots used to form the nth figure
2
3
-
=
n
∴Number of dots used to form the 6th figure
16
2
)
6
(
3
=
-
=
Exam Corner
Exam-type Questions (p. 2.45)
1.(a)By observing the pattern of the given sequence, we
find that
1
1
2
2
=
=
T
2
2
2
4
=
=
T
3
3
2
8
=
=
T
4
4
2
16
=
=
T
M
n
n
T
2
=
∴2n dots are used to form the nth figure.
(b)By substituting n = 6 into
n
n
T
2
=
, we have
64
2
6
6
=
=
T
∴64 dots are used to form the 6th figure.
2.When
7
=
r
,
462
)
7
(
7
22
3
3
2
2
=
÷
ø
ö
ç
è
æ
=
=
r
A
p
∴The total surface area of the hemisphere is 462 cm2.
3.
15
5
10
=
+
=
a
28
7
21
=
+
=
b
4.The 8th term of the sequence
60
6
)
1
8
)(
8
(
5
=
+
=
5.(a)
1
1
1
1
2
1
+
=
=
T
2
1
2
2
3
2
+
=
=
T
3
1
3
3
4
3
+
=
=
T
4
1
4
4
5
4
+
=
=
T
M
n
n
T
n
1
+
=
∴The general term of the sequence is
n
n
1
+
.
(b)The product of the first 20 terms of the sequence
21
20
21
19
20
...
4
5
3
4
2
3
1
2
=
´
´
´
´
´
´
=
6.Answer: C
3
)
(
)]
1
(
)
1
(
)
1
[(
)
1
(
)
1
(
)
1
(
)
)(
)(
(
x
x
x
x
x
x
x
x
x
x
-
=
´
´
´
-
´
-
´
-
=
´
-
´
´
-
´
´
-
=
-
-
-
7.Answer: B
y
y
y
y
y
y
3
-
=
-
-
-
-
� EMBED Equation.3 ���
� EMBED Equation.3 ���
� EMBED Equation.3 ���
� EMBED Equation.3 ���
42
43