Did you know? The diagrams show three scales. On each scale there are different objects
6
I C
V D
X M
etc. L
= =
= =
= =
= 1
100 5
500 10
1 000 50
, They used these numerals to make up numbers as follows:
I VI
II VII
III VIII
IV IX
V X
etc. =
= =
= =
= =
= =
= 1
6 2
7 3
8 4
9 5
10, So, for example, XCIX is 99. What is the value of XLVI?
A B
C D
E 42
44 46
64 66
ANSWER: C L = 50
XL = 40 i.e. 10 from 50 = 40 VI = 6 i.e. 1 added to 5 = 6
XLVI = 46
12. Did you know?
• An equilateral triangle is a regular polygon with 3 equal sides, and
each interior angle is 60
o
. •
A square is a regular polygon with 4 equal sides, and each interior angle is 90
o
.
If a regular polygon has n sides, then the formula to find the size of each interior angle is
n n
− × 2
180
D
. If each interior angle of a regular polygon measures 150°, then the number of sides n is
A B
C D
E 6
9 10
11 12
ANSWER: E
7
interior so if
then
Hence: ∠ =
− × ∠ =
= − ×
= − × =
− −
= −
= =
∴ = ,
n n
n n
n n
n n
n n
n n
2 180
150 150
2 180
150 2
180 180
360 180
150 360
180 150
360 30
360 12
D D
D D
D D
D D
D D
D D
D D
D D
.
13.
A solid right prism has a square base. The height is twice the length of the side of the base. The
surface area of this prism is 160 cm
2
. If 1 cm³ of the prism has a mass of 250 grams,
then the mass of the prism in kilograms is
A B
C D
E 28
32 36
40 44
ANSWER: B Surface Area = 2 bases + 4 sides.
Let the side of the base be s cm. The height of the prism will then be 2s cm.
So the Surface Area = 2
2
s s
s s
s s
+ ×
= +
= 4
2 2
8 10
2 2
2
But the Surface Area =
cm 160
10 160
16 4
2 2
∴ =
∴ =
∴ =
s s
s
8
The volume = length
breadth height
cm 1 cm has a mass of 250 g
1 4
kg The prism has a mass of 128
1 4
= 32 kg
3 3
s s
s s
× × ×
× =
= × =
= ∴
× 2
2 2
4 128
3 3
9