Chapter review
C
The diagram represents a right-angled triangle ABC.
7
__
__
( 7 � 2)
AB (
7 2 ) cm AC (
7 2 ) cm.
√
√
Work out, leaving any appropriate answers in surd form:
A
B
( 7 � 2)
the area of triangle ABC
a
the length of BC.
b
Chapter review
For non-zero values of a
a
0
1
For any number n
1
__
a
n
a
n
Standard form is used to represent very large (or very small) numbers.
A number is in standard form when it is in the form a 10
where 1 a 10 and n is an integer.
n
It is often easier to multiply and divide very large or very small numbers, or estimate a calculation, if the
numbers are written in standard form.
To input numbers in standard form into your calculator, use the �10 or EXP key
·
To enter 4.5 10
7
press the keys 4
5 �10
7
Indices can be fractions. In general,
1
__
__
n
a
a
n
√
A number written exactly using square roots is called a surd.
These two laws can be used to simplify surds.
__
__
m
__
__
___
√
___
m
__
√
m
n
mn
√
√
√
__
n
n
√
Simplifi ed surds should never have a surd in the denominator.
To rationalise the denominator of a fraction means to get rid of any surds in the denominator.
__
__
a
__
√
b
To rationalise the denominator of
you multiply the fraction by
, this ensures that the fi nal fraction has an
__
__
√
√
b
b
integer as the denominator.
Review exercise
B
Work out the values of
1
a
4
0
b
4
c
2
0
d
2
1
3
Work out the values of
2
(
)
1
0
__
a
3
0
b
(3)
0
c
3
d
1
3
Work out the values of
3
(
)
1
1
2
1
___
__
___
a
b
c
2 4
d
1
3
3
4
1
1
Write as ordinary numbers
4
3 10
1.67 10
2 10
3.8 10
a
4
b
3
c
d
4
5
Write in standard form
5
a
5000
b
64 400
c
0.07
d
0.000 607
623