Algebraic Manipulations Worksheet With Answer Key

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1 − 55
Algebraic
x −
4
11. Factorise completely
81
16
.

Manipulation
3
x
+
12. Express
as a single fraction in its
+ −
2
x
1
1
x
2
x
simplest form.

Questions
+
+ and hence deduce the
2
13. Factorise
12
x
11
x
2
x − .
2
factors of 121102.
1. Factorise
9
4


+
14. Factorise 6
ac bd
2
ad
3
bc
.
2. Express as a single fraction in its simplest form

4
5
+
.
− −
2
x
2 6
x x
2
c p

=
15. Make p the subject of the equation
x
.
+
2
q p
3. Factorise completely

2
2
(a)
6
p
7
pq
20
q
16. Express as a single fraction in its simplest form:
2
+
(b)
2
a
3
ab
2
ac
3
bc
.
5
x
1
+
.

2
+
2
2
x x
35 7
x x

4. Expand and simplify
(
) (
)
1
2
2
17. Factorise completely
+
+
3
a
2
3
a
2
4
a
9
a
.
a
4
2
(a)
n
9
n

+
2
(b)
3
p
18
p
15

+ −
2
5. Factorise completely
10
x
3
x
.

+
b
2
=
18. Given that
a
, express b in terms of a
p
c
1
+
=
6. Given
2(
p q
)
(5
p
2 )
q
, find the
.
2
q
and c .


19. Express the following as a single fraction, in its
7. Factorise completely:
simplest form,
− −
+
2
(a)
3
x
x
9
x
3
2
k
k
2
+
+
2
(a)
(b)
9
c
30
c
25 4
d
2
k
1

1
2
(b)
= −
2
2
x
3 3
x
8. Given that
b a
a
x
, express x in terms of

a and b .

2
2
+
20. Factorise fully
a
ac
9
b
3
bc
.

9. Express as a fraction in its lowest term.
3 2
x
x
.
+
+
2
2
+
21. Factorise
5
x
8
x
3
and hence, find all the
3
x
x
5
x
6

factors of 583.

3
y x
y
=
1
10. Given that
, find the value of
.
=
+
2
2
+
2
22. Given that
v
u
2
as
, make u the subject of
4
y
5
x
x
the fomula.


1.6
algebraic manipulation

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