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igcse-algebra-manipulation

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IGCSE Mathematics – Extended
Topic:
Algebra- Manipulation
Worksheet
Student Name:
Date:
Expanding Brackets
1.
(a)
Expand the bracket and simplify the expression
7x + 5 – 3(x – 4).
Answer (a) ……….…………………….……
[2]
(b)
Factorise 5x2 – 7x.
Answer (b) ……….…………………….……
[1]
2.
(x + 4) cm
4x cm
R
Q
(x + 12) cm
(a)
(i)
(x + 2) cm
NOT TO SCALE
Write down an expression for the area of rectangle R.
Answer (a) (i) …….…………………. cm2
[1]
(ii)
Show that the total area of rectangles R and Q is 5x2 + 30x + 24
square centimetres.
[1]
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(b)
The total area of rectangles R and Q is 64 cm2.
Calculate the value of x correct to 1 decimal place.
Answer (b) x = …………………………….
[4]
3.
Expand the brackets and simplify
3x2 – x(x – 3y).
Answer …………….…………..
[2]
4.
Expand the brackets and simplify
4x2 – x(x – 2y).
Answer ………………..……….
[2]
5.
Expand the brackets and simplify 5x – 6(3x – 2).
Answer …..….……….…………
[2]
6.
Expand the brackets and simplify 3x – 5(4x – 2).
Answer …………………………
[2]
7.
(a)
Expand and simplify
5(3c – 4d) – 8c.
Answer (a) …….……………………
[2]
(b)
Factorise
pq – q2.
Answer (b) ………….………………
[1]
Mathelaureate / IGCSE / Revision Worksheet / DJ
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8.
(a)
Expand and simplify 4(5c – 3d) – 7c.
Answer (a) …………………………
[2]
(b)
Factorise m2 – mn.
Answer (b) …………………………
[1]
Factorization
9.
Factorise 3xy – 2x.
Answer …………………….……………
[1]
10. Factorise completely
(a)
7ac + 14a,
Answer (a) ………….……….……………
[1]
(b)
12ax3 + 18xa3.
Answer (b) ………….……….……………
[2]
11. Factorise completely 2x2 – 6xy.
Answer ……………..……………………
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[2]
12. Factorise
(a)
4x2 – 9,
Answer (a) ………………………………
[1]
(b)
4x2 – 9x,
Answer (b) ……..…..……………………
[1]
(c)
4x2 – 9x + 2.
Answer (c) ……..…..……………………
[2]
13. Factorise completely
2a2b – 6a.
Answer …….………….…………………
[2]
14. Factorise completely xy2 – x2y.
Answer ……………………..
[2]
15. Factorise completely
4xy – 2x.
Answer …………………………
[2]
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16. Factorise completely
2pq – 4q.
Answer ….………………………
[2]
17. Factorise completely
6x – 9x2y.
Answer ……….….………..……
[2]
18. (i)
Factorise x2 – x – 20.
[2]
(ii)
Solve the equation x2 – x – 20 = 0.
[1]
19. y = m2 – 4n2.
(i)
Factorise m2 – 4n2.
[1]
(ii)
Find the value of y when m = 4.4 and n = 2.8.
[1]
(iii) m = 2x + 3 and n = x – 1.
Find y in terms of x, in its simplest form.
[2]
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(iv) Make n the subject of the formula y = m2 – 4n2.
[3]
20. (i)
m4 – 16n4 can be written as (m2 – kn2)(m2 + kn2).
Write down the value of k.
[1]
(ii)
Factorise completely m4n – 16n5.
[2]
21. (a)
Factorise
ax2 + bx2.
Answer (a) ……….….…………
[1]
(b)
Make x the subject of the formula
ax2 + bx2 – d2 = p2
Answer (b) x = …………………
[2]
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Simplification
22. Simplify the following expressions.
(a)
9r – 4s – 6r + s
Answer (a) ……….…………….…………
[1]
(b)
q4 ÷ q3
Answer (b) ……….…………….…………
[1]
(c)
p6 × p–2
Answer (c) ……….…………….…………
[1]
23. Simplify
(a)
p 2 × p 3,
Answer (a) ……………..…………………
[1]
(b)
q3 ÷ q–4,
Answer (b) ………..………………………
[1]
(c)
(r2)3.
Answer (c) ………………………..………
[1]
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24. Simplify the expression 5p – 2q – (p + q).
Answer ………………………………
[2]
25. Simplify
3x2y × x4y2.
Answer …….……...…..…………………
[2]
26. Simplify
x 5x 5x
.
3 9 18
Answer ……….….…….………
[2]
27. Simplify
x 7x 7x
.
3 9 18
Answer ……….….…………….
[2]
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