1.	(a)	(i)	Expand and simplify (a – b)2

(ii)	Show that	 = a2 + b2
(iii)	Hence, or otherwise, find the value of 102.52 + 97.52

(Total 5 marks)

2.	Simplify fully
(i)	m4 × m5
……………………………..
(ii)	p6 ÷ p2
………………………………
(iii)	5x3y × 2xy8
………………………………
(iv)	
……………………………..
(Total 5 marks)

3.	(a)	Expand and simplify
(x + y)2
.............................................................
(2)
(b)	Hence or otherwise find the value of
3.472 + 2 × 3.47 × 1.53 + 1.532
.............................................................
(2)
(Total 4 marks)

4.	Simplify fully
(a)	2(3x + 4) – 3(4x – 5)
.................................................
(2)
(b)	(2xy3)5
.................................................
(2)

(c)	
.................................................
(3)
(Total 7 marks)

5.	(a)	Factorise
9x2 – 6x + 1
……………………………
(2)
(b)	Simplify

……………………………
(3)
(Total 5 marks)

6.	(a)	Factorise x2 – 3x
..........................
(2)
(b)	Simplify k5 ÷ k2
..........................
(1)
(c)	Expand and simplify
(i)	4(x + 5) + 3(x – 7)
..........................
(ii)	(x + 3y)(x + 2y)
.......................................
(4)
(d)	Factorise (p + q)2+ 5(p + q)
......................................
(1)
(Total 8 marks)

7.	(a)	Simplify	k5 ÷ k2
.........................
(1)

(b)	Expand and simplify
(i)	4(x + 5) + 3(x – 7)
.........................
(ii)	(x + 3y)(x + 2y)
.........................
(4)
(c)	Factorise	(p + q)2 + 5(p + q)
.........................
(1)
(d)	Simplify	(m–4)–2
.........................
(1)
(e)	Simplify 2t2 × 3r3t4
.........................
(2)
(Total 9 marks)

8.	(a)	Solve	 = 4 + x
x = ....................
(3)
(b)	Simplify fully	
........................................
(3)
(Total 6 marks)

9.	Factorise
x2 + 7x + 6
..........................
(Total 2 marks)

10.	(a)	Simplify a3 × a4
……………………
(1)
(b)	Simplify 3x2y × 5xy3
……………………
(2)
(c)	Simplify 
……………………
(1)
(d)	Factorise    a2 – 9b2
……………………
(2)
(Total 6 marks)

11.	Simplify fully
(a)	(3xy2)4
…………………….
(2)
(b)	
…………………….
(3)
(Total 5 marks)

12.	Simplify fully 
.....................................
(Total 3 marks)

13.	(a)	Factorise	x2 + 6x + 8
………………………
(2)
(b)	Solve	x2 + 6x + 8 = 0
x =………………………
or x =………………………
(1)
(Total 3 marks)

14.	(a)	Simplify
(i)	x4 × x5
.....................................
(ii)	
.....................................
(iii)	3s2 t3 × 4s4t2
.....................................
(iv)	(q3)4 
.....................................
(5)
(b)	Expand	3(2g – 1)
.....................................
(1)

(c)	Expand	2d(d + 3)
.....................................
(2)
(d)	Expand and simplify	(x + 2)(x + 3)
.....................................
(2)
(Total 10 marks)

15.	(a)	Simplify fully	(3x2y4)3
.....................................
(2)
(b)	Expand and simplify	(2x + 5)(3x – 2)
.....................................
(2)
(c)	Simplify fully	
.....................................
(2)
(Total 6 marks)

16.	Factorise          x2 - 2x - 15

………………………………..
(Total 2 marks)

17.	(a)	Factorise      x2 - 2x - 15
…………………………
(2)

(b)	Hence, or otherwise, solve
	x2 - 2x - 15 = 0
x =  …………      or      x =  ………..
(1)
(Total 3 marks)

18.	Simplify	

…………………….
(Total 3 marks)

19.	Simplify fully
(i)	
……………………………..
(ii)	
………………………………

(iii)	
………………………………
(iv)	

……………………………..
(Total 4 marks) 

20.	(a)	Simplify
	12y3 ÷ 3y5
……………………………
(2)
(b)	Simplify
	2w3x2 × 3w4x
……………………………
(2)
(Total 4 marks)

21.	(a)	Expand and simplify
(x – 6)(x + 4)
……………………………
(2)
(b)	Factorise completely
12x2 – 18xy

……………………………
(2)
(Total 4 marks)

22.	(a)	Simplify fully

……………………………
(Total 3 marks)

23.	Simplify

.................................
(Total 1 mark)

24.	Simplify fully    5x3y4 × 7xy2
……………………………
(Total 2 marks)

25.	(a)	Factorise	x2 + x
……………..
(1)
(b)	Factorise	y2 - 2y - 35
…………………………….
(2)
(Total 3 marks)

26.	Simplify	
………..……
(Total 2 marks)

27.	Simplify

……………………
(Total 2 marks)

28.	(a)	Simplify	k5 ÷ k2

..........................
(1)
(b)	Expand and simplify 4(x + 5) + 3(x – 7)

..........................
(2)
(Total 3 marks)

29.	(a)	Expand and simplify	(3x + 2)(4x + 1)
............................................
(2)
(b)	Factorise completely	3x2 + 6xy

............................
(2)
(Total 4 marks)

30.	(a)	Factorise completely	2(x – 5)2 + 3(x – 5)

................................
(2)

(b)	Simplify	

................................
(1)
(Total 3 marks)

31.	Simplify fully	(3xy2)4

………………….
(Total 2 marks)

32.	(a)	Simplify	

.......................
(1)
(b)	Simplify	(w4)3
.......................
(1)
(c)	Simplify	5e3f × e2f 2
.......................
(2)
(Total 4 marks)

33.	(a)	Simplify	x4 ÷ x9
.....................................
(1)
(b)	Simplify	3w5y2 × 4w3y4
.....................................
(2)
(Total 3 marks)

34.	Simplify fully	

.....................................
(Total 2 marks)

35.	(i)	3s2t3 × 4s4t2
…………………….
(ii)	(q3)4
…………………….
(Total 2 marks)

36.	(a)	Simplify
(i)	x4 × x5
…………………….
(ii)	
…………………….
(iii)	3s2t3 × 4s4t2
…………………….
(iv)	(q3)4
…………………….
(5)
(b)	Expand 2d(d + 3)
…………………….
(2)
(Total 7 marks)

37.	Expand and simplify	(2x + 5)(3x – 2)

…………………….
(Total 2 marks)