1.
Expand and simplify 3 – 2 3 2
........................................
(Total 2 marks)
1
2. (a) Rationalise the denominator of
3
....................................
(1)
(b) Expand (2 3 )(1 3 )
Give your answer in the form a b 3 where a and b are integers.
....................................
(2)
(Total 3 marks)
3. Expand and simplify
(2 + 3 )(7 – 3)
Give your answer in the form a + b 3 , where a and b are integers.
....................................
(Total 3 marks)
4.
Diagram NOT accurately drawn
ABC is a right angled triangle.
D is the point on AB such that AD = 3DB.
AC = 2DB and angle A = 90.
k
Show that sin C = , where k is an integer.
20
Write down the value of k.
k = ………….
(Total 2 marks)
18 10
5. Write in the form p + q 2 , where p and q are integers.
2
p = ..….…….
q = ………….
(Total 2 marks)
6. Work out
(5 3 )(5 – 3 )
22
Give your answer in its simplest form.
.................................................
(Total 3 marks)
21
7. (i) Rationalise the denominator of and simplify your answer.
7
…………………………
(ii)
Expand 5 2 3 5 2 3
Express your answer as simply as possible.
…………………………
(4)
(Total 4 marks)
1
8. (a) Find the value of 16 2
........................
(1)
(b) Given that 40 k 10 , find the value of k.
........................
(1)
Diagram NOT
( 5 + 20) accurately drawn
8 5
A large rectangular piece of card is ( 5 20 ) cm long and 8 cm wide.
A small rectangle 2 cm long and 5 cm wide is cut out of the piece of card.
(c) Express the area of the card that is left as a percentage of the area of the large
rectangle.
.................................%
(4)
(Total 6 marks)
6
9. (a) Express in the form a b , where a and b are positive integers.
2
...................................
(2)
The diagram shows a right-angled isosceles triangle.
6
The length of each of its equal sides is cm.
2
Diagram NOT
accurately drawn
6 cm
2
6 cm
2
(b) Find the area of the triangle.
Give your answer as an integer.
............................ cm2
(2)
(Total 4 marks)
10. (a) Rationalise
1
7
.....................................
(2)
(b) (i) Expand and simplify
(3 + 15)2
Give your answer in the form n + m5, where n and m are integers.
.....................................
(ii)
A C
Diagram NOT
accurately drawn
k 3 +
All measurements on the triangle are in centimetres.
ABC is a right-angled triangle.
k is a positive integer.
Find the value of k.
k = .....................................
(5)
(Total 7 marks)
1
11. (a) Write down the value of 8 3
.....................................
(1)
8 8 be written in the form 8k
(b) Find the value of k.
k = .....................................
(1)
8 8 can also be expressed in the form m 2 where m is a positive integer.
(c) Express 8 8 in the form m 2
.....................................
(2)
1
(d) Rationalise the denominator of
8 8
2
Give your answer in the form where p is a positive integer.
p
.....................................
(2)
(Total 6 marks)
