1
1.
(a)
Write down the value of 16 4 .
(1)
3
(b)
Simplify (16 x12 ) 4 .
(2)
(Total 3 marks)
2.
Simplify
(a)
(3 √7)2
(1)
(b)
(8 + √5)(2 – √5)
(3)
(Total 4 marks)
1
3.
Simplify
5 3
2 3
,
giving your answer in the form a+b√3, where a and b are integers.
(Total 4 marks)
4.
Find the set of values of x for which
(a)
3(x – 2) < 8 – 2x
(2)
(b)
(2x – 7)(1 + x) < 0
(3)
2
(c)
both 3(x – 2) < 8 – 2x and (2x – 7)(1 + x) < 0
(1)
(Total 6 marks)
5.
(a)
Show that x2 + 6x + 11 can be written as
(x + p)2 + q
where p and q are integers to be found.
(2)
(b)
In the space below, sketch the curve with equation y = x2 + 6x + 11, showing clearly any
intersections with the coordinate axes.
(2)
3
(c)
Find the value of the discriminant of x2 + 6x + 11
(2)
(Total 6 marks)
6.
The equation kx2  4 x  (5  k )  0 , where k is a constant, has 2 different real solutions for x.
(a)
Show that k satisfies
k 2  5k  4  0.
(3)
(b)
Hence find the set of possible values of k.
(4)
(Total 7 marks)
4
7.
(a)
By eliminating y from the equations
y = x – 4,
2x2 – xy = 8,
show that
x2 + 4x – 8 = 0.
(2)
(b)
Hence, or otherwise, solve the simultaneous equations
y = x – 4,
2x2 – xy = 8,
giving your answers in the form a ± b√3, where a and b are integers.
(5)
(Total 7 marks)
5
8.
(Total 7 marks)
6
9.
(Total 8 marks)
7
10.
(Total 8 marks)
Total : 60 Marks
8