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