January 2007 - C2: Answers

Q 1(a): f’’(x) = 6x + 6
   (b): 15.75
 
Q 2(a): 1 - 10x + 40x² - 80x³
   (b): show
 
Q 3   : (x-1)² + (y-5)² = 20
 
Q 4   : 1.39
 
Q 5(a): f(-2) = 0
   (b): (x+3)(x+2)(x-1)
   (c): x = -3, x = -2, x = 1
 
Q 6   : π/6, 5π/6
 
Q 7   : 3.5 units²
 
Q 8(a): 70
   (b): d²C/dv² = 0.008 => +ve => MIN
   (c): £40
 
Q 9(a): 2π/3
   (b): show
   (c): 9√3 m²
   (d): 22.1 m²
   (e): 24.6 m
 
Q10(a): Proof
   (b): 204,600
   (c): 5/4
   (d): -1 < r < 1   or   |r| < 1