O'level 2011 Amath Paper 1 & 2 suggested answers

Paper 1
1)     x < 1
2)     a = 12, b = 3
3)     4 or -4 (rejected)
4)     2.42 or 3.86
5)     k = 0.75
6)     x = 4, y = 5.5

7i)    a = 0.5                                    (ii) coeff. = -0.5
8i)    A(-2,0)   B(-0.5,3)    C(1,0)   (ii) x = 2/3 or -4
9)     a = 5/6, b = 1 1/6
10i)  sq root 18 - sq root 3              (ii) 32 - sq root 24
11i)  B(0,13)   D(8, -3)                   (ii) 120 units
12i)   40.9m                                    (ii) 3.00m/s                                      (iii) 0.0499m/s2
13i)  a = 5, b = 3                             (ii) h = sq root 34sin( deta + 59.0)   (iii) 31.0    (iv) -14.0 (rej) or 76.0

Paper 2
1i)   -12 < k < 4                                  (ii) m = 10 or -6
2i)   Smallest b = 2                              (ii) a = 3             (iii) refer to image
3a)  a = -7, b = 2                                (ii) x = -2, (2+sq root 2)/2 or (2-sq root 2)/2
4ii)  a = -3.6, b = 4.2
5a)  x = 729                                        (b) a = 5, n = 3, k = 320
6i) l = (800+phi r^2)/(4r)                                    (iii) r = 7.72    (iv) P is a minimum
7)   refer to image
8i)  1/x + 2/(2x+1) - 3/(2x+1)^2         (ii) ln x(2x+1) + 3/[2(2x+1)] + c
9i)  QR = 2 units                                 (ii) Area = [9 + (3sq root3)/2] units^2
10i) (sq root 2)/2                                (ii) (sq root 6)/2               (iv) 15  (v) [(sq root 3) + 2]/4
11i) C(4,5), rad. = 5units                    (ii) (x-4)^2 + (y-5)^2 = 25
11iv) Since D is lowest pt., it is vert. below C. Hence, D is (4,0). Since y-coord. of D is zero, D lies on the x-axis. 
11v) (19,0)

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