Hi,
Paper 1 answers, for reference:
Q1 0 < x < 1
Q2 a = 12, b = 3
Q3 4
Q4 2.42, 3.86
Q5 3/4
Q6 x = 4, y = 11/2 or x = 5, y = 7/2
Q7(i) 1/2
(ii) -3/2
Q8(i) A (-2, 0), B (-1/2, 3), C (1, 0)
(ii) x = 2/3 or -4
Q9 a = 5/6, b = 7/6
Q10(i) a = 18, b = 3
(ii) c = 32, d = 24
Q11(i) B (0, 13), D (8, -3)
(ii) 120 sq units
Q12(i) 40.9 m
(ii) 3.00 m/s
(iii) 0.0499 m/s^2
Q13(i) a = 5, b
= 3
(ii) R = sqrt(34), alpha = 59.0 degrees
(iii) 31.0 degrees
(iv) 76.0 degrees
Paper 2 answers, for reference:
Q1(i) -12 < k < 4
(ii) -6 or 10
Q2(i) 2
(ii) 3
Q3(i) a = -7, b = 2
(ii) c = d = 2
Q4(ii) a = -18/5, b =
21/5
Q5(a) 729
(b) n = 3, a = 5, k = 320
Q6(i) l = (200/r) + (pi r)/4
(iii) r = 7.72, minimum
Q7(i) Consider Pythagoras' theorem or RHS.
(ii) Start from LHS, apply result from (i).
(iii) Apply Tangent-Secant theorem.
Q8(i) (1/x) + 2/(2x + 1) - 3/(2x +
1)^2
(ii) ln |x| + ln |2x + 1) +(3/2)/(2x + 1) + c
Q9(i) 2 sqrt(3) units
(ii) 27/2 sq units
Q10(i) 1/sqrt(2)
(ii) sqrt(3/2)
(iv) 15 degrees
(v) (1/2)(1 + sqrt(3)/2)
Q11(i) C (4, 5), radius = 5 units
(ii) (x - 4)^2 + (y - 5)^2 = 25
(iv) Because D is 5 units directly below C.
(v) (19, 0)
Thanks.
Cheers,
Wen Shih