1a) Tabulate x- 1,2,3,4 1- 1,2,3,4 2- 2_, 4, 0_ ,2_ 3- 3, 0_, 3, 0_ 4- 4_, 2_, 0_, 4 1b) I = PRT/100, p=N15000 R=10% and I=3years A = P I where I = 15000x10x3/100=N4500 A=4500 15000 =N19500 ================ 2a) using sine rule b/sin20 = 6/sin30 bsin30 = 6sin120 b 6sin120/sin30 b = 6x0.2511/0.4540 b = 5.7063/0.4540 b = 12.57 ≠ 12.6cm 2bi) the diagram is euivalent triangles. where |AX|/|BC| = |BY|/|AC| = |XY|/|YC| XY = 9, BY = 7 YC = 18-7=11 9/11 = 7/|AC| 9|AC| = 77 |AC| = 77/9 |AC| = 8cm 2bii) XY/AB = BY/AC 9/|AB| = 7/8.6 |AB| = 9x8.6/7 |AB| = 11cm ================= 3) let the son age be x man=5x son=x 4yrs ago;the man age = 5x - 4 the son age = x - 4 the product of their ages (5x - 4)(x - 4) =448 ================= 7a) 3^2n 1 - 4(3^n 1) 9=0 3^2-3 - 4(3^n -3) 9=0 (3^n)^2-3 - 4(3^n -3) 9=0 let 3^n = p p^2 -3 - 4(p-3) 9=0 3p^2/3 - 12p/3 9/3 = 0 p^2 - 4p 3 = 0 p^2 - 3p - p 3 = 0 p^2p(p-3) - 1(p-3) = 0 (p-1)(p-3) = 0 p-1 = 0 or p-3 = 0 p = 1 or 3 Recall 3^n = p when p=1 3^n = 3^0 n = 0 when p = 3 3^n = 3^1 n = 1 7b) log(x^2 4) = 2 logx - log^20 log(x^2 4) = log^100 = log^x - log^20 (x^2 4) = log(xx) x^2 4 = 5x x^2-5x 4 = 0 x^2-4x - x 4 = 0 x(x-4) - 1(x-4) = 0 (x-1)(x-4) = 0 x-1 = 0 or x-4 = 0 x = 1 or 4