Maths Obj 1EAACBAECBE 11CDABECBCCA 21AEDCBACEDE 31ADADCCDABD 41BCEBDCEABE 51DBAECBECBE NECO GCE MATHEMATICS THEORY ANSWERS =================== 1a (6y²)³ / 2 y^6 = 6³y^6 / 24y^6 =6³*y^6/24*y^6 = 216/24 =9 (2a) w*3√D W=k 3√D 10=k*3√27 10/3 =k*3/3 k=10/3 W=10/3*3√64 = 10/3*4*40/3=13 1/3 ================== 2b) X/2 y/6 = 2/3 L.C.M = 6 Rx y = 4 -----(1) X/3 - y/2 = 5/3 L.C.M = 6 2x - 3y = 10 -----(2) From eq (1) 3x y = 4 Y= 4 - 3x ------(3) Sub for y in eq (2) 2x - 3(4-3x) = 10 2x - 12 9x = 10 11x = 22 X=2 Sub for x in eq (3) Y = 4-3(1) Y = 4-3- Y = 1 ================= 1b Log10(2m² 5m-2)=1 2m² 5m-2=10 2m² 5m-2-10=0 2m² 5m-12=0 Using m=-b -√b²-4ac/2a a=2 b=5 c=-12 m=-5 -√5²-4*2*(-12)/2*2 m=-5 -√2 96/4 m=-5 -√98/4 m=-5 -9.9/4 m=-5 9.9/4 or m=-5-9.9/4 M=1.225 or -3.725 4a)V=2/3Πr 1527.4=2/3*22/7*r 1527.4=44r/21 32075.4=44r r=32075.4/44 r=728.98 =729cm 4b 3^3y 1 = 81^-y 3^3y= 3^-4y 3y 1=-4y 1=-4y-3y 1=-7y Y= - 1/7 5a) Red=4 Green = 6 Black= 10 Total=20 1)p(Red) = 4/20 = 1/5 2)p(green)= 6/20 = 3/10 3) p (black)= 10/20= 1/2 5b) ( X-1)(X-8) 12=0 X²-8x-X 8 12=0 X²-9x 20=0 X= -b √b²-4ai X= 9 /-√-9²-4×1×20÷ 2×1 X=9 /-√81-80÷2 X=9 /-√1÷2 X= 9 1/2 or 9-1/2 X= 10/2 or 8/2 X= 5 or 4 ============ (8a) 4a^2 b*3ab^- 2/4a^3*(3ab) =12 a^4 b^1/12a^4 b =6^-1/b^1 =b^-1-1 =b^2 6^-2 or 1/b^2 8b) Let the pocket money be x 2x/5 =stations X/4=school levies X/6= food X-(24x/5 x/4 x/6)=55 X-(24x 15x 10x)/60 =55 X-49x/60 =55 60*x-60-49x/60 = 55*60 60x-49x=#3,300 11x/11=3300/11 X=#300 The pocket money =#300 9a) solve using cosine rule m^2 = 70^2+40^2 - (2 x 70 x 40 x cos135) m^2 = 4900 + 1600 - (5600 x cos135) m^2 = 6500 - (5600 x cos135) m√6500-(5600 x cos135) m = √6500+5578.2 m = √12078.16 m = 109.9006 m == 109.9 9b) lets find tita (θ) using sine rule 70/sinθ = 109.9/sin135 70sin135/109.9 = 109.9sinθ/109.9 sinθ = 70 x sin135/109.9 sinθ = 0.45038 θ = sin^-1(0.45038) θ = 26.76935 θ == 27 :- Bearing of k from R 180° + 85° + 27° = 292° ============== 10a) 1/27^(x-2)=9^(2-x) 3^3(x-2)-1=3^2(2-x) 3-1(x-2)=4-2x 2x-4=4-2x 2x+2x=4+4 4x=8 X=8/4 X=2 10b 5x+y/x+5y= 3/1 5x+y= 3(x+5y) 5x+y=3x+15y 5x-3x=15y-y 2x=14y X/y= 14/2 =7, y/x= 1/7 X2-y2/4xy Divide all through by my (X²- y²/) ÷(4xy/xy) Xy- xy (X/y- y/x) ÷4 (7- 1/7)÷4 ~~~49-1/7×1/4 48/7× 1/4= 24/7 = 4 ============ 11a) A=(1 7,3 2) and B=(2 5,4 6) i)A^-1=1/det(2 -7,-3 1) Det= 2 -21=-19 A^-1=1/-19(2 -7,-3 1) -1/19(2 -7,-3 1) ii)B^T =(2 -4,5 6) iii)AB =(1 7,3 2) (2 5,4 6) (2 -28,6-8, 5+46,15+12) (-26,-2, 51,27,) 11b) 7x^2 + 12x + 5 = 0 7x^2/7 + 12x/7 = -5/7 X^2 + 12x/7 = -5/7 X^2 12x/7 + (6/7)^2 - -5/7 + (6/7)2 (X+6/7)^2= -5/7 + 36/49 (X+6/7)^2 = -35+36/49 (X +6/7)^2 = 1/49 (X +6/7) = + and - √1/19 X+ 6/7 = + and - 1/7 X = -6/7 + and - 1/7 X = -6+1/7 or -6-1/7 X= -5/7 or -7/7 X = -5/7 or -1 ============ Created at 2017-02-12 05:19:39