Waec Gce 2015 General Mathematics Obj And Theory Answers

Math obj 1CBADBDDBDA 11DCDBACDCCC 21CACBCDCBCA 31ADBABACDB 41DbBBDBCAAD. 10a) YX/XZ=XM/MZ W/10=8/15 15W=10*8 W=5.33cm 10bi) q^2=p^2 r^2-2prcos tita q^2=20^2 5-2*20*15 c0s 90 q^2=400 225-0 q^2=625 q=sqroot625 q=25km 10bii) p/sinP=q/sinQ=r/sinR 25/sin90=15/sinR sinR=15*1/25 sinR=0.6 R=sin^-1(0.6) R=36.86degrees The bearing of p from R =90 90 90 alpha alpha=45-36.86 =90 90 90 8.14 =278.14 =278degrees The bearing of p from R=278degrees ================================== 9a) CBA=180-(128-x) sum of angle on a straight line CBA=52 x ADC=180-(128-x) =52 x Also BCD=180-x(angle on a straight line) DCQ=180-(180-x) DCQ=180-180 x DCQ=x x 52 x 76=180 2x=180-52-76 2x/2=52/2 x=26degrees ===================================== 1a) 1/2log 25/4- 2log10 4/5 log10 320/125 Log(25/4)^1/2-log(4/5)^2 log10 320/125 Log10 sqrt25/4-log16/25 log10 320/125 Log10 5/2-log10 16/25 log10 320/125 Log10 5/2 log10 320/125-log10 16/25 Log10 [5/2*320/125÷16/25] Log10 [5/2*320/125*25/16] Log10 10=1 1b) % income= 20% Grant per land =GHC€15.00 Total population from 2003-2007 =1.2*1.2*1.2*1.2*3000=6220.8 Total grant=population*grant per head =6220.8*15 =ghc€93312 Total grant=GHC€93312 —————————- 2a) 1/x 1/x 3=1/2 L.C.M=x(x 3) X 3 x/x(x 3)=1/2 2(2x 3)/x(x 3)=1/2 2(2x 3)=x(x 3) 4x 6=x^2 3x X^2 3x=4x 6 X^2 3x-4x-6=0 X^2-x-6=0 (X^2-3x) (2x-6)=0 X(x-3) 2(x-3)=0 (X 2)(x-3)=0 X=-2 or x=3 2b) Let d bag of rice be X Let d bag of beans be Y X Y=17—>(I) 2250x 2400y=39600—>(2) From eqtn (I) X=17-y Using elimination method to eliminate Y 2250x 2250y=38250—>(3) 2250x 2400y=39600—>(4) Eqtn 4- eqtn 3 2400x-2250x = 39600-38250 150x=1350 X=1350/150 X=9 D trader bought 9bags of beans —————————- (3) =Draw The Diagram= Area of path –> 2[1/2 (x 2)] 2(x 1) = 17 x 2 2x = 17 3x 2 = 17 3x = 17 – 2 3x = 15 x = 15/3 x = 5 (a) Perimeter of garden = 4x = 4 x 5 = 20m (3b) =Draw The Diagram=Area Covered By Both Garden And path = (x 1) (x 2) = (5 1) (5 2) = 6×7 = 42m^2 —————————- (4a) Given: Sinx = 3/5 i.e Using pythogoras triple 3,4,5 CosX TanX/SinX =4/5 3/4 ÷ 3/5 = 16 15/20 ÷ 3/5 = 31/20 ÷ 3/5 = 31/20 x 5/3 = 31/12 (4b) =Draw The Diagram=Reflex P’Q’T R’Q’T P’Q’R = 360 (sum at a point) 200 32 P’Q’R = 360 232 P’Q’R = 360 P’Q’R = 360 – 232 P’Q’R = 128° From the Diagram Q’R’U = P’Q’R = 128° (alternate angles) X = Q’R’U S’R’U X = 128° 180 X = 308° —————————- 5a) =Draw The Diagram= 1. | 2. | 3. | 4. | 5. | 6. | —————————————— 1|1,1|1,2 |1,3 |1,4 |1,5 |1,6 | ——————————————- 2|2,1|2,2 |2,3 |2,4 |2,5|2,6 | ——————————————– 3|3,1|3,2 |3,3 |3,4 |3,5|3,6 | ——————————————— 4|4,1|4,2 |4,3 |4,4 |4,5|4,6 | ——————————————— 5|5,1|5,2 |5,3 |5,4 |5,5|5,6 | ———————————————– 6|6,1|6,2 |6,3 |6,4 |6,5|6,6 | ———————————————— B) pr(sum of outcome is 8 ) = 4/36 = 1/9 Bii) pr(product of outcom <10) = 30/36 = 5/6 Biii) pr(outcom contain atleast a 3) = 24/36 = 4/6 = 2/3 —————————- (6a) 2 X (37)x = 75x 2 X (3x 7)10 = (7x 5)10 2 (3x 7) = 7x 5 6x 14 = 7x 5 14 – 5 = 7x – 6x 9 = x :- x = 9 (6b) Let The Number Of boys be X Number Of girls in class = x 5 GIVEN: x 5/ 2 = 5/4 5(x 2) = 4(x 5) 5x 10 = 4x 20 5x – 4x = 20 – 10 x = 10 (i)Numbers of girsl in class = x 5 = 10 5 = 15 (ii)Total number of students = x x 5 = 10 10 5 = 25 (iii)Probability of selecting a boy as class prefect = 10/24 = 2/5 —————————- 7a) |PQ|^2 = |PB|^2 |BQ|^2 |PQ|^2 = (5 – x )^2 X^2 |PQ|^2 = 25 – 10x x^2 x^2 [note ^ means Raise to power] |PQ|^2 = 2x^2 – 10x 25 NB: PQ = QR (side of a square) Area of PQRS = PQ x QR = PQ x PQ = PQ^2 Area of PQRS = (2x^2 – 10x 25)m square GIVEN: 2x^2 – 10 25 = 3/5 of 25 = 2x^2 – 10x 10 = 0 = x^2 – 5 5 = 0 Using General Formular mthod X = -(-5) ± Square Root (-5)^2 – 4(1)(5)/ (2 x 1) X = 5 ± Square Root 25 – 20/ 2 X = 5 ± Square Root 5 / 2 X = 5 Square Root 5 / 2 OR 5 – Square Root 5 / 2 X = 3.62 or 1.68 7b ) L a / n – 1 = d ———— (I) 2s = n (a 1) —————- (2) From eq (1) L a = d (n – 1) ————– (3) Put eq (3 into 2) 2s = nd (n-1) 2s = d (n^2 – n) S = d ( n^2 – n ) / 2 or S = dn(n-1)/2 ————————— 8a) By using pythagoras r^2 = (r – 8 )^2 32^2 r^2 = r^2 – 16r 64 1024 16r = 64 1024 r = 1088/16 r = 68 r=68cm ===========good luck!==================

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