100% VERIFIED 2016/2017 WAEC MATHEMATICS ESSAY AND OBJ ANSWERS

1-10: BACBCCCBCD ___________________ 11-20: CBBACACBBC ____________________ 21-30: BBCCDACDCD ____________________ 31-40: ACAABADAAA ____________________ 41-50: DAABADCBAD

9a) x 62 63 64 65 66 67 68 tally 1 iiiii iiiii iiiii ii iiii iiii iiii iiiii iiiii iiiii i ii freq 1 5 12 14 10 6 2 total = 50 fx 62 315 768 910 660 402 136 tot = 3253 x-x- -3.06 -2.06 -1.06 0.06 0.94 1.94 2.94 (x-x-) 9.3636 4.2436 1.1236 0.0036 0.8836 3.7636 8.6436 f (x-x)2 9.3636 21.218 13.4832 0.0504 8.836 22.5816 17.2872 tot = 92.82 9bi) mean = EFX/EF = 3253/50 =65.06 9bii) Standard deviation = Square root of EF(x-x)2/Ef = Square root of 92.82/50 = square root of 1.8564 = 1.36 ================================ 7a) x-2/4 :x+2/2x Cross multiply 2x(x-2)=4(x+2) Opening the bracket 2x^2-4x = 4x+8 Collect like terms together 2x^2-4x-4x-8=0 2x^2-8x-8=0 Solving with completing the square method 2x^2-8x=8 Divide through with the coefficient of x^2 2x^2/2-8x/2=8/2 X^2-4x=4 Half of coefficient of x (-4 x 1/2)^2 = (-2)^2 X^2-4x+(-2)^2=4+(-2)^2 X^2-4x+(-2)^2=4+4 (x-2)^2=8 X-2:square root 8 X=2 + or - squar root 8 X=2+ square root 8 or x=2- square root 8 X=2+2.828=4.828 X=2-2.828= -0.828 X=4:83 or - 0.83. 9a) x 62 63 64 65 66 67 68 tally 1 iiiii iiiii iiiii ii iiii iiii iiii iiiii iiiii iiiii i ii freq 1 5 12 14 10 6 2 total = 50 fx 62 315 768 910 660 402 136 tot = 3253 x-x- -3.06 -2.06 -1.06 0.06 0.94 1.94 2.94 (x-x-) 9.3636 4.2436 1.1236 0.0036 0.8836 3.7636 8.6436 f (x-x)2 9.3636 21.218 13.4832 0.0504 8.836 22.5816 17.2872 tot = 92.82 9bi) mean = EFX/EF = 3253/50 =65.06 9bii) Standard deviation = Square root of EF(x-x)2/Ef = Square root of 92.82/50 = square root of 1.8564 = 1.36 No9)

(6a) first term9a)=1.0=1 common diff(d)=3-1=2 last term(L)=101 L=a+(n-1)d 101=1+(n-1)*2 (n-1)*2=100 n-1=100/2 n-1=50 n=501+1 n=51 sum(s)=n/2(2a+(n-1)d) S=51/2(2*1+(51-1)*2) s=25.5(2+100) S=25.5*102=2601

(6b)

UC=95 Bus & Train(B&T)=7 Train & Car( T & C)=3 B&T&C=8 Bus only(x)=B&C only Bus(b)=47 train(T)=30 (draw the venn diagram) Bus only= 47-(7+8+x) x=47-15+x 47=x+x+7+8 47=2x+15 2x=47-15 2x=32 x=32/2 =16 Train only= 30-(7+8+2) =30-18=12 (6bi)=x=16

(6bii) number who travelled by at leasttwo means =7+1+3+8 =19 7a) x-2/4 :x+2/2x Cross multiply 2x(x-2)=4(x+2) Opening the bracket 2x^2-4x = 4x+8 Collect like terms together 2x^2-4x-4x-8=0 2x^2-8x-8=0 Solving with completing the square method 2x^2-8x=8 Divide through with the coefficient of x^2 2x^2/2-8x/2=8/2 X^2-4x=4 Half of coefficient of x (-4 x 1/2)^2 = (-2)^2 X^2-4x+(-2)^2=4+(-2)^2 X^2-4x+(-2)^2=4+4 (x-2)^2=8 X-2:square root 8 X=2 + or - squar root 8 X=2+ square root 8 or x=2- square root 8 X=2+2.828=4.828 X=2-2.828= -0.828 X=4:83 or - 0.83. (7b) P+Q+S=180 degree(sum of angles in a triangle) 52 degree+ 90 degree+ S= 180 degree 142+ S=180 S=180-142 S=38 degree (i)52+38+SQT =180 degree SQT=180-90 SQT=90 degree (ii)PQT= 52 degree

2) ii Area if cross-section =Area of rectangle PQRU-Area of semi-circle =(PUxPQ) - pie ITSI/4 =(4x11)-22/7x7/4 =44-22/4 =44-5.5 =38.5m^2 (3b) h=7cm T=462cm^2 T=pie sqr + 2 pie rH 462= pie( r ^2 +2*7*r) 462/3.142 =r sqr= =14r r sqr+ 14r=147 r sqr +14r- 147=0 r= 14+-( (sqr(14))-4*1*147)/2*1 r=-(14 +-(196-4))/2 r=(-14+_12)/2 r=(-14+12)/2 or r=2/2 =1cm (4a) Pr(3)=x/total total=25+30+x+28+40+32 =155+x 0.225=x/155+ x =34.875+0.225x=x x-0.225x=34.875 =0.775x=34.875 degree x=34.875/0.775 =45 (4b) Pr(even)=30+28+40+32 =90 Pr(even)=90/200=9/20 Pr(prime no)=25=30+45+40 =140 Pr(prime no)=140/200=14/20 Pr(even or prime)=9/20 + 14/20 5a) Area of triangle=1/2bh where h=6 :. 1/2*6/1*b/1=36 6b/2=36/1 6b=72 B=72/6 Base of angle PSR=12cm Since |TS| //PQ QR=PR-PQ QR=12-8 QR=4cm 5b) Draw d triangle From angle ABC, to get |BC| Tan60/1=10cm/|BC| |BC|=10.65/tan60 |BC|=10.65/1.7321 =6.1486 =6.15m Hence |BC|=|DE| From angle AED, to get |AE| Draw d diagram |AB|=6.15tan45 6.15*1 =6.15m There4, th height of the tree =10.65-6.15 =4.50m ================