WAEC 2016 MATHEMATICS QUESTIONS AND ANSWERS NOW AVAILABLE FOR FREE

1-10: DCBCABBADA 11-20: CCBDABABBA 21-30: CACCDDDACC 31-40: BCDCDCBADA 41-50: ABACBBDADD (1a) (0.09*1.21)/(3.3*0.00025) =(9*10^-2*1.2*10^1)/(3.3*25*10^-5) =(1089^10^-4)/(82.5*10^-5) =1.32*10^(-4+6) =1.32*10^2 (1b) p=5600,T=3,A=1200+5600=6800 A=P(1+R/100)^3 6800=5600(1+R/100)^3 (1+R/100)^3=6800/5600 (1+R/100)^3=1.214 1+R/100=cuberoot(1.214) 1+R/100=1.0667 R/100=1.0667-1 R/100=0.0667 R=0.0667*100 R=66.7% (2a) 7(x+4)-2/3(x-6)<_2[x-3(x+5)] 7x+28-2x/3-4<_2[x-3x-15] 24+7x-2x/3<_2x-6x-30 7x-2x/3-2x+6x<_-30-24 11x-2x/3<_-54 33x-2x<_-162 31x<_-162 x<_-162/31 (2b) x = tricycles and y = taxi cabs 2x+4y=6b … (1) x+y=20 … (2) from equ..(2) y=20-x substitute for y in equ…(1) 2x+4(20-x) = 66 2x+80-4x=66 80-66=4x-2x 14/2 = 2x/2 x=7 number of tricycles = 7 (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 PSR=1/2*PR*SM PR=8+6=14cm 36=1/2 * 14* 6 36=1/2 * 14* 6 *QR QR=8.6cm (5b) diagram sin45 degree= 10.65/h h=10.65/sin 45 degree =10.65/0.7071 h=15.06cm =============================== (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) given; (x-2)/4=(x+2)/2x 2x*(x-2)=4*(x+2) 2x^2 -4x= 4x+8 2x^2-4x-4x-8=0 2x^2-8x-8=0 x^2-4x-4=0 x^2-4x=4 x^2-(4* 1/2)=4+(2)^2 (x-2)^2=4+4 (x-2)^2=8 (x-2)= sqr root(8) x-2=+-2.83 x=+-2.83 x=+_2.83+2 x=-2.83+2 x=4.83 or x=-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 ============================== (8a) diagram z=110 degree(sum of angles on a straight line) z=180-110 z=70 dgree w degree= 70 degree x+r+w degree= 180 degree(sum of angle in a triangle) x+2x+70 degree=180 degree 3x=110 x=110/3=36.7 dgeree (8b) B=10, G=12 TB=600.00 TB=TG+600 mean of TB=100+ mean of TG where TB= total collection of boys TG=total collection by girls mean of TB= ET/B mean of TB= (TG+600)/10 100+ mean of TG= (TG+600)/100 mean of TG= mean of TG/12 100+ mean of G/12= (TG+600)/10 (100+TG)/12=(TG+600)/10 10*(1200+TG)=12*(TG+600) =12000+10TG=12TG+7200 =12TG-10TG=12000-7200 2TG=4800 TG=N2400 TB=TG+600 TB=600+2400 Tb=N3000 ============================= (11a) Given (3p+4q)/(3p-4q) = 2 3p+4q=2*(3p-4q) 3p+4q=6p-8q 3p-6p=-4q-8q =-3p=-12q p/q=-12/-3 p/q=4/1, P=4, q=1 p:q=4;1 (11b) (i) perimeter(p)=PQ+PU+QR PQ=UT+TS+SR 34=PQ+UR+4+4 PQ=UR 34-8=2PQ PQ=26/2=13cm (ii) 13=2+TS+2 TS=13-4=9cm radius(r)=9/2=4.5cm Area(A)= pie r sqr+22/7*(4.5)^2 =445.5/7 63.64cm^2 ++++++++++++++++++++++++++++++