2014 WAEC GCE MATHEMATICS +++++++++++++++++++++++++++ ^ means raise to power +++++++++++++++++++++++++++ PLS DONT WRITE (power) on ur paper oooo. (power) means Raise to power. Anywhere u see me write (power), just raise d next digit up. Example: m power 2 means that 2 will be on top of m. QT(power)2 means that 2 will be on top of QT. ======== I KNEEL DWN DE BEG U, ABEG READ DIS WELL +++++++++++++++++++++++++++ TABULATE MEANS TO DRAW A TABLE. UNDER x, put 1,2,3,4,5,6 Under f, put 4,2,3,2,6,3 ========================== Verified MATHS OBJ: 1-10: BAABBCDBCC 11-20: ADDBCACACC 21-30: BDCBDABACA 31-40: CACCDCDDDB 41-50: DDDABADCCD (1) Given, m^2 - 2mn + n^2 - 9r^2 m^2 - 9r^2 + n^2- 2mn m^2 - (3r)^2 + n(n-2m) (m-n)^2 - 9r^2 =(m - n - 9r)(m -n +9r) (1b) 5x - 4y=6 ----eqn1 3^3y -3x=3^-3 3y - 3x = -3 -3x + 3y= -3 ----eqn2 5x - 4y =6 ------eqn1 -x + y= -1 -------eqn1 5x - 4y =6 -5x + 5y =-5 add eqn(1) and (2) together y=1 substitute y=1 into eqn(2) -x + 1= -1 -x= -1-1, x= -2 x=2, y=1 ============================= (2a) All taxable income is = 10% + 15% + 20% + 25% = 70% of 850 = 70/100*850 = #595 (2b) 1: 70/100*120 =#84 2: 70/100*30= #21 3: 70/100*100 =#70 4: 70/1 ============================ (3a) QT(power)2 =QS(power)2 + ST(power)2 5(power)2 =4(power)2 + ST(power)2 ST(power)2 =25 - 16 ST(power)2 =9 ST=sqrt (9)= 3cm Cos(tita)=3/5 cos(tita)= 0.6 tita= cos(power)-1(0.6) = 53degree cos53(degree)=SR/6 0.602 =SR/6 SR= 0.602*6 = 3.6cm /TR/=3.6/Sin53(degree)=4.5cm (3b) Adj=12 Opp=5 Hyp=13 cosx=12/13 Sinx=5/13, Tanx=5/12 Cosx - 2Sinx/2Tanx = 12/13-2(5/13) / 2(5/12) = (12/13 - 10/13) / 5/6 = (2/13) / (5/6) = 2/13*6/5 = 12/65 ================================== (4a) Log10(75/10) - Log10(5/9)(power)2 + Log10(100/243) = Log10(75/10) - Log10(25/81) + Log10(100/243) = Log10(75/10*81/25) + Log10(100/243) = Log10(3*81/10) + Log10(100/243) = Log10(243/10) + Log10(100/243) = Log10( 243/10* 100/243) =Log10(10)=1 (4b) X= (10,11,12,13,14,15 ) Y= (2,4,6,8,10,12,14,16 ) U= (10,11,12,13,14,15,16,17,18,19,20 ) (i) XnY = (10,12,14 ) (ii) X / / / = (16,17,18,19,20 ) X / / /nY= (16 ) n(X / / /nY)= (16 ) ================================= (5a) Considering change in WZX ZX(power)2 = Zw(power)2 + WX (power)2 ZX(power)2 = 6(power)2 + 8(power)2 = 36+ 64 ZX(power)2=100 ZX= sqrt(100) =10cm ZX= 2ZM ZM= ZX/2 Zm=10/2 =5cm Mx=5cm OM is the height of the pyramid OX(power)2= OM(power)2 + MX (power)2 13(power)2= OM(power)2 + 5(power)2 169= OM(power)2 + 25 OM(power)2 = 169 -25 OM(power)2 = 144 OM= sqrt(144) =12cm height of pyramid = 12cm (5b) COS < 0XZ = 12/13 (-2, 0,2) diagram (10b) /PQ/ = 10m Let KR be the height of pole tan 45(degree)= KR/PR KR= tan 45(degree) *(10-x) KR= (10 -x) --------------eqn(1) tan 58(degree)= KR/x KR= tan 58(degree) * X KR= 1.6 *X KR= 1.6x ---------------eqn(2) equation(1) and(2) 10 - x= 1.6x 10= 1.6x + x 2.6x = 10 x= 10/2.6 x= 3.85m (i) Distance from P to the pole is (10 - x) = (10 - 3.85)= 6.15m (ii) Height of pole = KR= 1.6x = 1.6 * 3.85 = 6.16m =========================== (11a) Pr(Manful pass) = 2/3 Pr(John)= 5/8 Pr(Ernest) = 3/4 Pr(all pass)= 2/3 * 5/8 * 3/4 = 5/16 (11b) Tabulate x: 1,2,3,4,5,6 f: 4,2,3,2,6,3 E(f) = 20 f1x1=4 , f2x2=4, f3x3=9 , f4x4 =8, f5x5=30, f6x6=18 Efx = 4+4+9+8+30+18 = 73 Cf = 4,6,9,11,17,20 Q1= Ef/4 = 20/4 = 5th Q3= 3Ef/4 = 3*20/4 =15th Q1 corresponds to 2 Q3 corresponds to 5 inter-quatile range = Q3 - Q1 = 5 - 2= 3 ============================== (12a) (i)
Posted on: Sat, 20 Sep 2014 21:01:47 +0000
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