Tuesday, 13 June 2017

Free Neco Mathematics Expo 2017/2018

Tell ur Friend's to always visit our site MAths-Obj 1ecadddceee 11ccdcaaceca 21dcdeeccded 31eaadbeeadc 41bbdccdcecb 51cadbaecdec completed MATHS ANSWERS 1a) Tabulate x - 1 ,2 ,3 ,4 1 - 1 ,2 ,3 ,4 2 - 2 _ , 4 , 0 _ ,2 _ 3- 3 , 0_ , 3, 0 _ 4 - 4 _ , 2_ , 0_ , 4 1 b ) I = PRT /100 , p = N15000 R = 10 % and I= 3 years A = P + I where I = 15000 * 10 * 3 / 100 = N4500 A = 4500+ 15000 = N19500 ================================== 2 a) No2 Using sine rule b/sin120 = 6/sin30 bsin30 = 6sin120 b= 6sin120/sin30 b=6sin30/0.5 b= 12*sin120 b=12*sin120 b= 10.4cm 2 bi ) the diagram is equivalent t triangles . where | AX | / | BC | = | BY | / | AC | = | XY | /| YC | XY = 9 , BY = 7 YC = 18 -7 = 11 9 /11 = 7 / | AC | 9 | AC | = 77 | AC | = 77 /9 | AC | = 8 cm 2 bii) XY /AB = BY /AC 9 /| AB| = 7 / 8 .6 | AB | = 9 x 8 .6 /7 | AB | = 11 cm ================================== 3) let the son age be x man = 5 x son= x 4 yrs ago; the man age = 5 x - 4 the son age = x - 4 the product of their ages (5 x - 4 )( x - 4 ) = 448 ================================== 4 a) volume of fuel = cross -sectional area of X depth of fuel rectangular tank 30, 000litres = 7 . 5* 4 .2 * d m ^ 3 but ; 1000litres = 1 m ^ 3 therefore ; 30( M ^3 ) = 7 .5 *4 . 2* d ( M ^ 3) 30= 31.5 d ==== d = 30/31. 5 = 0 .95( 2 d .p ) 4 b) to fill the tank /volume of fuel needed = 7 .5 * 4. 2 *1 .2 = 37.8 m ^ 3 = 37, 800 litres addition fuel = 37, 800- 30, 000 = 7 , 800 litres therefore , 7 , 800 more litres would be needed 5 a) sector for building project = 48000 /144000* 360 = 120degree sector for education = 32, 000 /144000* 360 =80degree sector for saving = 19200 /144000* 360 = 48degree sector for maintenance = 12000 / 144000*360 = 30degree sector for miscellaneous = 7200/144000* 360 =18degree sector for food items = 360 -( 120 + 80+ 48+30+ 18) = 360- 296 = 64degree 5 b) amount spent =144000- [48, 000 + 32000+ 19200 + 12000 +7200] = 144000-118400 = N 25600 6) /————————— — / 41.02 × √0.7124 / ———— ———— — — √42.87 × 0.207 × 0.0404 | No | Log | | 41.02 | 1.6130 | 1.6130 | 0.7124 | T. 8527 ÷ 2 | T.9263/1.5393 | 42.77 | 1.6321 | | 0.207 | T.3160 | | 0.0404 | 2. 6064 / | | | T.5544 | T.5544/1.9849 Antilog = 9658 ≈ 96.58 ================================= 7 a) 3^ 2 n + 1 - 4 ( 3 ^ n + 1 )+ 9 = 0 3^ 2 -3 - 4 ( 3^ n - 3) + 9 = 0 (3 ^ n )^2- 3 - 4 (3 ^ n -3 )+ 9 = 0 let 3^ n = p p ^ 2 -3 - 4 (p -3 ) + 9 = 0 3p ^ 2 /3 - 12 p /3 + 9 / 3 = 0 p ^ 2 - 4 p + 3 = 0 p ^ 2 - 3 p - p + 3 = 0 p ^ 2 p ( p - 3 ) - 1 (p - 3) = 0 (p - 1 ) (p - 3) = 0 p -1 = 0 or p - 3 = 0 p = 1 or 3 Recall 3 ^ n = p when p = 1 3^ n = 3^ 0 n = 0 when p = 3 3^ n = 3^ 1 n = 1 7 b ) log (x ^ 2 + 4 ) = 2 + logx - log ^ 20 log (x ^ 2 + 4 ) = log ^ 100 = log ^ x - log ^ 20 (x ^ 2 + 4 ) = log ( xx ) x ^ 2 + 4 = 5 x x ^ 2 -5 x + 4 = 0 x ^ 2 -4 x - x + 4 = 0 x (x -4 ) - 1 ( x -4 ) = 0 (x -1 ) (x -4 ) = 0 x -1 = 0 or x -4 = 0 x = 1 or 4 8 a) | AD | ^ 2 = 13^2 -5 ^ 2 | AD | ^ 2 = 169- 25 | AD | ^ 2 = 144 AD =sqr 144 AD =12CM | AD | = 12- r r ^2 = ( 12-r )^2 - 5 ^ 2 r ^2 = ( 12-r ) ( 12- r ) + 25 r ^2 = 144 -24r + 25 r ^2 = 169 -24r r ^2 + 24r -169 = 0 r ^2 + 24r = 169 r ^2 + 24r + 14^2 = 169 + 14^2 ( r + 14)^2= 169 + 196 ( r + 14)^2= 365 ( r + 14=sqr 365 r + 14=19. 105 r = 19.105 -14 r = 5. 105 r = 5. 1 cm 8 aii ) circumfrenece of a circle = 2 pie R C = 2 x22/ 2* ( 5 .1 )^2 C = 1144.44/ 7 C = 163 .4914cm C = 163 .5 cm 8 b) y2 -y1 / x2 -x1 = y- y1 /x- x1 6 -2 /2 - ( -1 )=y- 2/ x- ( -1 ) 4 /2 + 1 = y- 2 /x+ 1 4 /3 = y-2 / x+ 1 3 ( y-2 )=4 ( x+ 1 ) 3 y-6 = 4 x+ 4 3 y-4 x= 4 + 6 3 y-4 x= 10 y= 4 x/3 + 10/ 3 9 a) let Xy represent the two digit number x-y =5 --- -- ( i ) 3 xy - ( 10x + y)=14 3 xy - 10x - y = 14 - -- -( ii ) from eqn ( i ) x= 5 +y 3 y( 5 +y ) -10( 5 + y) -y= 14 15y+ 3 y^2 - 50 - 10y - y =14 3 y^2 + 4 y - 50 = 14 3 y^2 + 4 y - 50 - 14 = 0 3 y^2 + 4 y - 64 = 0 3 y^2 + 12y + 16y - 64 = 0 ( 3 y^2 - 12y ) ( + 16y - 64)=0 by ( y-4 ) + 16( y- 4)= 0 ( y-4 )=0 ii ) ( 3 y+ 16) ( y-4 )=0 3 y+ 16=0 or y- 4 =0 3 y= -16 or y= 4 y= -16/ 3 or y= 4 when y =4! x= 5 +y x= 5+y x= 5 +4 x= 9 the no is 94 9 b) 3 -2 x/ 4 + 2 x- Drop ur comments to appreciate dnt just copy d answers nd go without comments! notice dat

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