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Neco 2016 GENERAL MATHEMATICS Obj And Theory/ Essay Answers- June/July

• Neco 2016 GENERAL MATHEMATICS Obj And Theory/ Essay Answers- Expo June/July

  

  
  

  NOTICE NOTE

  / means DIVISION

  * means Multiplication

  tita You Should Know that.

  rais means Raise to power or

  ^ means Raise to power

  sqr rut/square rut means Square root

  —–(1) means Equation 1

  yr means Year

  f(x-xbar) means x MINUS x BAR as in statistics

  which means that MINUS will be on Top of x.

  , (Comma) means NEXT LINE,

  This means that The Following Number is Under

  The Number

  its Following ie.

  UNDER. It is usually used during STATISTICS when drawing a table.

  1) ,(comma) means next line.

  (e.g)

  x : 1,2,3

  fx : 4,5,6

  fx-xbar : 7,8,9

  x|fx |x¯¯|

  1| 4 | 7 |

  
  

  NECO (MATHEMATICS) ANSWER

  
  

  VERIFIED MATHS OBJ

  1-10 ecadddceee

  11-20 ccdcaaceca

  21-30 dcdeeccded

  31-40 eaadbeeadc

  41-50 bbdccdcecb

  51-60 cadaccbdee

  
  

  Math eassy

  8a )

  | AD | ^2= 13^2- 5^2

  | AD | ^2= 169- 25

  | AD | ^2= 144

  AD= sqr144

  AD= 12CM

  | AD | =12 -r

  r ^2=( 12- r )^2 - 5^2

  r ^2=( 12- r )(12 -r ) +25

  r ^2=144 -24 r +25

  r ^2=169 -24 r

  r ^2+24 r -169 =0

  r ^2+24 r =169

  r ^2+24 r +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. 1cm

  .

  8aii )

  circumfrenece of a circle = 2pie R

  C =2x 22 /2*(5. 1)^2

  C =1144 . 44/7

  C =163. 4914 cm

  C =163. 5cm

  .

  8b)

  y 2- y 1/x 2 -x 1 =y - y 1/x - x 1

  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)

  3y - 6=4x +4

  3y - 4x =4 +6

  3y - 4x =10

  y =4x /3+10/3

  ==============================

  ====

  9a )

  let Xy represent the two digit number

  x - y =5 -- -- - (i )

  3xy - ( 10x +y 14

  3xy - 10 x - y =14 -- - -( ii )

  from eqn (i )

  x =5+ y

  3y ( 5+y ) -10 (5+y )- y =14

  15y + 3y ^2 - 50 - 10 y - y =14

  3y ^2 + 4 y - 50 = 14

  3y ^2 + 4 y - 50 - 14 = 0

  3y ^2 + 4 y - 64 =0

  3y ^2 + 12 y + 16y - 64 =0

  (3y ^2 - 12 y ) (+16 y - 64 )=0

  by

  (y - 4) +16( y -4 )=0

  (y - 4)= 0

  ii )

  (3y +16) (y - 4)= 0

  3y +16 =0 or y - 4=0

  3y =- 16 or y =4

  y =- 16/3 or y =4

  when y =4

  x =5+ y

  x =5+ 4

  x =9

  the no is 94

  9b)

  3- 2x /4 + 2x -3/3

  =3( 3-2 x )+4 (2x - 3) /12

  =9- 6x +8 x -12 /12

  =2x - 2/12

  ==============================

  ====

  10a )

  y 2x ^2 + 3)^ 5

  let U =2x ^2 + 3

  Y =u^5

  du/dx = 4x

  dy /du = 5u^4

  dy /du = (2x ^2 + 3)^4

  dy /dx = du/dx dy /du

  dy /dx = 4x . 5 (2x ^2 + 3)^4

  dy /dx = 20x ( 2x ^2 + 3)^ 4

  .

  10b)

  y =3x ^2 + 2x +5

  dy /dx =6x + 2

  dy /dx =6( 3) +2

  dy /dx =18 +2

  dy /dx =20

  .

  10c )

  R -W=Wv ^2/gx

  Wv ^2=gx (R - W)

  Wv ^2=gRx - Wgx

  Wv ^2+Wgx =gRx

  W(v ^2 + gx ) =gRx

  W=gRx /V^2 + gx

  R =2, g= 10, x = 3/2, V =3

  W= 10 *2*3/2/3 ^2 + 10*3/5

  W=30/9 +15

  W=30/24

  W=5/4

  ====================

  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 

  
  1b)
  I = PRT/100,
  p=N15000
  R=10% and I=3years
  A = P+ I where I = 15000*10*3/100=N4500
  A=4500+15000 =N19500 

  
  2a)
  using sine rule
  b/sin20 = 6/sin30
  bsin30 = 6sin120
  b 6sin120/sin30
  b = 6x0.2511/0.4540
  b = 5.7063/0.4540
  b = 12.57 ≠ 12.6cm 

  
  2bi)
  the diagram is euivalent 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| = 8cm
  2bii)
  XY/AB = BY/AC
  9/|AB| = 7/8.6
  |AB| = 9x8.6/7 

  |AB| = 11cm

  
  

  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

  
  

  
  7a) 3²ⁿ+¹ — 4(3ⁿ+¹) + 9 = 0
  3²ⁿ × 3 — 4(3ⁿ× 3¹) + 9 = 0
  (3ⁿ)² × 3 — 4(30ⁿ× ) + 9 = 0
  Let 3ⁿ= x
  3x² — 4 × 3 × x + 9 = 0
  3x² — 12x + 9 = 0
  Divide all by 3
  3x²/3 — 12x/3 + 9/3 = 0
  x² — 4x + 3 = 0
  x² — 3x — x + 3 = 0
  x(x—3) -1(x—3) = 0
  (x—3)(x—3) = 0
  x—3 = 0 or x—1 = 0
  x = 3, x = 1
  Substitute x = 3
  3ⁿ = 3 or 3ⁿ = 1
  3ⁿ = 3¹ or 3ⁿ= 3°
  n = 1 or n= 0

  
  

  3)
  let the son age be x
  man=5x
  son=x
  4yrs ago;the man age = 5x - 4
  the son age = x - 4
  the product of their ages
  (5x - 4)(x - 4) =448.

  4b)

  to fill the tank/volume of fuel needed = 7.5*4.2*1.2 = 37.8m^3 = 37,800

  litres addition fuel = 37,800-30,000 = 7,800

  litres therefore, 7,800

  more litres would be needed

  ================

  5a)

  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

  5b)

  amount spent=144000- [48,000+32000+19200+12000+7200] =144000-118400 =N25600

  ===============

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