# MATHEMATICS (ESSAY/OBJ) Waec 2016 Expo Runz Answers

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Thursday 21st April 2016

MATHEMATICS 2 (ESSAY) 9.30AM - 12.00PM

MATHEMATICS 1 (OBJ) 2.00PM - 3.30PM

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4)

6)

7)

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8a)

2x = r = y

if=180 - 110 + Y = 70 + Y

nOW : X + r + 70 + y = 180

2x = r + - y

if 2x = r

x = r/2 =y

:x + 2x + 70 + 2x = 180

5x = 180 -70 = 110

x = 110/5 = 22degree

8b)

let A collection of boy be X and that of girl be y

Tot collected by boy

600 + Y = x

Tot collected by girl

x - 600 = y

x- y =600 --(i)

Ave collection for boys

x/10 = 100+y/12(multipled by 120)

x/10 * 120 = 100 * 120 + y/12 *120

12x = 12000 + 10y

12x -10y= 12000 ---(ii)/x - y = 600 *12

12x - 10y =12000 * 1

12x -12y = 7200----(iii)

12x - 10y = 12000

= -2y = -4800

y = 4800/2 = 2400

y = 4800/2 = 2400

subt 2400 for y in eq(i)

600 + y = x

600 + 2400 = x

x = 3000,

boys collection = #3000

girls collection = # 24000

total collected = #54000

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

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.

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

13a)

(x1,y1) =(2,-3)

for 2x + y =6

y=-2x +6

compare y = mx +6

m2 = -2

for parallel lines, m1=m2

: y-y1/x-x1 = m

y--3/x-2 =-2/1

y + 3 = -2(x -2)

y + 3 = -2x + 4

y = -2x + 4 -3

y = -2x +1

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

9)

11a)

3p+4q/3p-4q* 2/1 find p:q

1(rp+4q)= 2(3p-4q)

3p+4q=6p-8q

Collect like terms

3p-6p=-8q-4q

-3p=-12q

Ther4 p:q = -3p/-3=-12q/-3

P=4q, p=4, q=1

P:q= 4:1

11b)

Ts=pq-(2+2)

Ts=pq-4

Circumference of Ts= 2pie(TS)

11bi)

Ts=pq-(2+2)

Ts=pq-4

Circumference of Ts= 2pie(TS)

=2pie(pq-4)

Perimeter=pq+4+4+2+2+2pie(pq-4)

34=pq+12+2pie(pq-4)

34-12=pq+2piePQ-8pie

22=PQ(1+2pie)-8pie

22=pq(1(2*22/7)-8*22/7

22=pq(1+44/7)-176/7

22=PQ(7+44/7)-176/7

22+176/7 =pq(51/7)

154+176/7=Pq(51/7)

330/7=pq(51/7)

330/51=pq

Pq=6.4706

11bii)

TS=PQ-4=6.4706-4=2.4706m

Area of semi circle TS=pieD

=7.7626m^2

Area of rectangle PqRU=|pu|*|Pq|

4**6.4706=25.8824

Area of the cross section=area of rectangle-area of semi circle

=25.8824-7.7626

=18.1198m^2

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

6a)

Sn=n/2(2a+(n-1)d)

A=1, d=2, n=n

Sn=n/2(2*1+(n-1)2)

N/2(2+2,-2)

=n/2*2=n^2

6b)

n(E)=95, n(BnT)=7

N(U)=95, n(BnTnC')=7n(B'nTnC)=3,n(BnTnC)=8

n(BnT'nC')=x, n(BnT'nC),n(b)=47, n(T)=30

i)

Draw d venn diagram

ii)

To find x,

X+x+7+8=47

2x=47-15=32

X=32/2

=16

iii)

No of those who travelled by at least two means

7+3+16+8=34

Thursday 21st April 2016

MATHEMATICS 2 (ESSAY) 9.30AM - 12.00PM

MATHEMATICS 1 (OBJ) 2.00PM - 3.30PM

+++++++++++++++++++++++++++++

2016 WAEC MATHS OBJ:

1-10) DCBCABBADA

11-20) CCBCABABBA

21-30) AACCDCDABC

31-40) BCDCDCBABA

41-50) ACADBBDADD

2016 WAEC MATHS OBJ:

1-10) DCBCABBADA

11-20) CCBCABABBA

21-30) AACCDCDABC

31-40) BCDCDCBABA

41-50) ACADBBDADD

4)

6)

7)

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

8a)

if

nOW : X + r + 70 + y = 180

2x = r + - y

if 2x = r

x = r/2 =y

:x + 2x + 70 + 2x = 180

5x = 180 -70 = 110

x = 110/5 = 22degree

8b)

let A collection of boy be X and that of girl be y

Tot collected by boy

600 + Y = x

Tot collected by girl

x - 600 = y

x- y =600 --(i)

Ave collection for boys

x/10 = 100+y/12(multipled by 120)

x/10 * 120 = 100 * 120 + y/12 *120

12x = 12000 + 10y

12x -10y= 12000 ---(ii)/x - y = 600 *12

12x - 10y =12000 * 1

12x -12y = 7200----(iii)

12x - 10y = 12000

= -2y = -4800

y = 4800/2 = 2400

y = 4800/2 = 2400

subt 2400 for y in eq(i)

600 + y = x

600 + 2400 = x

x = 3000,

boys collection = #3000

girls collection = # 24000

total collected = #54000

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

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.

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

13a)

(x1,y1) =(2,-3)

for 2x + y =6

y=-2x +6

compare y = mx +6

m2 = -2

for parallel lines, m1=m2

: y-y1/x-x1 = m

y--3/x-2 =-2/1

y + 3 = -2(x -2)

y + 3 = -2x + 4

y = -2x + 4 -3

y = -2x +1

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

9)

11a)

3p+4q/3p-4q* 2/1 find p:q

1(rp+4q)= 2(3p-4q)

3p+4q=6p-8q

Collect like terms

3p-6p=-8q-4q

-3p=-12q

Ther4 p:q = -3p/-3=-12q/-3

P=4q, p=4, q=1

P:q= 4:1

11b)

Ts=pq-(2+2)

Ts=pq-4

Circumference of Ts= 2pie(TS)

11bi)

Ts=pq-(2+2)

Ts=pq-4

Circumference of Ts= 2pie(TS)

=2pie(pq-4)

Perimeter=pq+4+4+2+2+2pie(pq-4)

34=pq+12+2pie(pq-4)

34-12=pq+2piePQ-8pie

22=PQ(1+2pie)-8pie

22=pq(1(2*22/7)-8*22/7

22=pq(1+44/7)-176/7

22=PQ(7+44/7)-176/7

22+176/7 =pq(51/7)

154+176/7=Pq(51/7)

330/7=pq(51/7)

330/51=pq

Pq=6.4706

11bii)

TS=PQ-4=6.4706-4=2.4706m

Area of semi circle TS=pieD

=7.7626m^2

Area of rectangle PqRU=|pu|*|Pq|

4**6.4706=25.8824

Area of the cross section=area of rectangle-area of semi circle

=25.8824-7.7626

=18.1198m^2

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

6a)

Sn=n/2(2a+(n-1)d)

A=1, d=2, n=n

Sn=n/2(2*1+(n-1)2)

N/2(2+2,-2)

=n/2*2=n^2

6b)

n(E)=95, n(BnT)=7

N(U)=95, n(BnTnC')=7n(B'nTnC)=3,n(BnTnC)=8

n(BnT'nC')=x, n(BnT'nC),n(b)=47, n(T)=30

i)

Draw d venn diagram

ii)

To find x,

X+x+7+8=47

2x=47-15=32

X=32/2

=16

iii)

No of those who travelled by at least two means

7+3+16+8=34

2016 WAEC MATHS OBJ:

1-10) DCBCABBADA

11-20) CCBCABABBA

21-30) AACCDCDABC

31-40) BCDCDCBABA

41-50) ACADBBDADD

2016 WAEC MATHS OBJ:

1-10) DCBCABBADA

11-20) CCBCABABBA

21-30) AACCDCDABC

31-40) BCDCDCBABA

41-50) ACADBBDADD

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