FREE WAEC Mathematics Theory And Objective ANSWERS Apirl 21 2016

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Mathematics Theory And Obj

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COMPLETE MATHS OBJ:

1-10: BACBCCCBCD

11-20: CBBACACBBC

21-30: BBCCDACDCD

31-40: ACAABADAAA

41-50: DAABADCBAD.

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===============Theory===============

1-10: BACBCCCBCD

11-20: CBBACACBBC

21-30: BBCCDACDCD

31-40: ACAABADAAA

41-50: DAABADCBAD.

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===============Theory===============

2)

ii Area if cross-section

=Area of rectangle PQRU-Area of semi-circle

=(PUxPQ) - pie ITSI/4

=(4x11)-22/7x7/4

=44-22/4

=44-5.5

=38.5m^2

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

ii Area if cross-section

=Area of rectangle PQRU-Area of semi-circle

=(PUxPQ) - pie ITSI/4

=(4x11)-22/7x7/4

=44-22/4

=44-5.5

=38.5m^2

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

3a)

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(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

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

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

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 of triangle=1/2bh where h=6

:. 1/2*6/1*b/1=36

6b/2=36/1

6b=72

B=72/6

Base of angle PSR=12cm

Since |TS| //PQ

QR=PR-PQ

QR=12-8

QR=4cm

Area of triangle=1/2bh where h=6

:. 1/2*6/1*b/1=36

6b/2=36/1

6b=72

B=72/6

Base of angle PSR=12cm

Since |TS| //PQ

QR=PR-PQ

QR=12-8

QR=4cm

5b)

Draw d triangle

From angle ABC, to get |BC|

Tan60/1=10cm/|BC|

|BC|=10.65/tan60

|BC|=10.65/1.7321

=6.1486 =6.15m

Hence |BC|=|DE|

From angle AED, to get |AE|

Draw d diagram

|AB|=6.15tan45

6.15*1

=6.15m

There4, th height of the tree =10.65-6.15

=4.50m

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

Draw d triangle

From angle ABC, to get |BC|

Tan60/1=10cm/|BC|

|BC|=10.65/tan60

|BC|=10.65/1.7321

=6.1486 =6.15m

Hence |BC|=|DE|

From angle AED, to get |AE|

Draw d diagram

|AB|=6.15tan45

6.15*1

=6.15m

There4, th height of the tree =10.65-6.15

=4.50m

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

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

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

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

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

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

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

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

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

No9)

CLICK HERE

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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

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

bi) mean = EFX/EF = 3253/50 =65.06

bii) Standard deviation = Square root of EF(x-x)2/Ef

= Square root of 92.82/50

= square root of 1.8564

= 1.36

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= Square root of 92.82/50

= square root of 1.8564

= 1.36

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(4a & b)

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(7a &B)

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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

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.

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.

(7B)

=4.83 or _0.83 ( correct to 2 d.p)

7b)

But

=4.83 or _0.83 ( correct to 2 d.p)

7b)

But

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

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

(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

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

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

==========

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

==========

(No.6b)

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/ 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,

* 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,

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