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**Reflesh this page after 2 minutes to load more General Mathematics…**### 2018 WAEC Mathematics Answer

Cost price for Lami= #300.00

Profit made by lami = x%

Ie selling price for lami=(100+x/100)×#300

=#3(100+x)

=#(300+3x)

Bola's cost price = #3(100+x)

Profit made by bola =x%

Selling price for bola =(100+x/100)×#3(100+x)

=#3/100(100+x)²

James cost price =#3/100(100+x)²=300+(6x+3/4)

expanding;

3/100(10000+200+x²) = 300+3/4+6x

3(10000+200x+x²)=30000+75+600x

30000+600x+3x²=30000+75+600x

3x²=75

X² = 75/3

X² = 25

X = square root 25

X = 5

(8b)

3x-2<10+x<2+5x

3x-2<10+x & 10+x<2+5x

3x-x<10+2 & 10-2<5x-x

2x<12 8<4x

X<12/2 4x>8

X<6 x>8/4

X>2

Also; 3x-2<2+5x

-4<2x

2x > -4

X > -2

Therefore; Range is -2<X<6

(1)

On February 28th 2012, value = (100-30/100) * #900,00.00

= 70/100 * #900,00

= #630,000.00

On february 28th 2013, value = (100-22/1000 * #630,00

= 78/100 8 #630,000

= #491,400

On february 28th 2014, value = 78/100 8 #491,400

=383,292

On february 28th 2015, value = 78/100 * #383,292

= #298,967.76

= #299,000

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

(2a)

Given y-2px^2-p^2x-14

At (3,10)

10=2p(3)^2-p^2(3)-14

3p^2-18p+24=0

p^2-6p+8==0

Using factor method

P^2-2p-4p+8=0

P(p-2)-4(p-2)=0

(p-4)(p-2)=0

p=4 or p=2

(2b)

The lines must be solved simultaneously

3y-2x=21--(i)

4y+5x=5--(ii)

Using elimination method

=>12y-8x=84--(iii)

=>12y+15x=15--(iv)

eq(iv) minus (eqiii)

23x=-69

x=-69/23

x=-3

Put x into eq(i)

3y-2(-3)=21

3y+6=21

3y=21-6

3y=15

y=15/3

Coordiantes of Q is (-3,5)

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

(3a)

Using pythagoras theorem

L^2=5.1^2 + 4.65^2

L^2=26.01 + 21.6225

L^2=47.6325

L=sqroot(47.6325)

L=6.9cm(1 d.p)

Perimeter of rhombus=4

=4*6.9

=27.6cm

(3b)

Sin x=3/5

DRAW THE TRIANGLE

Using pythagoras tripple the third side=4

therefore cosx=4/5

tanx=3/4

therefore 5cosx-4tanx

=5(4/5)-4(3/4)

=4-3

=1

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

(4ai)

Draw the diagram

ai X + 90 = 3x + 15

90 = 3x - X + 15

90 = 2x + 15

2x + 15 = 90

2x = 90 - 15

X = 75/2

X = 37.5•

(4aii)

(4b)

2N4seven = 15Nnine

Converting both to base 10

2×7+N×7¹+4×7 = 1×9²+5×9¹+N×9

98 + 7N + 4 = 81 + 45 + N

7N + 102 = 126 + N

7N - Ń = 126 - 102

6N = 24

Ń = 24/6

Ń = 4

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

(5a)

m+n+s+p+q/5=12

m+n+s+p+q=60......(1)

Now;

(m+4)+(n-3)+(5+6)+p-2)+(q+8)/5

=(m+n+s+p+q)+(4-3+3+6-2+8)/5

=60+13/5

=73/5

=14.6

(b)

75% of 500 = 375 people

Number of people above 65 years = 500-375

=125

25% of 500 = 125

Number of people below 15 years = 125

Number between 15 years and 65 years

=500-(125+125)

=500-250

=250 people

(6)

Total number of cars on road worthiness = 240

60% passed ie 60/100×240/1 = 144cars.

Number that failed = 240-144 = 96cars

(6a)

Draw the Venn diagram

C = clutch

B = brakes

S = steering

(6b)

From the diagram above

E = 28+12+8+6+x+6+2x

96=60+3x

96-60=3x

36/3 = 3x/3

Therefore X = 12

(i) The no of cars that had faulty brakes

=12+8+6+x (Since X = 12)

=12+8+6+12 = 38

(ii) Only one fault = (no of clutch only) + (no of brakes only) + (no of steering only)

=28+x+12x = 28+12+24

=64cars

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

(7a)

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-5)/(x-2)=(-7-5)/(-4-2)

(y-5)/(x-2)=-12/-6

(y-5)/(x-2)=2

Cross multiply

y-5=2(x-2)

y-5=2x-4

2x-y-4+5=0

2x-y+1=0

(7bi)

DRAW THE DIAGRAM

(7bii)

(I)

p^2=q+r^2-2qrcosP

p^2=8^2+5^2-2*8*5*cos90

p^2=64+25-0

p^2=89

p=sqroot(89)

p=9.4339km

therefore |QR|=9.43km(3 sf)

(II)

q/sinQ=p/sinP

8/sinQ=9.4339/sin90

sinQ=(8*sin90/9.4339

sinq=(8*1)/9.4339 =0.8480

Q=sin^1(0.8480)=57.99 degrees

but Q=30+ A

A=Q-30

=57.99-30

A=27.99 degrees

The bearing of R from Q

=180-A

180-27.99

=155.01

=>152 degrees

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

(8a)

Cost price for Lami= #300.00

Profit made by lami = x%

Ie selling price for lami=(100+x/100)×#300

=#3(100+x)

=#(300+3x)

Bola's cost price = #3(100+x)

Profit made by bola =x%

Selling price for bola =(100+x/100)×#3(100+x)

=#3/100(100+x)²

James cost price =#3/100(100+x)²=300+(6x+3/4)

expanding;

3/100(10000+200+x²) = 300+3/4+6x

3(10000+200x+x²)=30000+75+600x

30000+600x+3x²=30000+75+600x

3x²=75

X² = 75/3

X² = 25

X = square root 25

X = 5

(8b)

3x-2<10+x<2+5x

3x-2<10+x & 10+x<2+5x

3x-x<10+2 & 10-2<5x-x

2x<12 8<4x

X<12/2 4x>8

X<6 x>8/4

X>2

Also; 3x-2<2+5x

-4<2x

2x > -4

X > -2

Therefore; Range is -2

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

(9a)

Draw the diagram

Angles PTR and PSR are similar

|PT|/|PS| = |TQ|/|SR|

In angle PTR

|TQ|²=|PT|²+|PQ|²-2|PT||PQ|cos30degrees

=4²+6²-2×4×6×cos30

=16+36-48×0.8660

=52-41.568

=10.432

|TQ|=√10.432 =3.22cm

4/10 = 3.22/|SR|

4|SR| = 10×3.22

|SR| = 32.2/4

|SR| = 8.05cn

Approximately 8cm(to the nearest whole number)

(9b)

Atqrs = AΔPSR - AΔPTR

AΔPTR = 1/2×4×6×sin30

=2×6×0.5

=6cm²

AanglePTQ/AanglePSR = |PT|²/|PS|²

6/AanglePSR = 4²/10²

6/AanglePSR = 16/100

16×AanglePSR = 6×100

AanglePSR = 600/16 = 37.5cm2

ATQRS = 37.5 - 6

=31.5cm2

=32cm2

3a)

The diagonal = 10.2m and 9.3cm

Using Pythagoras theory

Ac² = 10.2² + 9-3²

Ac² = 104.04 + 86.49

Ac² = 190.53

Ac² = √190.53

Ac² = 13.80

3b)

DRAW THE DIAGRAM

Using Pythagoras theory

5² = 3² + x²

x² = 5² - 3²

X²= 25 - 9

X² = √16

X= 4cm

CosX = adjacent/hyp

= 4/5

Tan X = opp/adj. = 3/4

5cos x - 4tan x

5(4/5)- 4(3/4)

20/5 - 12/4

4-3= 1

4ai)

sum of angle in a D =180degree

xdegree + 90degree + 180degree - (3x+15)=180degree

xdegree + 90degree + 180degree - 3x+15=180degree

-2x=180degree - 255

+2x/2=+75/2

x=37.5

4aii)

<RsQ =180 - (3x+15)

<RsQ =180-(3*37.5+15)

=180-(112.5 + 15)

=180 - 127.5

<RsQ= 52.5degree

4b)

2N4seven =15Nnine

2*7^2+N*7^1+4*7degree =1*9^2 + 5*9^1+N*9degree

9*49+N*7+4*1=1*81+5*9+N*1

98+7N+4=81+45+N

7N+102=126+N

7N-N=126-102

6N/6 =24/6

N=4

[4/18, 9:58 AM] +234 807 814 4449: NO1) On February 28th 2012, value = (100-30/100) * #900,00.00

= 70/100 * #900,00

= #630,000.00

On february 28th 2013, value = (100-22/1000 * #630,00

= 78/100 8 #630,000

= #491,400

On february 28th 2014, value = 78/100 8 #491,400

=383,292

On february 28th 2015, value = 78/100 * #383,292

= #298,967.76

[4/18, 10:12 AM] +234 807 814 4449: NO2) Given that y = 2pxˆ² – p² x – 14

AT (3, 10)

10 = 2p(3)² – p² (3) – 14

10 = 18p – 3p² – 14

3p² – 18p + 24 = 0

p² – 6p + 8 = 0

using factor method,

p² – 2p -4p + 8 = 0

p(p-2) – 4(p-2) = 0

(p-4)(p-2) = 0

p-4 = 0 or p-4 = 0

p= 4 or p =2

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