waec 2018/2019 mathematicsobj qnd thoery
waec 2018/2019 mathematicsobj qnd thoery
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
*4A ii*
RSQ=(x+90)°
RSQ=37.5°+90°
RSQ=127.5°
General mathematics answer
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
===============
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
=================
4a)
Rate = 2/100 * N0.02 per month Rate per annum = 0.02 * 12 = 0.24 per annum
(4b) Draw the Diagram =======================
(4A ii)
RSQ=(x+90)°
RSQ=37.5°+90°
RSQ=127.5°
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*MATHEMATICS ANSWERS*
(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
=============================
(2)
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
2b)
The lines must be solved simultenously
3y – 2x = 21 ——- (1)
4y + 5x = 5 ——-(2)
using elimination method,
(4) 3y – 2x = 21
(30 4y + 5x = 5
12y – 8y = 84 ——— (3)
12y + 15x = 15 ——-(4)
equ (4) minus equ(3)
23x = -69
x = -69/23
x = -3
Put this into equation (1)
3y -2(-3) = 21
3y = 6 = 21
3y = 21 -6
3y = 15
y =15/3
y = 5
coordinates of Q is (-3, 5)
(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
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
(4ai) x + 90 degrees = 3x+15(sum of two inter <s= exterior <)
Collecting like terms
90-15= 3x -x
75= 2x
x= 75/2
x= 37.5
(4aii) x^degrees + 90+<RSQ = 180deggrees(sum of <s in a Triangle)
37.5 + 90+ <RSQ= 180
127.5 + <RSQ= 180
<RSQ= 180 - 127.5
<RSQ= 52.5 degrees
(4b) If 2N4 seven = 15N nine. Find N
Converting all to base 10
2x7^2+Nx7^1+4x7^0= 1x9^2+5x9^1+Nx9^0
2x49+7N+4x1= 1x81+5x9+Nx1
98+7N+4= 81+45+N
Collecting like terms
7N-N= 81+45-98-4
6N= 24
N=24/6
N=4
(3a)Using Pythagoras theorem let the side of the rhombus = x
x^2= (10.2/2)^2 + (9.3/2)^2
x^2= 5.1^2 + 4.65^2
x^2= 26.01 + 21.62
x^2= 47.63
x= sqroot of 47.63
x= 6.9
Sides= 6.9cm
But perimeter of rhombus = 4x
Perimeter = 4x6.9
Perimeter = 27.6cm
(3b) Sin x= 3/5
Opp= 3, Hyp= 5
Let adjacent = x
From Pythagoras theoren
5^2= 3^2+x^2
25= 9+x^2
x^2= 25-9
x^2= 16
x= sqroot of 16
x= 4
5cosx-4tanx
=4 - 3= 1
5cosx-4tanx= 1
(10a) Using Pythagoras theorem from SPQ
|SQ|^2 = 12^2 + 5^2
= 144+25
=169
SQ= sqroot of 169
= 13cm
Sin tita= 5/13 = 0.3846
Tita= Sin^-1(0.3846)
= 22.6degrees
From PRQ
Sin tita= |PR|/12
Sin 22.6 = PR/12
Sin 22.6= PR/12
PR= 12xsin 22.6
PR= 12x0.3843
PR= 4.61cm
(10bii)Let the height at which m touches the wall= y
Cos x^degrees= 8/10= 0.8
x^degrees= Cos^-1(0.8)
= 36.87degrees
Sin x^degrees = y/12
Sin 36.87= y/12
y= 12xsin36.87
y= 12x0.60000
y= 7.2m
*MATHEMATICS ANSWERS*NO9) Using cosine rule,
|TQ|ˆ² = 4ˆ² + 6 ˆ² – 2(4)(6) cos30°
|TQ|ˆ² = 16 + 36 – 48(0.8660)
|TQ|ˆ² = 52 – 41.568
|TQ|ˆ² = 10.432
TQ = √10.432
TQ = 3.23CM
From similar triangles;
|PT|/|TQ| = |PS|/|SR|
4/3.23 = 10/|SR|
4|SR| = 32.3
|SR| = 32.3/4
|SR| = 8CM (nearest whole number)
(10a) Using Pythagoras theorem from SPQ
|SQ|^2 = 12^2 + 5^2
= 144+25
=169
SQ= sqroot of 169
= 13cm
Sin tita= 5/13 = 0.3846
Tita= Sin^-1(0.3846)
= 22.6degrees
From PRQ
Sin tita= |PR|/12
Sin 22.6 = PR/12
Sin 22.6= PR/12
PR= 12xsin 22.6
PR= 12x0.3843
PR= 4.61cm
(10bii)Let the height at which m touches the wall= y
Cos x^degrees= 8/10= 0.8
x^degrees= Cos^-1(0.8)
= 36.87degrees
Sin x^degrees = y/12
Sin 36.87= y/12
y= 12xsin36.87
y= 12x0.60000
y= 7.2m
(6a)
Draw the Venn diagram
Let the number of cars with faults in brakes only be x
(6b) Number that passed = 60% × 240 = 144
Number that failed =
240 - 144 = 96
Therefore; 28+2x+x+14+6+6-x+8 = 96
2x + 62 = 96
2x = 96 - 62
2x = 34
X = 34/2
X = 17
(i) faulty brakes cars = 8+6+x+6-x
= 8+6+6
=20
(ii) only one fault = 28+x+2x
=28+3x
=28+3(19)
=28+51
= 79
(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
=============================
(2)
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
2b)
The lines must be solved simultenously
3y – 2x = 21 ——- (1)
4y + 5x = 5 ——-(2)
using elimination method,
(4) 3y – 2x = 21
(30 4y + 5x = 5
12y – 8y = 84 ——— (3)
12y + 15x = 15 ——-(4)
equ (4) minus equ(3)
23x = -69
x = -69/23
x = -3
Put this into equation (1)
3y -2(-3) = 21
3y = 6 = 21
3y = 21 -6
3y = 15
y =15/3
y = 5
coordinates of Q is (-3, 5)
===========================================
NO3) DRAW THE DIAGRAM.
Using pythagoras theorem,
lˆ² = 5.1ˆ² + 4.65ˆ²
lˆ² = 26.01 + 21.6225
lˆ² = 47.6325
l = √47.6325
l = 6.9cm (1d.p)
perimeter of phombus = 41
4 * 6.9
= 27.6cm
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
waec 2018/2019 mathematicsobj qnd thoery
waec 2018/2019 mathematicsobj qnd thoery
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