Waec 2019 Mathematics Obj And Theory Now Available May/June Expo

Waec 2019 Mathematics Obj And Theory Now Available May/June Expo

Waec 2019 Mathematics Obj And Theory Now Available May/June Expo

Maths Obj
11-20 ACBCBBAACD
21-30 DCCBCCABBA
31-40 AABBDCDDCC
41-50 BBCDCCBCCD

Completed✅

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2019 Waec General Maths Special Symbols

* means multiplication
/ means division
^ means raise to power
= means equality
θ means theta
β means beta
α means alpha
Ø means empty set
μ means population mean
π means pi constant
√ means square root

Question 1.
110ₓ = 40₅
change all to base ten.
110ₓ = 40₅

1x²+1x ¹+0x⁰ = 45¹+0*5⁰
x² + x + 0 = 20
x² + x – 20 = 0

x² + 5x – 4x – 20 = 0
x(x+5) – 4(x+5) = 0
(x-4)(x+5) = 0
Either x-4 = 0 or x + 5 = 0
x = -5 or 4
therefore, x= 4

1b) 15/√75 + √108 + √432
= 15/√253 + √363 + √144*3
= 15/5√3 + 6√3 + 12√3
= 3/√3 + 18√3
= 3√3/3 = 18√3
= √3 + 18√3
=19√3

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Question 2.
M = -3-7/2+2 = m = (y₂-y₁/-10)/4
m = -5/2

Equation line = y – y₁ = m(x-x₁)
= y – 7 = -5/2(x+2)
= 2y – 14 = -5(x+20)
= 2y – 14 = -5x – 10
5x + 2y – 14 + 10 = 0
5x + 2y – 4 = 0

2b) 5b -a /8b + 3a = 1/5
5b – a = 1 * 3
8b + 3a = 5
15a – 3b = 3
8b + 3a = 5/23b = 8
b = 8/23 = 0.35
using equation (1)
5b – a = 1
5(0.35) – a = 1
1.75 – a = 1
-a = 1 – 1.75
-a = -0.75 (- divide -)
a = 0.75
a/b = 0.75/0.35
a/b = 2.14

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Question 3.
Ali : Musah : Yusif = ₦420,000
3 : 5 : 8
Sum of ratio shared;
3 + 5 + 8 = 16

therefore, Ali share = 3/16 * ₦420,000
= ₦78,750

Musah share = 5/16 * ₦420,000
= ₦131,250

Yusif share = 8/16 * ₦420,000
= ₦210,000

therefore, sum of Ali + Yusif = ₦78,750 + ₦210,000
=₦288,750

3b)
Solve: 2(1/8)^x = 32^x-1
2^1 x (8^-1) = 32^x-1
2^1 x (8^-1) = 32^x-1
2^1 x (2^3(-1))^3 = 2^5(x-1)
2^1 x (2^-3)^x = 2^5x-5
2^1 x 2^-3x = 2^5x-5
2^1+(-3x) = 2^5x-5
2^1-3x = 2^5x-5 (2 cancel 2)
1-3x = 5x -5
-3x – 5x = -5 -1
-8x/-8 = -6/-8
x = 3/4

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(4)
Since <PQR = <PRS = 90°
Using Pythagoras theorem
|PR|² = |PQ|² + |QR|²
|PR|² = 3² + 4²
|PR|² = 9 + 16
|PR|² = 25 PR = √25
|PR| = 5cm
Considering PRS
|PS|² = |PR|²+|SR|²
13² = 5² + |SR|²
169 = 25 + |SR|²
|SR|² = 169 – 25
|SR|² = 144
|SR| = √144 = 12cm

Hence the area of the quadrilateral = Area of triangle PQR + area of PRS
= 1/2bh + 1/2bh
= 1/2×4×3 + 1/2×12×5
= 6+30 = 36cm

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(5a)
No of red balls = 3
No of green balls = 5
No of blue balls = x
Prob.(red ball) = no of total outcome/no of possible outcome
Pr(red) = 3/3+5+x = 1/6
3/8+x = 1/6
6(3) = 1(8+x)
18 = 8 + x
X = 18 – 8 = 10
Therefore the no of blue ball = 10

(5b)
Probability of picking a green ball
P(g) = no of green balls/no of possible outcome
P(g) = 5/3+5+10 = 5/18
=5/18

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Question 6.

Draw the digram
6 ai) F = m ₁ m₂/d^2
Given F = 20N, m=25kg, m₂ = 10kg and d = 5m
20 = k(25)(10)/5^2
250k = 500
k = 500/250 = 2

=> Expression is: F = m ₁ m₂/d^2

6aii) making d subject,
d = √m ₁ m₂/f
d = √27.54/30
d = √60/30 = √2
d = √2m or 1.41m

6b) x+x+60+x+80+x+40+x+20 = 540 (sum of angles in a pentagon)
5x + 200 = 540
5x = 540 – 200
5x = 340
x = 68

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(8a)
1/3x – 1/4(x+2)>_ 3x -1⅓
1/3x – 1/4(x+2)>3x – 4/3 Multiply through by the L. C. M(12), we have 4x – 3(x + 2)>_36x – 16 4x – 3x – 6 > 36x – 16
-6+16 >36x + 3x – 4x 10 > 35x
35x _< 10
X = 10/35
X = 2/7

(8bi)
Draw the triangle
|AB|/66 = sin35
|AB| = 66sin35 = 66×0.5736 = 37.8576

Draw the right angled triangle
|AD| = 37.8576 × Tan52° = 37.8576 × 1.2799 = 48.45m
Height of tower = 48.45m

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(11ai)
ar² = 1/4 ……(1)
ar^5= 1/32 …..(2)
Divide eqn (2) by eqn(1)
ar^5/ar² = 1/32÷1/4
r³ = 1/32 × 4/1
r³= 1/8
r³ = 2-³
r = 2-¹
r = 1/2
Common ratio = 1/2
Put this into eqn (1)
a(1/2)² = 1/4
a(1/4) = 1/4
a = (1/4)/(1/4) = 1
First term, a = 1

(11aii)
Seventh term, T7 = ar^6
=(1)(1/2)^6
=1/64

(11b)
Given : X = 2 and X = -3
(X – 2)(X + 3) = 0
X² + 3x – 2x – 6 , 0
X² + x – 6 = 0
Comparing with ax²+bx+c = 0
a = 1
b = 1
C = -6

(12a)
Given : siny = 8/17
Draw the right angle
From Pythagorean triple, third side is 15
Draw the right angle triangle
tan y = 8/15

tan y/1+2tany = 8/15/1+2(8/15) = 8/15/1+16/15

tany /1+2tan y = 8/31

(12b)
Amount shared = #300,000
Otobo’s share = #60,000
Ade’s share = 5/12 × #(300,000-60,000)
= 5/12 × #240,000
=#100,000

Adeobi’s share = #300,000 – (#60,000 + #100,000)
= 300,000 – 160,000
=#140,000

60,000 : 100,000 : 140,000
60 : 100 : 140
6 : 10 : 14
3 : 5 : 7

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