2025/2025 WAEC/NECO Answers: WAEC 2025 - MATHS ANSWERS

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(1)

110â‚“ = 40â‚…

change all to base ten.

110â‚“ = 40â‚…

1x²+1x ¹+0x⁰ = 4×5¹+0×5⁰

x² + x + 0 = 20

x² + x – 20 = 0

Solve quadratically

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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(2)

(2a)
The equation of the line through the points
A(-2,7) and B(2,-3)
Using the equation Y=mx+b
Where m=slope of the gradient, b=the intercept at the vertical axis
Hence slope=Change in Y/Change in X
=>Y2-Y1/X2-X1=Y-y1/X-x1
=(-3-7)/(2--2)=Y-7/X+2
=-10/4=(Y-7)/(X+2)
=4(y-2)=-10(x+2)
4y-28=-10x-20
4y=-10x+8
5x+2y=4

(2b)
(5b-a)/(8b+3a)=1/5
5(5b-a)=1(8b+3a)
25b-5a=8b+3a
25b-8b=3a+5a
17b=8a
Therefore a/b=17/8

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(3a)

Total ratio =3+5+8=16

Ali's share =3/16 * 420,000/1

=210,000

Son's of Ali and Yusuf's share = N78,750+ N210,000

= N288,750

(3b)

2(1/8)^x=32^x-1

2¹(2^-3)^x=2⁵(x-1)

2¹* 2^-3x=2⁵(x-1)

2^-3x+1=2⁵(x-1)

-3x+1=5(x-1)

-3x+1=5x-5

-5x-3x= -5-1

-8x/-8= -6/-8

x=3/4

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(4)
Since 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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(6ai)
F α M1M2/d²
F = KM1M2/d²
Given F = 20N, M1= 25kg, M2 = 10kg and d = 5m
20 = k(25)(10)/5²
250k = 500
k = 500/250 = 2
Expression is 
F = 2M1M2/d²

(6aii) 
Making d subject 
d = √2M1M2/F
d = √2 ×7.5×4/30
d = √60/30 = √2
d = √2m or 1.41m

(6b) 
Draw the diagram 
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 = 340/5
X = 68


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(8a) 
1/3x - 1/4(x+2)>_ 3x -1â…“
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|/|AB| = Tan52
|AD| = 37.8576 × Tan52° = 37.8576 × 1.2799 = 48.45m
Height of tower = 48.45m




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(10)
130kg of tomatoes for #52,000 
Half of the tomatoes 
130/2 = 65kg sold at 30%
Profit = #52,000/2 = 26,000
#26,000 = 100%
X = 130%
X = 26000 × 130/100
= #33,800

Then 65kg was then sold at reduction of 12% per kg
Recall that the initial cost price = 52000/130
=400kg
65kg sold at = 33,000/65
=#520/kg
Then for 12% reduction 
520 × 88/100 = 457.6/kg
(a) 
The new selling price per kg = #457.6/kg

(b) 65kg - 5kg = 60kg
(60kg×457.6kg)+33,800
= #61,256.00

#profit = selling price /cost price × 1000/1
=61256/52000×100/1= 117.8
= 17.8%


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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


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(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

Ratio : Otobo : Ade : Adeola
60,000 : 100,000 : 140,000
60 : 100 : 140
6 : 10 : 14
3 : 5 : 7

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