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Solution Centre for All Examinations both WAEC/WASSCE/SSCE, NECO, NABTEB, JAMB (UTME), Post-UTME, WAEC GCE, NECO GCE, NABTEB GCE etc

**Maths Essay – 9.30am – 12.00pm Maths Obj – 3.00pm – 4.30pm**

Mathematics OBJ:

1DCBBDCCADB

11ACBACCAADA

21DAAAABCDCB

31ABCDABCBCA

41DCABCCABBB

1)CLICK HERE FOR THE IMAGE

1a)

sn=n/2{2a+(n-1)d}

n=10, sn=130

130=10/2{2a+(10-1)d}

130=5(2a+ad)

130=10a+45d———(eq1)

Tn=a+(n-1)d

T5=3*a=3a,n=5

3a=a+(5-1)d

3a=a+4d

3a-a-4d=0

2a-4d=0———-(eq2)

Solve equation 1 and 2 simultaneously

10a+45d=130*1

2a-4d=0*5

10a+45d=130

10a-20d=0

65d/65=130/65

d=2

1b)

putting d = 2 into equation(2)

2a-4(2)=0

2a=8

a=8/2=4

First term = 4

1c)

Given Tn = 28 = a+(n-1)d

28 = 4+(ń – 1)2

28 = 4+2n – 2

28 = 2+2n

2n = 26

n = 26/2 = 13

number of terms of the AP is 13

2a)

Draw the triangle

Using Pythagoras rule

a² = b² + c²

5² = 3² + c²

25 = 9 + c²

c² = 25 – 9

c² = 16

C = √16 = 4, Cos X = 4/5

5(cosx)² – 3 = 5((4/5))² – 3

= 5(4/5 × 4/5) – 3

= 16/5 – 3/1 L. C. M = 5

= 16 – 15/5 = 1/5.

2b)

Volume of a pyramid

=1/3b×L×h

Volume of a cone = 1/3πr²h

Vp = volume of pyramid

Vc = volume of cone

Hp = height of pyramid

Hc = height of cone

Vp = Vc; Hp = Hc

Vp ± Vc

1/3bLh = 1/3πr²h

42 × 11 = 22/7r²

21 = 1/7 × r²

r² = 21 × 7

r² = 147

r = √147

r = 12 3/25cm

3)CLICK HERE FOR THE IMAGE

4a)

(2y+x) + (6y-2x+1) + 4y = 28 …(1)

6y-2x + 1 = 4y …(2)

2y+ x +6y – 2x + 1 +4 = 28

12y + x +6 -2x + 1 + 4 = 28

12y – x + 1 = 28

12y – x = 29 …(3)

6y-2x + 1 = 4y, 6y-2x – 4y = 1

2y – 2x = -1… (iv)

24y – 2x = 54

2y – 2x = 1

22y/2w = 55/22 y = 2.5

12y – x = 27

12 (2.5) – x = 27

30 x 27 x=3

b)

2y + x = 2 (2.5) + 3 = 5+3 = 8cm

6y – 2x + 1 = (2.5)-2 (3) + 1

= 15-6 + 1 = 10cm

4y = 4(2.5) = 10cm

5)CLICK HERE FOR THE IMAGE

5a)

5 – X > 1 9 + X >_ 8

5 – 1 > X X >_ 8 – 9

4 > X X >_ -1

Range is

-1_< X < 4 OR 4 >X >_ -1

5b)

PQR + PSR = 180(supplementary angles of a cyclic quad)

PQR + 56 = 180

PQR = 180 – 56

PQR = 124°

Next, join P to R

QRP = QPR(base angles of an isosceles)

PQR + 2QRP = 180(Sum of angles in a triangle)

124 + 2QRP = 180

2QRP = 56°

QRP = 56/2 = 28°

PRS = 90°(angle in a semi – circle)

= 28 + 90

= 118°

6ai)

The profit y = X²/8 + 5x

y = GHc20,000.00

Hence 20,000 = X²/8 + 5x

160,000 = X² + 40x

X² + 40x – 160,000 = 0

Since X is in thousands

X² + 40x – 160 = 0

6aii)

Using quadratic formula

X = -b±√b² – 4ac/2a

Where; a = 1, b = 40 & c = -160

X = -40±√40² – 4(1)(-160)/2(1)

X= -40 ±√1600 + 640/2

X = -40 ±√2240/2

X = -40 ± 47.32/2

X = -40±47.32/2

= 7.32/2

X = 3.66

X ≈ 4

6b)

Draw the diagram

Using ΔTOP

tan 28 = H/OP

OP = H/tan28

Then for ΔROP

tantita = H/2/OP

OP = H/2/tantita

Hence H/tan 28 = H/2/tantita

tantita = H/2 × tan 28/H

tantita = tan28/2

Hence Tita = 28/2 = 14°

7) CLICK HERE FOR THE IMAGE

7a)

√^2(2x^3-4x+6)dx

2x^4/4-4x^2/2+6x

X4/2-2x^2+6x

(2)^4/2-2(2)^2+6(2)

16/2-8+12=8-8+12=12

x^4/2x^2+6x

(1)^4/2-2(1)^2+6(1)

1/2-2/1+6/1=10-14/+12/2

=13-14/2=9/2

=12/1-9/2=24-9/2

=15/2=7^1/2

PLEASE USE BELOW 7b

7b)

Given; P^-1 = (-1 1)

(4 -3)

P = (p-1)^-1 = C^T/|p^-¹|

=(-3 -1)

(-4 -1)/3 – 4

=(-3 -1)

(-4 -1)/-1

=(3 1)

(4 1)

8)CLICK HERE FOR THE IMAGE

8ai)

Diagram in above link

V1=4.158liters

R=21cm

8aii)

V = 1/3 Ah, = x r²

V = 1/3 xr²h

V = 4.158 liters

V = 4.158cm³, V = 1/3 xr²h

4158 = 1/3 x 22/7 x 21 x 21 x h

4158 x 3 = 22 x 63h

h = 4158/21 x 22 = 9cm

h = 9cm

8b)

d = 28cm, r = d/2 = 28/2 = 14cm

V2 = 1/3 xr²h

V2 = 1/3 x 22/7 x 14 x 14 x 9

V2 = 1/2 x 22/1 x 2 X 14 x 3

= 1848cm³

V2 = 1.845 liters

12a) CLICK HERE FOR THE IMAGE

12bi)

using sinθ rule

307/sin78 = 285/sinθ

sinθ=285sin78/307

sinθ=0.908

θ=sin^-1 0.908

=650 to the nearest whole number

the bearing of X from Z = 360-65=295degree

12bii)

|YZ|/sin37 = 307/sin78

|YZ| = 307sin37/sin78

=189m to the nearest whole number

13)CLICK HERE FOR THE IMAGE

Good Luck

PLEASE NOTE THESE SYMBOL

/ means DIVISION

* means Multiplication

tita You Should Know that.

^ means Raise to power

sqr rut/square rut means Square root

—–(1) means Equation 1

yr means Year

CLICK HERE TO STUDY THE MATHS SYMBOLS

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