**MATHS OBJ**

*VERIFIED MATHS-OBJ*

1-10 CBCDACDCCD

11-20 AADBDACBBC

21-30 BDDABDADAD

31-40 CDACCCCCDA

41-50 BBBCDCACDB

==Completed==

**IF YOU NEED FULL OBJ,KINDLY COMMENTS ‘I NEED IT’ AT THE CONMENT BOX**…

2ai).

p = (rk/Q -ms)2/3

p3/2 = (rk/Q -ms)2/8 * 3/2b

p3/2 = rk/Q = ms

p3/2 + ms = rk/Q

q(p3/2 + ms ) = rk

Q =rk/p3/2 + ms

2aii)

Where :

r = 10, k = 4, s = 0.2

p = 3, m = 15

Q = 10 * 4/3^3/2 + (15 * 0.2)

Q = 40/5.2 + 3

Q = 40/8.2

Q = 4.88

[17/08, 10:30 AM] Martail Jr: 5a)

Using elimination method

2x: 2p-4q=4

3x: 4p+2q=9

Hence

4p-6q=8

9p+6 =27

Adding equation (i) to (ii)

Therefore

13p=35

Thus p=35/13

Substituting P=35/13 in equation (ii)

Hence

3p+2q=9……….. (ii)

3(35/13) + 2q= 9

=105/13+2q=9

Multiplying throughout by 13

~13~ *105/ ~13~ + ~13~*2q =13*9

Thus 105+26q=117

Collecting like terms

26q =117-105

26q=12

Q=12/26 or 6/13

(1a)

Given A={2,4,6,8,…}

B={3,6,9,12,…}

C={1,2,3,6}

U= {1,2,3,4,5,6,7,8,9,10}

A’ = {1,3,5,7,9}

B’ = {1,2,4,5,7,8,10}

C’ = {4,5,7,8,9,10}

A’nB’nC’ = {5, 7}

(1b)

Cost of each premiere ticket = $18.50

At bulk purchase, cost of each = $80.00/50 = $16.00

Amount saved = $18.50 – $16.00

=$2.50

============================≠

(5a)

Total income = 32+m+25+40+28+45

=170+m

PR(²)=m/170+m = 0.15/1

M=0.15(170+m)

M=25.5+0.15m

0.85m/0.85=25.5/0.85

M=30

(5b)

Total outcome = 170 + 30 = 200

(5c)

PR(even numbers) = 30+40+50/200

=115/200 = 23/40

(5a)

Total income = 32+m+25+40+28+45

=170+m

PR(²)=m/170+m = 0.15/1

M=0.15(170+m)

M=25.5+0.15m

0.85m/0.85=25.5/0.85

M=30

(5b)

Total outcome = 170 + 30 = 200

(5c)

PR(even numbers) = 30+40+50/200

=115/200 = 23/40

4a) Total Surface Area = 224πcm²

r:l = 2:5

r/l = 2/5

Cross multiply

2l/2 = 5r/2

L = 5r / 2

Total surface = πrl + πr²

= πr (l + r)

24π/π = πr (5r/2 + r )/ π

224 = 5r²/2 + r²/1

L.c.m = 2

448 = 5r² + 2r²

448 / 7= 7r²/7

r² = 64

r = √64 = 8cn

L = 5*8/2 = 20cm

4b)

Volume = 1/2πr²h

= 1/3 * 22/7 * 8 * 8 * 18.33

= 1228.98cm³

L² = h² + r ²

20² = h² + 8²

400 – 64 = h²

h² = 336

h = √ 336

h = 18.33cm

(8a)

Let Ms Maureen’s Income = Nx

1/4x = shopping mall

1/3x = at an open market

Hence shopping mall and open market = 1/4x + 1/3x

= 3x + 4x/12 = 7/12x

Hence the remaining amount

= X-7/12x = 12x-7x/12 =5x/12

Then 2/5(5x/12) = mechanic workshop

= 2x/12 = x/6

Amount left = N225,000

Total expenses

= 7/12x + X/6 + 225000

= Nx

7x+2x+2,700,000/12 =Nx

9x + 2,700,000 = 12x

2,700,000 = 12x – 9x

2,700,000/3 = 3x/3

X = N900,000

(ii) Amount spent on open market = 1/3X

= 1/3 × 900,000

= N300,000

(8b)

T3 = a + 2d = 4m – 2n

T9 = a + 8d = 2m – 8n

-6d = 4m – 2m – 2n + 8n

-6d = 2m + 6n

-6d/-6 = 2m+6n/-6

d = -m/3 – n

d = -1/3m – n

(3a)

Diagram

CBD = CDB (base angles an scales D)

BCD+CBD+CDB=180° (Sum of < in a D)
2CDB+BCD=180°
2CDB+108°=180°
2CDB=180°-108°=72°
CDB=72/2=36°
BDE=90°(Angle in semi circle)
CDE=CDB+BDE
=36°+90
=126
(3b)
(Cosx)² - Sinx given
(Sinx)² + Cosx
Using Pythagoras theory thrid side of triangle
y²= 1²+√3
y²= 1+ 3=4
y=√4=2
(Cosx)² - sinx/(sinx)² + cosx
(1/2)² - √3/2/
(√3/2)² + 1/2 = 1/4 - √3/2 = 1-2√3/4
3/4+1/2 = 3+2/4
=1-2√3/4 * 4/5
=1-2√3/5
(9a)
Draw the triangle
(9b)
(i)Using cosine formulae
q² = x² + y² - 2xycosQ
q² = 9² + 5² - 2×9×5cos90°
q² = 81 + 25 - 90 × 0
q² = 106
q = square root 106
q = 10.30 = 10km/h
Distance = 10 × 2 = 20km
(ii)
Using sine formula
y/sin Y = q/sin Q
5/sin Y = 10.30/sin 90°
Sin Y = 5 × sin90°/10.30
Sin Y = 5 × 1/10.30
Sin Y = 0.4854
Y = sin‐¹(0.4854), Y = 29.04
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