2024 NABTEB GCE MATHEMATICS: Nabteb Gce 2024. Maths answers (1533)

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OBJ

1-10: DABBABBBAD

11-20: CDBDCCCBBA

21-30: CDABDACCCC

31-40: BCBCABABBC

41-50: DACCCCDBDB

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*SECTION A*

*_(Answer ALL QUESTIONS From This Section)_*

(1a)

6^n+1*9^n*4^2n/18^n*2^n*12^2n

=(2*3)^n+1*(3*3)^n*(2*2)^2n/(2*3*3)^n*2^n*(2*2*3)^2n

=2^n+1*2^n+1*3^n*3^n*2^2n*2^2n/2^n*3^n*3^n*2^n*2^n*2^n*3^2n

= 2^n*2^1*2^n*2^1*3^n*3^n*2^n*2^n*2^n*2^n/2^n*3^n*3^n*2^n*2^n*2^n*2^n*2^n*3^n*3^n

= 2^6n*3^2n*2*2/2^6n*3^4n

= (2^6n / 2^6n) *(3^2n / 3^4n)*2*2

=2^6n - 6n * 3^2n - 4n * 4

= 2^0 * 3^-2n * 4

= 4*3^-2n

= 4 * 1/3^2n

= 4/3^2n

(1b)

Log 243/log 27

= log 3^5/log 3^3

= 5log3/3log3 = 5/3 = 1 whole no 2/3

============================================

(2a) 

3t - 2p = 8×2 ...(I) 

2t - 3p = 14×2...(II) 

6t - 4p = 16 ...(III) 

6t - 9p = 42 ...(IV) 

  9P - 4P = -42 + 16

  5p = -26

P = -26/5 = -5 1/5

Put p = -26/5 into eqn (I) 

3t - 2(-26/5) = 8

3t + 52/5 = 8

3t = 8 - 52/5

3t = 40 - 52/5 = -12/5

Divide both sides by 3

36/3 = -12/5 / 3

t = -12/5 × 1/3

= -12/15 = -4/5

(2b)

3/√3(2/√3 - √12/6)

2/√3 × 3/√3 - 3/√3 × √12/6

6/√9 - 3√12/6/√3

6/3 - 3√12/6√3

2 - √12/2√3

2 × 2√3 - √12/2√3

4√3 - (√4 × 3)/2√3

= 4√3 - 2√3/2√3

= 2√3/2√3 = 1

============================================

(3)

P(k) = 2/3

P(Y) = 5/8

P(I) = 3/4

P(k fail) = 1- 2/3 = 1/3

P(Y fail) 1 - 5/8 = 3/8

P(I fail) = 1 - 3/4 = 1/4

(a) 2/3*5/8*3/4 = 5/16

(b) 1/3*3/8*1/4 = 1/32

(c) 2/3*5/8*1*4 = 5/48

==============================================

(4)

Draw the triangle 

<GFN = 180 - ( 68+90)

Sum of angles in a Δ

= 180 - 158 = 22

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