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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**

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

========

**(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**

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

========

**(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**

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

Nabteb Gce 2021. Maths answers (ESSAY, OBJ, THEORY, PRACTICALS ETC)

=

**(4)**

**Draw the triangle **

**<GFN = 180 - ( 68+90)**

**Sum of angles in a Δ**

**= 180 - 158 = 22
**

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Updated At: June 16th 2021, (02:06:08)

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