2014 - WAEC Mathematics Past Questions and Answers - page 3

cos x(\frac{12}{13})

13² = 12² + a²

169 = 144 + a²

a² = 169 - 144

a² = 25

a (\sqrt{25})

a = 5

tan x = (\frac{5}{12})

(\frac{1 - \tan x}{\tan x} = \frac{1 - \frac{5}{12}}{\frac{5}{12}})

(\frac{\frac{1 - \frac{5}{12}}{12 - 5}}{12} = \frac{\frac{7}{12}}{\frac{5}{12}})

= (\frac{7}{2} \div \frac{5}{12})

= (\frac{7}{12} \times \frac{12}{5} = \frac{7}{5})

(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16})

= (\frac{\sqrt{2^{3(2)} \times 2^{2(n + 1)}}}{2^{2n} \times 2^4})

= (\frac{\sqrt{2^6 \times 2^{2n + 2)}}}{2^{2n} + 4})

= (\frac{\sqrt{2^6 + 2^{2n + 2)}}}{2^{2n} + 4})

= (\frac{\sqrt{2^{2n + 8}}}{2^{2n} + 4})

= (\sqrt{2^{2n + 8} \div 2^{2n} + 4})

= (\sqrt{2^{2n - 2n} + 8 - 4})

= (\sqrt{2^4})

= (\sqrt{16})

= 4

(\frac{2}{x - 3} - \frac{3}{x - 2}) = (\frac{p}{(x - 3)(x - 2)})

(\frac{2(x - 2) - 3(x - 3)}{(x - 3)(x - 2)}) = (\frac{p}{(x - 3)(x - 2)})

= (\frac{2x - 4 - 3x + 9}{(x - 3)(x - 2)}) = (\frac{p}{(x - 3)(x - 2)})

(\frac{-x + 5}{(x - 3)(x - 2)} = \frac{p}{(x - 3)(x - 2)})

p(x - 3)(x - 2) = -x + 5(x - 3)(x - 2)

p = -x + 5 or p = 5 - x

(\frac{1}{2})(a - b + c) + (\frac{1}{2})(a + b - c) - [(\frac{1}{2}) (a - b - c)]

(\frac{1}{2}a - \frac{1}{2}b + \frac{1}{2}c + \frac{1}{2}a + \frac{1}{2}b - \frac{1}{2}c - \frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c)

= (\frac{1}{2}a + \frac{1}{2}b + \frac{1}{2}c)

= (\frac{1}{2}(a + b + c))

tan (\theta = \frac{opp}{adj} = \frac{6.6}{13})

tan (\theta = 0.5077)

(\theta) = tan^-1 0.5077

(\theta = 27^o)

perimeter of minor sector

2r + (\frac{\theta}{360} \times 2 \pi r)

= 2 x 3.5 + (\frac{120^o}{360^o} \times 2 \frac{22}{7} \times 3.5)

= 7 + (\frac{154}{21})

= 7 + 7.33

= 14.33

= 14(\frac{1}{3})cm

There are 3 triangles: (\bigtriangleup)MRS, (\bigtriangleup) and (\bigtriangleup) PRQ

Area PRMS has 2 triangles: (\bigtriangleup) MRS and (\bigtriangleup) RSP

the fraction = (\frac{2}{3})