2013 - WAEC Mathematics Past Questions and Answers - page 3

p = (y : 2y (\geq) 6)

2y (\leq) 6

y (\leq \frac{6}{2})

y = (\leq) 3

and Q = (y : y -3 (\geq) 4)

y - 3 (\geq) 4

y (\geq) 4 + 3

y (\geq) 7

therefore p = {3, 4, 5, 6, 7} and Q = {7, 6, 5, 4, 3....}

P(\cap)Q = {3, 4, 5, 6, 7}

6k² = 5k + 6

6k² - 5k - 6 = 0

6k² - 0k + 4k - 6 = 0

3k(2k - 3) + 2(2k - 3) = 0

(3k + 2)(2k - 3) = 0

3k + 2 = 0 or 2k - 3 = 0

3k = -2 or 2k = 3

k = (\frac{-2}{3}) or k = (\frac{3}{2})

k = ((\frac{-2}{3}), k = (\frac{3}{2}))

y (\alpha) \sqrt{x + 1}), y = k\sqrt{x + 1})

6 = k(\sqrt{3 + 1})

6 = k(\sqrt{4})

6 = 2k

k = (\frac{6}{2}) = 3

y = (\sqrt{(x + 1)})

9 = 3(\sqrt{(x + 1)})(divide both side by 3)

(\frac{9}{3}) = (\frac{3\sqrt{x + 1}}{3})

3 = (\sqrt{x + 1})(square both sides)

9 = x + 1

x = 9 - 1

x = 8

y = x² + 2x + k at point(2,0) x = 2, y = 0

0 = (2)² + 2(20 + k)

0 = 4 + 4 + k

0 = 8 + k

k = -8

Let the number be y, subtract y from 2 i.e 2 - y

2 - y = 4 < (\frac{1}{5}) x y, 2 - y = 4 < (\frac{y}{5})

2 - y - 4 < (\frac{y}{5})

2 - 4 - y (\frac{x}{5} - 4), multiplying through by 5

5(2 - x) = 5((\frac{x}{5})) - 5(4)

10 - 5x = x - 20

-5x - x = -20 - 10

-6x = -30

x = (\frac{-30}{-6})

= 5

(\frac{2}{x + 3} - \frac{1}{x - 2}) = (\frac{2(x - 2) - (x - 3)}{(x + 3) (x - 2)})

= (\frac{2x - 4 - x - 3}{x^2 - 2x + 3x - 6})

= (\frac{x -7}{x^2 + x - 6})

= (\frac{x - 7}{x^2 + x - 6})

Let the interior angle = x^o

interior angle = 5x^o (sum of int. angle ann exterior)

(angles = angle or straight line)

6x = 180

x = (\frac{180}{6})

x = 30^o

no. of sides = (\frac{\text{sum of exterior angles}}{\text{exterior angle}})

= (\frac{360}{30}) = 12

P = x² + 4x - 2, Q = 2x - 1

Q - p = 2, (2x - 1) - (x² + 4x - 2) = 2

2x - 1 - x² - 4x + 2 = 2

-2x - x² + 1

-x² - 2x - 1 = 0

x² + 2x + 1 = 0

x² + x + x + 1 = 0

x(x + 1) + 1(x + 1) = 0

(x + 1)(x + 1) = 0

x + 1 = 0 or x + 1 = 0

x = -1 or x = -1

x = -1

Volume of pyramid = (\frac{1}{3}) x base area x height

= (\frac{1}{3} \times 12^4 \times 8 \times 14)

= 4 x 8 x 14 = 448m³