Question Library

\(\frac{3}{2x} - \frac{2}{3x} = 4\) \(\frac{9 - 4}{6x}\); \(\frac{5}{6x}\) = 4 5 = 24x ; x = \(\frac{5}{24}\)

(2x + 3 )2 = 125 2n + 3 = 3\(\sqrt{125}\) 2x + 3 = 5 2x = 5 - 3 x = \(\frac{2}{2}\) = 1

x2 - 2x - 3xy + 6y = x(x - 2) -3y(x - 2) = (x - 3y)(x - 2)

2.7864 x 10-3 = 0.0027864 = 0.0028(approx. 2 s.f)

92x = \(\frac{1}{3}\)(27x) (22)2x = \(\frac{(3^{3x})}{3}\) (34x) = 33x - 1 4x = 3x - 1 4x - 3x = -1 x = -1

85% of x = 3230 \(\frac{85}{100} \times x\) = N3230 x = \(\frac{100}{85}\) x N3230 x = N3800.00

1 litre = 1000cm3 1800 litre = 1800 x 1000cm3 l x b x h = capacity 600 x 150 x h = 1800000 h = \(\frac{1800000}{600 \times 150}\)cm h = 20cm

\(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0 \(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 0 -10x + 10 = 0 -10x = -10 x = \(\frac{-10}{-10}\) x = 1

6 - x - x2 = 0 a = -1; b = -1; c = 6 Sum of roots = c + k = -\(\frac{-b}{a}\) = \(\frac{-(-1)}{-1}\) = -1

No. of buckets of water = \(\frac{\text{Capacity of reservoir}}{\text{Capacity of buckets}}\) = \(\frac{800 \times 700 \times 500}{10 \times 1000}\) = \(\frac{28000 0000}{10000}\) = 28000

\(\frac{1}{2}\sqrt{32} - \sqrt{18} + \sqrt{2}\) = \(\frac{1}{2} (4\sqrt{2}) - 3\sqrt{2} + \sqrt{2}\) = 2\(\sqrt{2} - 3\sqrt{2} + \sqrt{2}\) = 3\(\sqrt{2} - 3\sqrt{2} - 3\sqrt{2}\) = 0

(x - 3y)2 - (x + 3y)2 = [(x - 3y) - (x + 3y)] [(x + 3y + x + 3y)] = [-6y] [2x] = -12xy

30 + x = 100 x = 100 - 30 = 70o

\(\frac{/PS/}{/PQ/} = \frac{/PT/}{/PR/}\) \(\frac{x}{4 + x} = \frac{7}{7 + 5}\) \(\frac{x}{4 + x} = \frac{7}{12}\) (2x = 7)(4 + x); 12x = 28 + 7x 12x - 7x = 28 5x = 28 x = \(\frac{28}{5}\) x = 5.6

\(\frac{\text{science}}{\text{graduates}}\) = \(\frac{\theta}{360}\) x 4320 where \(\theta\) + 100 + 80 + 108 = 360 \(\theta\) = 360 - 288 = 360 \(\frac{\text{science}}{\text{graduates}}\) = \(\frac{72}{360} \times 4320\) = 864