The Real Number System - SS1 Mathematics Past Questions and Answers - page 1

(i) \(6 \times \left( 2 + 3^{2} \right) - 4\ \ \ \ \ \ = 6 \times (2 + 9) - 4\)

= \(6 \times 11 - 4\)

= \(66 - 4\)

= \(62\)

(ii) \(\left( 18 \div 2\ of\ \frac{1}{4} \right)\ \times \left( \frac{2}{3} \div \frac{3}{4} \times \frac{5}{8} \right) \div \left( \frac{2}{3} \div \frac{3}{4}of\frac{3}{4} \right) = \ \left( 9\ of\ \frac{1}{4} \right)\ \times \left( \frac{2}{3} \div \frac{3}{4} \times \frac{5}{8} \right) \div (\frac{2}{3} \div \frac{3}{4}of\frac{3}{4})\)

= \(\left( \frac{9}{1} \times \frac{1}{4} \right)\ \times \left( \frac{2}{3} \div \frac{15}{32} \right) \div (\frac{2}{3} \div \frac{9}{16})\)

= \(\frac{9}{4}\ \times \left( \frac{2}{3} \times \frac{32}{15} \right) \div (\frac{2}{3} \times \frac{16}{9})\)

= \(\frac{9}{4}\ \times \frac{64}{45}\ \div \ \frac{32}{27}\)

= \(\frac{9}{4} \times \frac{64}{45}\ \times \ \frac{27}{32}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ \frac{9}{4}\ \times \ \frac{64}{15}\ \times \ \frac{9}{32}\ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ \frac{9}{4}\ \times \ \frac{2}{15}\ \times \ \frac{9}{1}\)

= \(\frac{3}{2} \times \frac{1}{5} \times \frac{9}{1}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ \frac{27}{10}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ 2\frac{7}{10}\)

(i) \(+ 12 - 14 + 10 = \ - (14 - 12) + 10 = \ - 2 + 10 = \ + (10 - 2) = \ + 8\)

(ii) \(- 11 - 12 + 3 = \ - (11 + 12) + 3 = \ - 23 + 3 = \ - (23 - 3) = \ - 20\)

(i) \(- 28\ \div \ - 3\frac{1}{2} = \ - \frac{28}{1} \div - \frac{7}{2} = \ - \frac{28}{1}\ \times \ - \frac{2}{7} = \ + \left( \frac{28}{1} \times \frac{2}{7} \right) = \ + \frac{8}{1} = \ + 8\)

 

(ii) \(9\ \times \ - 4\frac{1}{2} = \ \frac{9}{1} \times - \frac{9}{2} = \ - \frac{81}{2} = \ - 40\frac{1}{2}\)

 

(iii) \(- 63 \times - 6 = \ + (63 \times 6) = \ + 378\)

2	70		2	120
5	35	2	60
7	7	2	30
	1	3	15
		5	5
			1

Thus, \(70 = 2 \times 5 \times 7\),

\(120 = 2 \times 2 \times 2 \times 3 \times 5\)

Common factors are one set of \(2\) and \(5\).

Hence, the Highest Common Factor = \(2 \times 5 = 10\)

2	108	150
2	54	75
3	27	75
3	9	25
3	3	25
5	1	25
5	1	5
	1	1

The Lowest Common Multiple is thus, \(2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 = 2,700\)