Chapter 1. Real Numbers

Chapter 1. Real Numbers

1.	Express 140 as a product of its prime factors.	(1-mark)
2.	Find the LCM and HCF of 12, 15 and 21 by the prime factorization method.	(1-mark)
3.	Find the LCM and HCF of 6 and 20 by the prime factorization method.	(1-mark)
4.	State whether ${{13} \over {3125}}$ will have a terminating decimal expansion or a non-terminating repeating decimal.	(1-mark)
5.	State whether ${{17} \over 8}$ will have a terminating decimal expansion or a non-terminating repeating decimal.	(1-mark)
6.	Find the LCM and HCF of 26 and 91 and verify that LCM x HCF = product of the two numbers.	(3-marks)
7.	Use Euclid’s division algorithm to find the HCF of 135 and 225	(3-marks)
8.	Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.	(3-marks)
9.	Prove that $\sqrt 3$ is irrational.	(3-marks)
10.	Show that $5 - \sqrt 3$ is irrational.	(3-marks)
11.	Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.	(3-marks)
12.	An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

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