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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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