Question The first, second and third terms of a geometric progression are , and respectively. (i) Show that satisfies the equation 7k2 − 48k + 36 = 0. (i) Find, showing all necessary working, the exact values of the common ratio corresponding to each of the possible values of k. (ii) One of […]
Question a) Over a 21-day period an athlete prepares for a marathon by increasing the distance she runs each day by 1.2 km. On the first day she runs 13 km. (i) Find the distance she runs on the last day of the 21-day period. (ii) Find the total distance […]
Question A runner who is training for a long-distance race plans to run increasing distances each day for 21 days. She will run km on day 1, and on each subsequent day she will increase the distance by 10% of the previous day’s distance. On day 21 she will run 20 km. i. Find […]
Question Two heavyweight boxers decide that they would be more successful if they competed in a lower weight class. For each boxer this would require a total weight loss of 13 kg. At the end of week 1 they have each recorded a weight loss of 1 kg and they both find that in each […]
Question i. In the binomial expansion of , the first three terms are . Find the remaining three terms of the expansion. ii. Hence find the coefficient of in the expansion of . Solution i. Expression for the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: Hence; […]
Question a.In an arithmetic progression, the sum of the first ten terms is equal to the sum of the next five terms. The first term is . i.Show that the common difference of the progression is . ii.Given that the tenth term is 36 more than the fourth term, find the value of . b.The […]
Question a) The third and fourth terms of a geometric progression are and respectively. Find the sum to infinity of the progression. b) Two schemes are proposed for increasing the amount of household waste that is recycled each week. Scheme A is to increase the amount of waste recycled each month by 0.16 tonnes. Scheme […]
Question i. The first and second terms of a geometric progression are p and 2p respectively, where p is a positive constant. The sum of the first n terms is greater than 1000p. Show that 2n > 1001. ii. In another case, p and 2p are the first and second terms respectively of […]