Question 1 - 25 marks This question is based on your work on MU123 up to and including Unit 3. (a) (i) Use a factor tree or similar method to write 12600 as a product of prime factors. Display your factor tree in your answer. If you choose to use an alternative method, then clearly show your working: just writing down the answer is not sufficient. [4] (ii) Calculate 5 7 14 10 15 leaving your answer as a fraction in its simplest form, showing all your working. [4] (iii) Simplify the surd 7v5 V35 + V63 by writing it as a surd in its simplest form, showing your working. [3] (b) A group of 520 students are required to take a test. Of these, 480 actually take the test, and 40 are absent that day. (i) Write down the ratio of the number of students who take the test to the number of students who are absent. Simplify this ratio as far as possible. [3] (ii) Of the 480 students who take the test, the numbers of students obtaining grades A, B, C and D are in the ratio 4 : 12 : 9 : 5, respectively. Calculate the number of students obtaining each grade. Explain how you could check that your answers are plausible. [4] (c) Novak Djokovic played in tennis matches for a total of 16 hours and 57 minutes to retain the 2021 Australian Open men's singles title. Although the winner's prize money was reduced this year, he still won $2 130 000. (i) Calculate how long Novak played (in minutes) for each dollar that he won in this tournament. Give your answer to three significant figures in both ordinary notation and scientific notation. [4] (ii) Calculate how much Novak won (in dollars) for each hour that he played in this tournament. Give your answer to three significant figures in both ordinary notation and scientific notation. [3]