Instructions for completing TMAs and math questions
You will find instructions for completing TMAs in the ‘Assessment’ area of the MU123 website. Please read these instructions before beginning work on this TMA.
Reviewing your tutor’s comments on your previous TMA will help you as you work on this one.
Remember that you need to explain your reasoning and communicate your ideas clearly, as described in Subsection 5.3 of Unit 1. This includes:
explaining your mathematics in the context of the question the correct use of notation and units appropriate rounding. Your score out of 5 for good mathematical communication (GMC) will be recorded against Question 5. You do not have to submit any work for Question 5.
PLAGIARISM WARNING – the use of assessment help services and websites The work that you submit for any assessment on any module should be your own. Submitting work produced by or with another person, or a web service or an automated system, as if it is your own is cheating. It is strictly forbidden by the University.
You should not: provide any assessment question to a website, online service, social media platform or any individual or organisation, as this is an infringement of copyright. request answers or solutions to an assessment question on any website, via an online service or social media platform, or from any individual or organisation. use an automated system (other than one prescribed by the module) to obtain answers or solutions to an assessment question and submit the output as your own work.
The University actively monitors websites, online services and social media platforms for answers and solutions to assessment questions, and for assessment questions posted by students. Work submitted by students for assessment is also monitored for plagiarism. A student who is found to have posted a question or answer to a website, online service or social media platform and/or to have used any resulting, or otherwise obtained, output as if it is their own work has committed a disciplinary offence under Section SD 1.2 of our Code of Practice for Student Discipline. This means the academic reputation and integrity of the University has been undermined.
The Open University’s Plagiarism policy defines plagiarism in part as: using text obtained from assignment writing sites, organisations or private individuals. obtaining work from other sources and submitting it as your own. If it is found that you have used the services of a website, online service or social media platform, or that you have otherwise obtained the work you submit from another person, this is considered serious academic misconduct and you will be referred to the Central Disciplinary Committee for investigation.
Mathematical Questions on Prime Factors, Ratios, and Time and Money Calculations
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 3780 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.
3 1 7
4 − 9 + 12 ,
leaving your answer as a fraction in its simplest form, showing all your working.
(iii)Simplify the surd
√40 + 45
by writing it as a surd in its simplest form, showing your working.
(b)A group of 420 students are required to take a test. Of these, 390 actually take the test, and 30 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
(ii)Of the 390 students who take the test, the numbers of students obtaining grades A, B, C and D are in the ratio 5 : 13 : 9 : 3, respectively. Calculate the number of students obtaining each grade. Explain how you could check that your answers are plausible.
(c)Naomi Osaka played in tennis matches for a total of 8 hours and 59 minutes to win the 2021 Australian Open women’s singles title.
Although the winner’s prize money was reduced this year, she still won $2 130 000.
(i)Calculate how long Naomi played (in minutes) for each dollar that she won in this tournament. Give your answer to three significant figures in both ordinary notation and scientific notation.
(ii)Calculate how much Naomi won (in dollars) for each hour that she played in this tournament. Give your answer to three significant figures in both ordinary notation and scientific notation.
Question 2 –30 marks
This question is based on your work on MU123 up to and including Unit 4. An IT company develops software for the hospitality sector. It tests its code using an industry standard software package. Aiming to expand its business and be more competitive in the sector, the company has decided to pilot an in-house software package to test its code. A company researcher wishes to compare the times taken for each package to complete tests. Both software packages were run on 20 occasions testing the same code. The researcher records the times taken on each occasion, and these are shown in Table.