Question2 - 30marks

ThisquestionisbasedonyourworkonMU123uptoandincludingUnit4.

AnITcompanydevelops softwareforthehospitalitysector. Ittestsitscode usinganindustrystandard softwarepackage. Aimingtoexpanditsbusiness 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 1.

Table 1 Comparison of test times in minutes for the industry standard and in-house software testing packages

Testnumber	Industrystandardsoftwarepackage	In-housesoftwarepackage
1	349	318
2	332	327
3	336	303
4	395	337
5	368	311
6	391	329
7	296	321
8	361	327
9	648	330
10	375	347
11	302	311
12	347	331
13	379	340
14	384	343
15	358	328
16	369	341
17	308	317
18	341	325
19	385	346
20	378	337
(a)(i)	Whichofthethreetypes ofinvestigationdiscussedon pages210-214ofUnit4isthis? Explainyouranswer briefly.
(ii)	Are these primary or secondary data, from the researcher's point of view? Explain your answer briefly.

1. Spendafewminutesscanning thesedatasetsbyeye.
   1. List any threefeatures thatyou shouldbe lookingfor when

scanningdatasetsbyeye.

1. Commentonwhetherornotyouthinktheremightbeaproblem

withanyofthemostextremevaluesineachcolumn.

1. Copyandcompletethefollowing tableusingthedatasetsgivenaboveto

workoutthemissingvalues.

	Numberofminutestocompletethetest
Industrystandard	In-house
Minimum(Min)
Lowerquartile (Q1)	338.5	319.5
Median	364.5	328.5
Upperquartile(Q3)	381.5	338.5
Maximum(Max)
Mean	370.1	328.45
Standarddeviation(SD)	69.8	12
Interquartilerange(IQR)
Range
Sizeofdataset(n)	20	20

1. (i) Identify thetwo measuresof locationfrom thetable inpart (c).

Usebothofthesemeasures todeterminewhich ofthetwodatasets

hasthehigherlocation.

(ii) Identifythethreemeasuresofspreadfromthetableinpart(c).

Whichof the two datasets has the wider spread,as measured by

eachofthese threemeasures?

1. (i) Theresearcherconcludes thatthein-house softwarepackageruns quicker than the industry standard software package. Is this a reasonableconclusion?Explain youranswerbriefly.

(ii) Which stageofthestatisticalinvestigationisusedinpart(e)(i)?

Brieflyjustifyyouranswer.

1. The researcher notices that the industry standard software packageentry for the ninth test was a typing error.The correct value should have been 348. The revised mean and median for the industry standard softwarepackage datawiththecorrectvalue fortheninth testaregiven in the following table.

	Industrystandardsoftwarepackage
Withtypingerror	Withcorrectvalue
Mean	370.1	355.1
Median	364.5	359.5

Whatistheeffectonthemeanandonthemedianofincluding the

typingerrorinstead ofthecorrectvalue?Explain whythishappens.

1. Wouldhavingthecorrectvalue affecttheresearcher'sconclusionin part(e)(i)?Explainyouranswer briefly.

Please answer all parts accurately. Many thanks

(2) Show how the student should have performed the check. Question 4 - 25 marks This question is based on your work on MU123 up to and including Unit 5. (a) Simplify each of the following expressions as far as possible; multiply out any brackets, expand any algebraic fractions, and collect like terms together. Show your working. (1) 8(7 -6t) (ii) 11 + m(15 - 7m) - 15m (iii) 16t - 8(78 -5t) (iv) 8p(7 + 9p2) - 4(8p - 6+ 3p3) (v) 4x 4 36x - 28 4x (b) Solve the following equations. Show your working and check that your answers are correct. (i) 18a - 16 - 8 4 12a [4] (ii) 4 - 5- 3(3 -9) Question 5 5 marksQuestion 3 15 marks This question is based on your work on MU123 up to and including Unit 5. In this question, you are asked to comment on a student s incorrect attempt at answering the question detailed below. The question (1) Simplify the following expression as far as possible, showing all your working: 9y - 12 - 4y + 37. (ii) Solve the following equation, showing all your working: (t + 6) = 28. The student's incorrect attempt: Given: 9y - 12 - 4y + 37 Group like terms: 9y - 4y - 12 + 37 Collect like terms: = 5y + 25 Subtract 25: - 25 = 5y Divide by 5: 5 =y The solution is y = 5 (1i) Given: (t + 6) = 28 Clear the fraction: Multiply by 4: 4(t + 54) =252 Subtract 216 4t + 216 = 252 Divide by 4: 4t = 36 t= 9 The solution is t = 9. (a) The student has made a mistake in both parts of their attempt. Identify these mistakes and explain, as if directly to the student, why, for each mistake, their reasoning is incorrect. [4] (b) Write out your own solution to each part of the question, explaining your working.(c) The student decides to check if the solution they got to part (ii) of the question was correct using the following approach: Check Substitute 9 for t: (9+6) = 28 y Work out the brackets: - (15) = 28 y Giving: DU = 28 9 This is incorrect so the solution t = 9 is incorrect. (1) Explain why the approach to checking that they have chosen is incorrect. (2) Show how the student should have performed the check. Question 4 25 marksQuestion 1 25 marks This question is based on your work on MU123 up to and including Unit 3. (a) (1) 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. [4] (ii) Calculate 3 1 7 4 9 12' leaving your answer as a fraction in its simplest form, showing all your working. [4] (iii) Simplify the surd 5 8 + 45 40 by writing it as a surd in its simplest form, showing your working. [3] (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 as possible. (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. [3]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. (ii) Calculate 7 19 12 leaving your answer as a fraction in its simplest form, showing all your working. [4] (iii) Simplify the surd 5V8 VAO V45 by writing it as a surd in its simplest form, showing your working. [3] (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 as possible. [3) (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. [4] (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. [4) (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. [3