Part II consists of a separate question and answer book.

TD1 FURMATH CAT 2BSUPERVISOR TO ATTACH PROCESSING LABEL HEREFiguresWordsSTUDENT NUMBERLetterB O A R DOFSUIESVictorian Certificate of Education1999MATHEMATICS: FURTHERCommon Assessment Task 2: Written examination(Facts, skills and applications)Monday 1 November 1999: 11.45 am to 1.30 pmReading time: 11.45 am to 12 noonWriting time: 12 noon to 1.30 pmTotal writing time: 1 hour 30 minutesPART IIQUESTION AND ANSWER BOOKThis task has two parts: Part I (multiple-choice questions) and Part II (short-answer questions).Part I consists of a separate question book and must be answered on the answer sheet provided formultiple-choice questions.Part II consists of this question and answer book.You must complete both parts in the time allotted. When you have completed one part, continueimmediately to the other part.A detachable formula sheet for use in both parts is in the centrefold of the Part I question book.At the end of the taskPlace the answer sheet for multiple-choice questions (Part I) inside the front cover of this question andanswer book (Part II).© BOARD OF STUDIES 1999

FURMATH CAT 2B 2Structure of bookNumber ofquestionsNumber of questionsto be answered3 3Directions to studentsMaterialsQuestion and answer book of 5 pages.You may bring to the CAT up to four pages (two A4 sheets) of pre-written notes.You may use an approved scientific and/or graphics calculator, ruler, protractor, set-square and aids forcurve-sketching.The taskDetach the formula sheet from the centre of the Part I book during reading time.Ensure that you write your student number in the space provided on the cover of this book. Answer allquestions.The marks allotted to each question are indicated at the end of the question.There is a total of 10 marks available.␣You need not give numerical answers as decimals unless instructed to do so. Alternative forms mayinvolve, for example, π, e, surds or fractions.Unless otherwise indicated, the diagrams in this book are not drawn to scale.All written responses should be in English.At the end of the taskPlace the answer sheet for multiple-choice questions (Part I) inside the front cover of this question andanswer book (Part II).

3 FURMATH CAT 2BSpecific instructions for studentsThere are three short-answer questions.Answer all parts of the questions in the spaces provided in this question and answer book.The table below shows the monthly rainfall (in millimetres) and the number of days on which it rained eachmonth for a Victorian rural city in 1998.Table 1: Monthly rainfall data for 1998Jan Feb Mar Apr May June July Aug Sept Oct Nov DecRainfall (mm) 28 31 33 41 53 65 64 56 47 48 34 26Number of rain days 4 5 3 6 9 11 14 12 9 8 6 5Question 1a. Complete the following table by classifying each of the variables in the table as numerical or categorical.VariableType of dataMonthRainfall (mm)numericalNumber of rain days2 marksb. Use the information in Table 1 to determine the percentage of months in 1998 which had more than 10rain days. Write your answer in the space provided.percentage =1 markc. Using the data in Table 1, calculate the standard deviation of the number of rain days. Write your answercorrect to two decimal places in the space provided.standard deviation =2 marksTotal 5 marksTURN OVER

FURMATH CAT 2B 4The following scatterplot was constructed from the data in Table 1 to investigate the relationship betweenmonthly rainfall and the number of days it rains each month.706050rainfall(mm)4030201000 5 10 15number of rain daysQuestion 2a. Plot the point that represents the data for December on the scatterplot.1 markb. The value of Pearson’s product moment correlation coefficient, found from the data in Table 1, isr = 0.9308, correct to four decimal places. What is the value of the coefficient of determination, correct tothree decimal places?1 markc. The key assumption made about the nature of the relationship between monthly rainfall and the number ofrain days, when calculating Pearson’s product moment correlation coefficient, is that the relationship is1 markTotal 3 marks

5 FURMATH CAT 2BWhen a least squares regression line is fitted to the data in Table 1, its equation is found to berainfall = 15.2 + 3.7 × number of rain days.Question 3a. Complete the following sentence by filling in the box.From the regression equation we can conclude that monthly rainfall increases on average bymillimetres for each extra day it rains in the month.1 markb. Use the regression equation to predict the rainfall (in millimetres) of a month in which it rains for 10 days.rainfall = mm1 markTotal 2 marksEND OF PART II QUESTION AND ANSWER BOOK