Victorian Certificate of Education 2021

1 further MATHEMATICSW ritten examination 1 Friday 29 October 2021 Reading time: pm to pm (15 minutes) Writing time: pm to pm (1 hour 30 minutes)MULTIPLE-CHOICE QUESTION BOOKS tructure of bookSectionNumber of questionsNumber of questions to be answeredNumber of modulesNumber of modulesto be answeredNumber of marksA Core242424B Modules32164216 Total 40 Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners, rulers, one bound reference, one approved technology (calculator or software) and, if desired, one scientific calculator. Calculator memory DOES NOT need to be cleared. For approved computer-based CAS, full functionality may be used. Students are NOT permitted to bring into the examination room: blank sheets of paper and/or correction supplied Question book of 35 pages Formula sheet Answer sheet for multiple-choice questions Working space is provided throughout the Check that your name and student number as printed on your answer sheet for multiple-choice questions are correct, and sign your name in the space provided to verify this.

2 Unless otherwise indicated, the diagrams in this book are not drawn to the end of the examination You may keep this question book and the formula are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room. Victorian CURRICULUM AND ASSESSMENT AUTHORITY 2021 Victorian Certificate of Education 20212021 FURMATH EXAM 1 2 THIS PAgE IS BLANK 3 2021 FURMATH EXAM 1 TURN OVERTHIS PAgE IS BLANK 2021 FURMATH EXAM 1 4 SECTION A continuedSECTION A CoreInstructions for Section AAnswer all questions in pencil on the answer sheet provided for multiple-choice the response that is correct for the correct answer scores 1; an incorrect answer scores will not be deducted for incorrect marks will be given if more than one answer is completed for any otherwise indicated, the diagrams in this book are not drawn to analysisUse the following information to answer Questions 1 percentaged segmented bar chart below shows the age (under 55 years, 55 years and over) of visitors at a travel convention, segmented by preferred travel destination (domestic, international).

3 Under 55 years55 years and over10095908580757065605550percentage454 035302520151050 Keydomesticinternationalage (years)Question 1 The variables age (under 55 years, 55 years and over) and preferred travel destination (domestic, international) areA. both categorical both numerical a numerical variable and a categorical variable a categorical variable and a numerical variable a discrete variable and a continuous variable respectively. 5 2021 FURMATH EXAM 1 SECTION A continuedTURN OVERQ uestion 2 The data displayed in the percentaged segmented bar chart supports the contention that there is an association between preferred travel destination and age becauseA. more visitors favour international 35% of visitors under 55 years favour international 45% of visitors 55 years and over favour domestic 65% of visitors under 55 years favour domestic travel while 45% of visitors 55 years and over favour domestic the percentage of visitors who prefer domestic travel is greater than the percentage of visitors who prefer international FURMATH EXAM 1 6 SECTION A continuedQuestion 3 The results could also be summarised in a two-way frequency one of the following frequency tables could match the percentaged segmented bar chart?

4 Travel destinationUnder 55 years55 years and overdomestic 91 90international travel destinationUnder 55 years55 years and overdomestic 65 35international 45 55 Total110 travel destinationUnder 55 years55 years and overdomestic 35 55international 65 travel destinationUnder 55 years55 years and overdomestic 50 70international 100 travel destinationUnder 55 years55 years and overdomestic 71 39international 29 61 Total100100 7 2021 FURMATH EXAM 1 SECTION A continuedTURN OVERQ uestion 4 The boxplots below show the distribution of the length of fish caught in two different ponds, Pond A and Pond APond BBased on the boxplots above, it can be said thatA. 50% of the fish caught in Pond A are the same length as the fish caught in Pond 50% of the fish caught in Pond B are longer than all of the fish caught in Pond 50% of the fish caught in Pond B are shorter than all of the fish caught in Pond 75% of the fish caught in Pond A are shorter than all of the fish caught in Pond 75% of the fish caught in Pond B are longer than all of the fish caught in Pond FURMATH EXAM 1 8 SECTION A continuedQuestion 5 The stem plot below shows the height, in centimetres, of 20 players in a junior football : 14|2 = 142 cm n = 201422478 891500125 568160112179A player with a height of 179 cm is considered an outlier because 179 cm is greater than A.

5 162 cmB. 169 cmC. cmD. 173 cmE. cmQuestion 6 The relationship between resting pulse rate, in beats per minute, and age group (15 20 years, 21 30 years, 31 50 years, over 50 years) is best displayed usingA. a a parallel a time series a back-to-back stem the following information to answer Questions 7 and participants auditioned for a stage musical. Each participant was required to complete a series of ability tests for which they received an overall overall scores were approximately normally distributed with a mean score of points and a standard deviation of 7 Only the participants who scored at least points in the audition were considered the 68 95 rule, how many of the participants were considered unsuccessful?

6 A. 127B. 128C. 272D. 672E. 673 9 2021 FURMATH EXAM 1 SECTION A continuedTURN OVERQ uestion 8To be offered a leading role in the stage musical, a participant must achieve a standardised score of at least participants names and their overall scores are given in the table one of the following statements is true?A. Only Amy was offered a leading Only Cherie was offered a leading Only Brian was not offered a leading role. D. Both Brian and Cherie were offered leading All three participants were offered leading 9 The heights of females living in a small country town are normally distributed: 16% of the females are more than 160 cm tall. of the females are less than 115 cm mean and the standard deviation of this female population, in centimetres, are closest toA.

7 Mean = 135 standard deviation = 15B. mean = 135 standard deviation = 25C. mean = 145 standard deviation = 15D. mean = 145 standard deviation = 20E. mean = 150 standard deviation = 10 Question 10 Oscar walked for nine consecutive days. The time, in minutes, that Oscar spent walking on each day is shown in the table least squares line is fitted to the data. The equation of this line predicts that on day 10 the time Oscar spends walking will be the same as the time he spent walking on A. day 3B. day 4C. day 6D. day 8E. day 92021 FURMATH EXAM 1 10 SECTION A continuedQuestion 11 The table below shows the weight, in kilograms, and the height, in centimetres, of 10 (kg)Height (cm)591736718069184841956417374180761925 61695816466180A least squares line is fitted to the data.

8 The least squares line enables an adult s weight to be predicted from their number of times that the predicted value of an adult s weight is greater than the actual value of their weight isA. 3B. 4C. 5D. 6E. 7 11 2021 FURMATH EXAM 1 SECTION A continuedTURN OVERQ uestion 12 The time series plot below shows the quarterly sales, in thousands of dollars, of a small business for the years 2010 to ($000s)yearThe time series plot is best described as havingA. seasonality irregular fluctuations seasonality with irregular a decreasing trend with irregular a decreasing trend with seasonality and irregular FURMATH EXAM 1 12 SECTION A continuedQuestion 13 The time series plot below shows the points scored by a basketball team over 40 games.

9 150140130120110100900510152025303540game numberpointsscoredThe nine-median smoothed points scored for game number 10 is closest toA. 102B. 108C. 110D. 112E. 117 Question 14A garden centre sells garden table below shows the daily quantity of garden soil sold, in cubic metres, over a one-week MondayTuesdayWednesdayThursdayFridaySatu rdaySundayQuantity (m3)234186346346 The quantity of garden soil sold on Wednesday, Thursday and Friday is not shown. The five-mean smoothed quantity of garden soil sold on Thursday is 206 three-mean smoothed quantity of garden soil sold on Thursday, in cubic metres, is A. 143B. 166C. 206D. 239E. 403 13 2021 FURMATH EXAM 1 SECTION A continuedTURN OVERQ uestion 15 The table below shows the number of visitors to an art gallery during the summer, autumn, winter and spring quarters for the years 2017 to quarterly average is also shown for each of these quarter29 68525 42031 496autumn quarter27 46223 32029 874winter quarter25 56421 09727 453spring quarter26 06522 89728 149 Quarterly average27 seasonal index for summer is closest to A.

10 16 The number of visitors to a regional animal park is is collected and deseasonalised before a least squares line is equation of the least squares line isdeseasonalised number of visitors = 2349 month numberwhere month number 1 is January seasonal indices for the 12 months of 2020 are shown in the table number123456789101112 Seasonal actual number of visitors predicted for February 2020 was closest toA. 1562B. 1697C. 1952D. 2245E. 24402021 FURMATH EXAM 1 14 SECTION A continuedRecursion and financial modellingQuestion 17 The following recurrence relation can generate a sequence of = 37, Ln + 1 = Ln + CThe value of L2 is value of C isA. 6B. 4C. 4D. 6E. 37 Use the following information to answer Questions 18 and invests $500 000 in an annuity that provides an annual payment of $44 is calculated first five lines of the amortisation table are shown numberPayment ($)Interest ($)Principal reduction ($)Balance ($)0 18 The principal reduction associated with payment number 3 isA.