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QUESTION 1 Four linear models have been developed for a data set. Identify the residual plot that indicates that the developed linear model is justified. (A) (B) ©) (D)
QUESTION 2 The standard Australian time zones are shown on the map. : GMT 9.5 All states and territories except Western Australia (WA) Queensland (QLD) and the Northern Territory (NT) have daylight saving in summer. Daylight saving time is 1 hour ahead of standard time. When it is 10:00 am daylight saving time in New South Wales (NSW) it is (A) 9:30 am in South Australia (SA) and 9:00 am in QLD. (B) 9:30 am in SA and 11:00 am in QLD. (C) 10:30 am in SA and 9:00 am in QLD. (D) 10:30 am in SA and 11:00 am in QLD.
QUESTION 3 For the sequence 4 2 0 —2 —4 ... the common difference is (A) 4 B) 2 C) =2 (D) -4
QUESTION 4 Which of the following graphs could be modelled using a geometric sequence? (A) © 30 25 20 t 15 10 5 - - (B) (D) 30 25 20 t 15 10 5 0 30 25 20 {15 10 - o 1 2 3 4 5 6
QUESTION 5 Determine the equation of the least-squares line where » =0.926 x =5.2 s = 2.3 y = 68.6 and s =41.7. (A) y=16.79x—-1146.51 (B) y=16.79x-18.70 (C) y=0.05x+68.33 (D) y=0.05x+1.70
QUESTION 8 The following scatterplot shows a linear association between two numerical variables. 30 25 20 y 15 10 Choose the best description for the direction and strength of the association. (A) strong positive (B) strong negative (C) weak positive (D) weak negative
QUESTION 9 It 1s observed that as the number of ice blocks sold each month increases the number of fans sold also increases. Which of these statements is therefore true? (A) (B) ©) (D) There 1s a negative causation between the number of ice blocks sold and the number of fans sold each month. There 1s a positive causation between the number of ice blocks sold and the number of fans sold each month. There 1s a negative association between the number of ice blocks sold and the number of fans sold each month. There 1s a positive association between the number of ice blocks sold and the number of fans sold each month.
QUESTION 10 Which of the following graphs represents a time series plot with a three-point moving average? (A) 20 —e—original data 15 -3 - smoothed data Number 10 5 0 I ] S Q (B) 20 15 —e—original data -3- smoothed data Number 10 ON <t O o0 S o <t \O < > - o — — — — O S S S ) S O S [@\| o o o o o o o Year ©) 20 . ——original data 15 - - smoothed data Number 10 5 0 I (] S [@\| (D) 20 15 —e—original data -3 - smoothed data Number 10
QUESTION 14 A sample of university staff and students was asked whether they preferred catching public transport or driving their own car to university. The data collected is shown in the table. Public transport Drive own car What percentage of university students prefer to drive their own car? A) 12% (B) 15% C) 20% (D) 40%
QUESTION 17 (3 marks) Calculate the distance along the parallel of latitude between Mount Gambier South Australia (37° 50' S 140° 47 E) and Bairnsdale Victoria (37° 50' S 147° 37 E) to the nearest kilometre.
QUESTION 18 (4 marks) Exhibition organisers believe that the number of attendees increases each day as an arithmetic sequence. The organisers know that 353 people attended the first day and 439 people attended the third day. a) Determine the common difference. [2 marks] b) Use the result from 18a) to predict the number of people who will attend the sixth day. [2 marks]
QUESTION 19 (4 marks) Data was collected relating the number of hours spent fishing and the total number of fish caught. The linear model for this data was found to be y = 2.3x + 31.4 where x is the number of hours spent fishing and y is the total number of fish caught. a) Use the model to predict the number of fish caught if 12 hours were spent fishing. [1 mark] b) The correlation coefficient for this data is 0.688 and the coefficient of determination is 0.473. Use each of these to describe the strength of the linear association between the two variables and decide if your prediction is valid. [3 marks]
QUESTION 22 (4 marks) A store asked its junior and senior staff whether or not they would like to change the store uniform. The results are in the frequency table. Change uniform ‘ Do not change uniform Junior staff Senior staff a) Convert the two-way table into a percentaged two-way frequency table using column totals. [2 marks] b) Explain whether there is an association between staff groups and a desire to change the store uniform. [2 marks]
QUESTION 23 (4 marks) A plane leaves Brisbane (UTC +10) at 10:45 pm on Monday and takes 14 hours and 35 minutes to fly to Dubai (UTC +4). Determine the local time and day in Dubai when the plane arrives.
QUESTION 24 (4 marks) The following data for the height of five seedlings was collected and the least-squares line was developed and graphed. 34 30 e 26 2 en 22 = ':g 18 S 14 = 10 i 6 i O 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Time since planting (days) a) Use the least-squares line to estimate the height of a nine-day-old seedling. [1 mark] b) Classify the prediction for 24a) as either interpolation or extrapolation. [1 mark] c) Based on the graph the following statement was made: ‘A seedling will reach a height of about 32 cm by day 29. Comment on the reasonableness and the possible dangers of this statement. [2 marks]
QUESTION 26 (5 marks) A scientist observed that the population of a specific bird species is decreasing by 17% each year and that at the beginning of 2016 there were 483 birds. a) Use a geometric sequence to model the bird population. [2 marks] b) Using the model from 26a) predict the number of birds remaining at the beginning of 2021. [3 marks]
QUESTION 1 (5 marks) A water tank contains 12 500 L of water. The tap is accidently left on and the tank loses 135 L per minute. The tap 1s turned off when the tank has 5000 L of water left. Use a mathematical model to determine how long the tap was left on to the nearest minute.
QUESTION 2 (5 marks) The number of people living in each household and the average daily household water usage measured in litres (L) were recorded for 10 households. Number of people average dailyhousehold 160 | 320 | 480 | 410 | 280 | 240 | 130 | 940 | 1340 water usage (L) Calculate Pearson’s correlation coefficient and then evaluate the appropriateness of using this coefficient for the association between daily water usage and the number of people living in a household. 1400 1200 1000 800 600 400 200 Average daily household water usage (L) 0 1 2 3 4 5 6 7 8 Number of people in each household
QUESTION 3 (6 marks) The least-squares line for a sample of five data points was found to be y = 2.1875x + 0.0625 with a correlation coefficient of » = 0.875. Determine a set of values for p and ¢ given that these values differ by 3.
QUESTION 4 (5 marks) The following data shows the profits per quarter for a company for the last two years. Quarter Profit ($°000s) Deseasonalise the data and plot this on the same set of axes as the original data in the graph on the next page. Profit ($°000s) 190 180 170 160 150 140 130 120 110 100 90 80 70 60 > Ql Q2 Q3 Q4 Ql Q2 Q3 Q4 ———-— 2018 ———— e ) =]
QUESTION 1 The second smoothed value for the 3-point moving average is Day | 123|456 awe | 5 [0 w9 0w (A) 32 (B) 25 (C) 20 (D) 18
QUESTION 3 The table shows the results of a student survey about their preferred movie genre. 2 Of the students who preferred comedy what percentage were in Year 9 or higher? (A) 25% (B) 30% (C) 60% (D) 75%
QUESTION 4 A confounding variable is a variable that (A) can only take on a certain number of values. (B) remains constant throughout a statistical investigation. (C) 1s used to predict a difference in the response variable. (D) other than the explanatory variable influences the response variable.
QUESTION 6 These scatterplots show the number of high-rises in a city and their distance from the city centre. Which scatterplot was used to extrapolate that 25 km from the city centre there were 20 high-rises? (A) ©) 250 p— S O Number of high-rises N O - 250 Number of high-rises o O N O == 0 5 10 15 20 25 Distance from city centre (km) \ y=-5x+ 160 0 5 Distance from city centre (km) 10 15 20 25 (D) Number of high-rises Number of high-rises p— S S N S S 250 p— S S N S S 0 5 10 15 20 25 Distance from city centre (km) y=-3.75x+ 100 0 5 Distance from city centre (km) 10 15 20 25
QUESTION 9 A staircase is to be extended by installing » additional stairs. Each stair is 25 cm high. If the existing staircase reaches 1.2 m off the ground which rule models the total height the stairs will reach in centimetres? (A) t =25+(n-1)x1.45 B) 1 =12+(n-1)x25 (C) t =145+(n-1)x25 (D) 1 =25+(n-1)x120
QUESTION 10 City A is located at 55° N 120° E and City B is located at 40° N 165° E. The sun will rise in City A approximately (A) 1 hour before it rises in City B. (B) 1 hour after it rises in City B. (C) 3 hours before it rises in City B. (D) 3 hours after it rises in City B.
QUESTION 11 Which option is an example of bivariate data? (A) (B) ©) (D) The rating given to a brand of meat pies as poor fair or good. The number of people in a household and amount of water used. The number of cars passing through a particular set of traffic lights. The time a person spends using a mobile phone on a Friday evening.
QUESTION 14 A town’s current population of 15480 is predicted to grow steadily at an annual rate of 12%. The predicted population after 10 years is approximately (A) 48079 (B) 34056 (C) 18576 (D) 17338
QUESTION 16 (4 marks) The table shows the values of bivariate data with variables g and 4. a) Construct a scatterplot of the data with g as the explanatory variable. [2 marks] 11 10 0 1 2 3 4 5 6 7 8 9 10 11 b) Describe the association in terms of form and strength. [2 marks]
QUESTION 18 (4 marks) The table shows the profit made each year (in thousands of dollars) by a small business. a) Use a mathematical model to determine the equation of the least-squares line to fit this data. [2 marks] b) Use the least-squares line to forecast the profit in 2021 to the nearest hundred dollars. [2 marks]
QUESTION 20 (4 marks) A farmer bought a tractor for $45 100 at the start of 2012. It depreciates by $2700 each year. Identify and use a mathematical model to determine the value of the tractor at the start of 2021.
QUESTION 21 (6 marks) The map shows regional federal electorates in Victoria. — — 34°S S — 35°S 36° S 37°S Gippsland 38°S 39° S 141°E 142°E 143° E 144° E 145° E 146° E 147° E 148° E 149°E 150°E a) In which federal electorate is the position 37° 10 S 146° 30 E? [1 mark] b) Determine the distance between point A in the electorate of Mallee and point B in the electorate of Gippsland along the same parallel of latitude to the nearest 100 km. [5 marks]
QUESTION 24 (3 marks) The population of fish in a fish farm pond was recorded every three months. The graph shows the data. 1400 1200 1000 800 600 Population of fish 400 200 0 4 8 12 16 Quarters Describe the time series plot by identifying three key features.
QUESTION 25 (4 marks) A conference is being held in Singapore (UTC +8). a) b) A conference attendee got a flight from Brisbane (UTC +10) at 10:30 am Brisbane time on Monday 7 December. If the flight from Brisbane to Singapore took 7 hours and 40 minutes determine the time day and date in Singapore when the flight lands. [2 marks] A conference attendee from Dubai (UTC +4) arrived in Singapore at 5 pm Singapore time on Monday 7 December. If the flight from Dubai to Singapore took 8 hours and 25 minutes determine the time day and date in Dubai when the flight departed. [2 marks]
QUESTION 1 (4 marks) A sailor anchors her yacht near Rocky Island at 14° 52 S 145° 29 E. Her yacht is at the same latitude as her home but the sun rises exactly 1 hour and 13 minutes later at home. What are the coordinates of her home?
QUESTION 5 (6 marks) Researchers gathered a set of data to determine if a model could reliably predict systolic blood pressure given a person’s age. One candidate was 31 years old and had a systolic blood pressure of 119. For this data the correlation coefficient () 1s 0.875 the standard deviation for the person’s age (Sx) is 4 and the standard deviation for the systolic blood pressure (s y) is 6. A residual plot was produced for the model. 7.5 Age Residual (actual — predicted) (e Determine the actual systolic blood pressure to the nearest whole number for the oldest person in the sample (40 years old).
QUESTION 7 (6 marks) The table shows the total number of times a new song is played on a music service in the days following its first release. Number of days since first release Total number of times played (’000s) The songwriter is paid 0.175 cents every time their song is played and will be paid after 60 days. They predict that by that time they will be owed at least $1000. Given that the number of times the song is played is increasing exponentially evaluate the reasonableness of this prediction.
QUESTION 3 The table shows the minimum and maximum temperatures on January 1 each year in Bundaberg. (A) ©) Temperature (°C) Temperature (°C) N N 24 23 22 21 2017 2018 2019 2020 2021 Year 2017 2018 2019 2020 2021 Year (B) (D) Which time series plot best represents the mean temperatures? Temperature (°C) Temperature (°C) 33 U DN 31 30 29 28 2017 2018 2019 2020 2021 Year 2017 2018 2019 2020 2021 Year
QUESTION 4 A swimmer has a weekly training routine to improve their fitness as modelled by the recursive function T =T +2 where T is the number of laps they swim in week n and 7} = 4. Which graph best represents the swimmer’s routine? (A) (B) 16 0 % 14 —o 0 - 2 = 12 o s g 38 o 5 5 . 5 2 Z s 4 zZ 2 0 0 2 4 6 8 10 12 14 16 2 3 -+ 5 6 Number of laps per week Number of weeks © 6 » (D) s 24 5 d § Gy 5 & o & < 5 O ; = o S S g 2 s = = / o Z = 3 1 /! > 0 ® 0 2 4 6 8 10 12 14 16 0 1 2 3 4 5 6 Number of laps per week Number of weeks
QUESTION 5 The table lists the number of books sold per month by an online bookstore. If the simple 3-point moving average in October is 54 what is the simple 3-point moving average in May? o [ weo [ v [ aor [y [ [ [ e [ sep [ o [ [ e 5w e 6w e 5w 0] 0w (A) 69 (B) 73 (C) 74 (D) 89
QUESTION 8 The scatterplot shows the annual number of visitors to the Great Barrier Reef Marine Park. Visitor number (millions) 3.5 0.5 0 2010 2011 20 12 2013 2014 2015 Year For 2018 the annual number of visitors could best be (A) 1nterpolated as 2.7 million. (B) extrapolated as 2.7 million. ©) interpolated as 3.2 million. (D) extrapolated as 3.2 million. 2016 2017 2018 20 19 2020
QUESTION 10 Which example states an explanatory variable followed by a response variable? (A) car manufacturers and car colours (B) dog breeds and frequency of names (C) plant growth and amount of fertiliser used (D) daily temperatures and daily ice cream sales
QUESTION 11 The equation of a fitted line for the number of free throws in basketball ¢z and the number of hours in a training session 4 18t =26.781 + 12.974 h The predicted number of free throws for a 5-hour training session when rounded to the nearest whole number is (A) 64 (B) 65 (©) 91 (D) 92
QUESTION 12 Identify the scatterplot that best demonstrates a strong negative association. A) (B) o'.. o'.. o'.. o... o... C) & (D) ° ‘: .. ° o . o o e o “o ° ° > 3o 0o ©® o oo ° % Y : ..0 ..O ° o
QUESTION 13 The two-way table summarises the semester 1 results for students enrolled in two courses Machinery and Electrical. Students achieved either satisfactory (S) or unsatisfactory (U). Machinery S U The 10% cell in the table indicates that (A) 10% of all students achieved satisfactory in Electrical. Electrical (B) 10% of all students achieved unsatisfactory in Machinery. (C) 10% of the students who achieved satisfactory in Electrical achieved unsatisfactory in Machinery. (D) 10% of the students who achieved unsatisfactory in Machinery achieved satisfactory in Electrical.
QUESTION 14 A rugby fan in Perth (Australia) plans to watch a live match played in New Zealand next winter. The time zone for Perth is UTC +8. The time zone for New Zealand is UTC +13 in winter and UTC +12 in summer. If the match 1s played at 6:30 pm New Zealand time what time will the match be viewed in Perth? (A) 1:30 pm (B) 2:30 pm (C) 10:30 pm (D) 11:30 pm
QUESTION 15 The actual distance between two cities has been correctly calculated as 556 km. The latitude and longitude respectively of these two cities could be (A) 2°N 104° W and 3° S 104° W. (B) 2°N 104° W and 3° N 104° W. (C) 25°N 150° E and 30° S 150° E. (D) 25°N 145° E and 25° N 150° E.
QUESTION 16 (3 marks) The table shows the number of sales for a small business in their first six months of trading. 4 226 240 335 a) Use your calculator to determine the equation of the least-squares line. [1 mark] b) Use the equation from Question 16a) to predict the number of sales in the 21st month. [2 marks]
QUESTION 18 (4 marks) The number of songs on a person’s playlist n in each week since joining a music streaming service ¢ forms an arithmetic sequence as shown by the graph. 700 % 600 575 > % 500 = 0453 o 2 400 S ®33] «w 300 o _qné 200 e209 Z 100 eR7 0 0 1 2 3 4 5 6 Time (weeks) Use the arithmetic sequence to predict the number of songs on this person’s playlist 25 weeks after joining the streaming service.
QUESTION 19 (4 marks) The graph shows the amount of rainfall (in mm) for each quarter from 2016 to 2021. 250 200 e g = 150 g s (2 o = 100 o £ < 50 O i | | | i ' | i | | | | | i | | | i 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 | | | ] L 1 2016 2017 2018 2019 2020 2021 Quarters (each year) a) Describe the long-term trend and seasonality of the time series data. [2 marks] b) A least-squares line was fitted to the data with y representing the amount of rainfall and x representing the number of quarters since the beginning of 2016 (e.g. x = 5 for the first quarter of 2017). y=1.763x+ 156.5 Interpret the y-intercept and slope of the fitted line. [2 marks]
QUESTION 22 (4 marks) Marovoay and Iakora are located on the same meridian at 46.6° E as shown on the map of Madagascar. 45°E 50°E 15°S ° Marovoay 20° S Iakora ° 25° S a) Determine the latitudes of Marovoay and lakora. [1 mark] b) Use the result from Question 22a) to determine the shortest distance between Marovoay and Iakora. [3 marks]
QUESTION 23 (4 marks) The least-squares line has been provided for a scatterplot that shows the association between an employee’s years of experience n and their hourly pay p. 60 50 » 40 3 > 30 5 S = 20 10 0 2 4 6 8 10 12 Years of experience a) Given that the least-squares line passes directly through the points (2 20) and (7 40) determine its equation. [2 marks] b) Use the equation from Question 23a) to predict the hourly pay of an employee with 15 years experience. [2 marks]
QUESTION 24 (5 marks) The maximum temperature and the number of pies sold each day at a bakery are provided in the table. Maximum e [ [ [ » [ [ [ ] a) Construct a scatterplot to display the data on the grid provided. [3 marks] b) Describe the association between the maximum temperature and the number of pies sold in terms of direction and strength. [2 marks]
QUESTION 1 (4 marks) The table shows a swimwear company’s seasonally adjusted swimsuit sales (in thousands). Season e Seasonally adjusted swimsuit sales (in thousands) The long-term seasonal indices for spring summer and winter are 1.11 1.42 and 0.62 respectively. Determine the actual swimsuit sales for autumn.
QUESTION 3 (5 marks) In a company’s first 10 years of operation the average annual profit (y) was $9660 with a standard deviation (s ) of $3010. Fitting a least-squares line to the data comparing annual profit (») to the year of operation (x) produced a correlation coefficient of 0.9987. Show that the predicted profit to the nearest dollar for this company in the 11th year of operation will be $15121.
QUESTION 6 (7 marks) The first three lines in a pattern have the equations given. Their slopes form the terms of one sequence and their y-intercepts form the terms of another sequence. Each sequence is either arithmetic or geometric. Line 1: y=-0.8x + 1.2 Line2: y=0.4x+2.7 Line3: y=-0.2x+ 4.2 Determine the coordinates of the point where Line 5 in the pattern intersects Line 1.
QUESTION 7 (7 marks) You live in Queensland and your friend is on a cruise ship holiday. As their ship departs from X to travel 1350 km due west to Tarawa your friend sends you a message saying ‘Local time 6:12 am Wednesday and enjoying the sunrise as our ship begins its trip to Tarawa’. Queensland Not to scale Key ==—=-International date line = «sseeeeee Time zone You plan to phone your friend as soon as they arrive in Tarawa. Assuming their ship is travelling at 50 km/h determine the time in Queensland when you will phone your friend.
QUESTION 1 A linear association with a correlation coefficient of 0.23 is best described as (A) weak positive. (B) weak negative. (C) strong positive. (D) strong negative.
QUESTION 2 A time series plot is shown. Profit ($’000) oO 0 2 + 6 8 10 12 14 16 Time (years) It could best be described as (A) cyclical. (B) seasonal. (C) irregular. (D) increasing.
QUESTION 4 Athletes were surveyed about their preferred shoe brand: X Y or Z. The results are shown in the frequency table. mw | | | | The percentage of field athletes who prefer brand Y is (A) 12% (B) 15% (C) 30% (D) 40%
QUESTION 5 A scatterplot is created to identify the nature of the relationship between two variables: vehicle age and distance travelled. Which statement is correct? (A) The vertical axis should show vehicle age as the response variable. (B) The horizontal axis should show vehicle age as the explanatory variable. (C) The horizontal axis should show distance travelled as the response variable. (D) The vertical axis should show distance travelled as the explanatory variable.
QUESTION 6 In January 2022 40 fish were released into a new dam that has the capacity to support 10 000 fish. It is predicted that the dam will reach its capacity in January 2030 if the fish population doubles every year. Which sequence rule models the prediction? (A) ¢ =tr° ) where t = 40 r=2 n=8 (B) ¢ =t r° Y where t = 40 r= 2 n=9 (C) t =t +(n—l)d where t; = 40 d=2 n=8 (D) ¢ =t +(n—l)d where t = 40 d=2 n=9
QUESTION 7 Which statement is always true for a causal relationship between an explanatory variable and a response variable? (A) (B) (C) (D) One of the variables is a confounding variable. The relationship is explained by a third variable. There is a positive association between the variables. The response variable is dependent on the explanatory variable.
QUESTION 9 Determine the 6th term of the arithmetic sequence that begins 3 9 ... (A) 21 (B) 33 (C) 45 (D) 729
QUESTION 10 Annual sales data and related quarterly indices are shown. The quarterly indices were calculated by applying the average percentage method using the mean. 0 Determine the values for x and y.
QUESTION 14 A calculator is used to determine the equation of the least-squares line for the plant growth data in the table. What is the correct equation? (A) d=0.6h+5.7 (B) h=0.6d+5.7 (C) d=5.7h+0.6 (D) h=5.7d+0.6
QUESTION 15 The resale value of a boat shows geometric decay. Resale value ($) 50000 40000 32 000 Determine the resale value four years after purchase. (A) $16 000 (B) $20 480 (C) $22 000 (D) $25 600
QUESTION 16 (3 marks) If it is 2:00 am local time in town A (30° N 90° W) calculate the local time in town B (26° S 120° E).
QUESTION 18 (4 marks) The locations of three space research sites in Australia are listed in the table. 120° E 130° E 140° E 10°S 10°S Northern Territory 20° S 20° S Western Australia 30°S 30°S 40° S 40° S 110° E 120° E 130° E 140° E a) Which site is closest to the equator? [1 mark] b) Name the state or territory in which site A 1s located. [1 mark] c) Determine and explain which two sites are in the same standard time zone. [2 marks]
QUESTION 22 (4 marks) A person used a fitness tracker to monitor their hours of sleep and the distance they travelled each day. Sleep (hours) Distance (km) a) Using distance as the response variable display the data in a scatterplot with labelled axes. [3 marks] a a a a b) Identify the direction of the association between hours of sleep and distance travelled. [1 mark]
QUESTION 25 (5 marks) The map shows a land border from X to Y. 130° E 134° E 138° E 142° E 146° E 150° E 6°S 8°S 10°S 130° E 134° E 138° E 142° E 146° E 150° E a) State the latitude and longitude of X to the nearest degree. [1 mark] b) State the latitude and longitude of Y to the nearest degree. [1 mark] c) Calculate the distance between X and Y in kilometres. [3 marks]
QUESTION 2 (4 marks) Buffalo fly bites cause skin wounds on cattle. The table shows the average number of skin wounds per animal in a herd for two years. Deseasonalise the data.
QUESTION 4 (5 marks) Hiroki believes that more fish are caught on warmer days. Jiro believes that the number of fish caught in a day is more dependent on the number of people fishing. Bivariate datasets for six days are shown. Temperature ¢ (°C) Number of fish caught f Calculate the correlation coefficient for each dataset and use the results to identify the explanatory variable for the stronger linear association. Use the least-squares line equation for the stronger linear association to predict the number of fish caught on a 25 °C day when 50 people are fishing.
QUESTION 5 (7 marks) At 9:00 am a security guard begins their patrol of the eight work sites represented in the network diagram starting and ending at site A. They drive at 40 km/h on the roads between sites and check every site once for 15 minutes. The length (km) of each road corresponds to the terms of the arithmetic sequence ¢ = ¢ + 2(n — 1) where ¢ = 1. Determine the earliest possible time the security guard can finish their patrol and identify the route they must follow. B ty C
QUESTION 6 (7 marks) The table shows the average superannuation account balance for workers of various ages in two different industries. The coefficient of determination R? for age versus account balance is 0.95 for industry A and 0.96 for industry B. 40-year-old Leigh works in the industry for which age explains a higher percentage of the account balance variation. Tony is 10 years older than Leigh and works in the other industry. Account balance ($) Age (years) Industry A Industry B 42.000 60.000 Use linear models to predict the difference in current superannuation account balances for Leigh and Tony.
QUESTION 4 A sequence is defined by aAn =0a -1 + 14 Given that as = 56 the value of a is A) 14 (B) 28 ©) 42 (D) 70
QUESTION 5 Bivariate data involves (A) two values. (B) two variables. (C) two data displays. (D) two data varieties.
QUESTION 6 25°E 30°E 33 E MEDIT: ERREANEAN SEA : Damietta Alexandria o Port Said : Tanta : o : ;Shubra al : Khaymah ‘e Q 30° N T N Al“J’iZéiH *GAIRO Suez SDFN : Qattara Depression Mount Catherine A Al fayyum o Al Minya ¢ 5 Sharm ash : Shaykh Asyut ® RED 2 SEA /(@ L |oseN 25°E 30°E 35°E Use the map to determine which city is located closest to (31° N 31° E). (A) Tanta (B) Damietta (C) Alexandria (D) Al Fayyum
QUESTION 7 To calculate the number of degrees of longitude across the Earth’s surface for a time zone difference of one hour use 90 @A) 7 90 (B) 54 360 © 0 (D) 360 24
QUESTION 10 The fourth fifth and sixth terms of a geometric sequence are 7.5 3.75 and 1.875 respectively. The sum of the first and second terms in the geometric sequence is A) 15 (B) 30 (C) 45 (D) 90
QUESTION 11 Two variables are displayed on a scatterplot. Which statement below is correct? (A) Only if there 1s a causal relationship between the two variables will they have a positive association. (B) Ifthe two variables have a negative association then there is not a causal relationship between the two variables. (C) [Ifthe two variables are associated either positively or negatively then there could be a causal relationship between the two variables. (D) Ifthe two variables are associated either positively or negatively then there is definitely a causal relationship between the two variables.
QUESTION 12 Quarterly sales figures for a company between 2005 and 2017 were used to determine the following seasonal indices. First quarter Second quarter Third quarter Fourth quarter Swimia | s || o | The table below shows the sales figures for 2018. Season First quarter Second quarter Third quarter Fourth quarter Sales figures ($) 450 075 497 660 480 085 505 025 Determine the seasonally adjusted sales figure for the second quarter of 2018 to the nearest dollar. (A) $428 643 (B) $448 342 (C) $472 579 (D) $552 403
QUESTION 15 The prime meridian is located at (A) 0° latitude. (B) 0° longitude. (C) the intersection of 0° latitude and 0° longitude. (D) the intersection of 0° latitude and 180° longitude.
QUESTION 20 Fitting a least-squares line to create a model from a set of time series data ensures that (A) the distances between the data points and the line of best fit are minimised. (B) the same number of data points are above and below the line of best fit. (C) the distances between the data points and the axes are minimised. (D) the least-squares distances of all data points are added together.
QUESTION 22 (7 marks) A sequence has been defined as t 4 =t +4 t =5 a) Sketch the first six terms of the sequence in graphical form using the grid below. [3 marks] b) Use the rule t = t; + (n — 1)d to model the sequence in simplified form. [2 marks] c) Use the results from 22b) to calculate the 27th term. [2 marks]
QUESTION 23 (6 marks) The number of meals sold (y) by a restaurant each month (x) for the first six months of business is shown on the scatterplot below. The line of best fit its equation and the coefficient of determination (R?) are also shown. Number of meals Month The restaurant was closed for renovations for most of one month. a) Identify the number of meals sold in that month. [1 mark] b) Describe the effect that this outlier has on the coefficient of determination. [1 mark] c) Use the line of best fit to predict the number of meals that will be sold in the 18th month of the business operation. [2 marks] d) Evaluate the reasonableness of your solution for 23c). [2 marks]
QUESTION 24 (4 marks) Students were surveyed regarding their attitudes towards dancing and swimming. The resulting data is displayed in the table below. Enjoy dancing Do not enjoy dancing Enjoy swimming Do not enjoy swimming a) b) ©) Calculate how many students enjoy swimming [1 mark] Calculate how many students were surveyed. [1 mark] Calculate the percentage of students who enjoy both activities. Express your answer correct to two decimal places. [2 marks]
QUESTION 26 (2 marks) The number of students (s) and the number of computers (c) in four secondary schools in Queensland are shown in the table below. Number of students (s) Number of computers (c) 348 307 507 427 798 671 1202 986 a) Identify the response variable. [1 mark] b) Determine a linear relationship for this data by fitting a least-squares line to the data. [1 mark]
QUESTION 27 (3 marks) Use the recursive rule t .q; = 0.65t t; = 120 to complete the following. a) Calculate the percentage by which each term decreases. [1 mark] b) Calculate t4. [2 marks]
QUESTION 28 (3 marks) The approximate coordinates of Geelong Australia are 38°09’ S 144°21 ' E and Kushiro Japan are 43°01' N 144°21' E. Calculate the distance between Geelong and Kushiro to the nearest kilometre.
QUESTION 29 (4 marks) Seoul South Korea is located at approximately 37.6° N 127.0° E. San Francisco United States of America 1s located at approximately 37.6° N 122.4° W. Determine the shortest distance between these two cities to the nearest kilometre.
QUESTION 1 (4 marks) Sara departs from Sydney Australia on Saturday at 6:15 am on a flight to Johannesburg South Africa. The flight takes 14 hours and 18 minutes. Her friend Marcus arrives in Johannesburg from Lima Peru at the same time on a flight that took 18 hours and 15 minutes. The time zones are shown in the following table. Johannesburg South Africa Determine the local time and day that Marcus left Lima.
QUESTION 3 (4 marks) Music students in a school were asked how many hours they practised their musical instrument each week. Seventy-two Year 7 music students were surveyed. The results are shown below. 15 students practised for 2 hours or less. 53 students practised for more than 2 hours and up to 4 hours. 4 students practised for more than 4 hours per week. Seventeen Year 12 music students were surveyed. The results are shown below. 2 students practised for 2 hours or less. 11 students practised for more than 2 hours and up to 4 hours. * 4 students practised for more than 4 hours per week. Determine any patterns that suggest the presence of an association providing reasons for your conclusion.
QUESTION 6 (3 marks) At midnight on 29 December 2011 the International Date Line was moved. This resulted in Samoa and Tokelau changing from the eastern side of the date line to the western side (see map below). PHILIPPINE HAWAII%’D SEA NORTH PACIFIC OCEAN 7 S 2011 date line % TOKELAU®S——57 ) CORAL =~ SAMOAs—=} SEA o o OO ‘.' N\ ' SOUTH PACIFIC : OCEAN AUSTRALIA TASMAN | SEA —e New 2012 date line 9 | NEW | ZEALAND : | J N ® Map not to scale v JJ Determine what time date and year it was in Samoa one minute after this change.
QUESTION 7 (7 marks) In 2011 Chris was earning a salary of $67 500. Chris receives the same pay increase each year and in 2018 was earning a salary of $84 300. In 2015 Sam was earning a salary of $79 500. Sam receives the same pay increase each year and in 2019 was earning a salary of $87 900. Determine when Chris will earn more than Sam.
QUESTION 8 (3 marks) A teacher wants to know the best way for their students to improve their marks. They surveyed a sample of students who graduated last year and asked them three questions: « What was the overall mark you achieved on the final assessment? * On a typical night how many hours sleep would you get? * During a typical school term how many classes did you miss? They obtained the following data: Overall percentage mark (%) Construct a mathematical argument to determine which explanatory variable is the better predictor for the overall mark.
QUESTION 9 (4 marks) The table below shows the seasonally adjusted rainfall data (in mm) for a town in Australia. 2015 2016 Summer 96.77 101.61 Winter 100.00 101.39 Spring 100.97 102.91 Autumn 98.04 101.96 The seasonal indices are shown in the table below. Summer 1.24 i Spring 1.03 In 2017 the actual rainfall in summer was 127 mm autumn was 106 mm winter was 75 mm and spring was 107 mm. Analyse the data to predict the total rainfall for each season in 2025.
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