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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 6 A loan of $10 000 has interest charged on a reducing balance at 6% p.a. compounding quarterly with quarterly repayments of $700. The balance after 6 months is (A) $8696.75 (B) $8891.75 (C) $8900.00 (D) $9794.00
QUESTION 7 What is the length of the minimum spanning tree for this network? All distances are in kilometres (km). (A) 22km (B) 14 km (C) 12km (D) 3 km
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 11 Determine the adjacency matrix that represents this graph. o1 H o oo o N — — O O Y — O —~ O o —~— O O n H (B) N — — O RIOI oo —~ — O w (A) H o oo o N oo o AN O Ao <o oo O wn = (D) o o — o N — — O — Y — O —~ O o —~ — O Ox n H= ©)
QUESTION 12 The activity times in the project network shown are in days. Key (for activity E) -Latest start time ; E 5 Earliest start time “Time to complete Finish The greatest float time for a non-critical activity in this network is (A) 2 days. (B) 4 days. (C) 5 days. (D) 12 days.
QUESTION 13 Which of the following is a planar graph with 5 vertices and 4 faces? ) L j ) % ©) J\ (D) ‘§‘
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 15 The graph shows the value of three different annuities over time. 3000 —e— Annuity 1 --%-- Annuity 2 2500 — 4 — Annuity 3 2000 1500 1000 Value of investment ($) 500 Number of terms Which of the following statements gives a plausible explanation for the different values after seven terms? (A) (B) ©) (D) Annuity 1 and Annuity 2 have higher regular deposits than Annuity 3. Annuity 1 and Annuity 2 have shorter interest terms than Annuity 3. Annuity 2 and Annuity 3 have a lower initial value than Annuity 1. Annuity 2 and Annuity 3 have higher interest rates than Annuity 1.
QUESTION 16 (3 marks) Use the graph to identify whether each of the following is a cycle an open walk an open trail or a closed trail. D a) AFCFB [1 mark] b) AFCEFBA [1 mark] c) ABCDEFA [1 mark]
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 20 (4 marks) Determine the monthly repayment on a $350 000 home loan over 25 years with 6.5% p.a. fixed interest compounded monthly.
QUESTION 21 (5 marks) This network shows the maximum number of supplies (in tonnes) that can be transported from a warehouse to a cyclone shelter along each road each day during an emergency. A 50 20 Warehouse Cyclone shelter 40 30 € a) Use the ‘maximum flow minimum cut’ theorem to determine the maximum amount of supplies that can reach the cyclone shelter each day. [3 marks] b) During a cyclone the intersection at vertex A is damaged and no longer allows for any supplies to pass through it. What is the new maximum amount of supplies each day that can reach the cyclone shelter? [2 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 25 (5 marks) A financial institution offers two investment options: Option 1: 7% p.a. compounding quarterly Option 2: 6.8% p.a. compounding monthly Use the effective interest rate formula to determine the option that will provide the better return.
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 ($°000s) 190 180 170 160 150 140 130 120 110 100 90 80 70 60 > Ql Q2 Q3 Q4 Ql Q2 Q3 Q4 ———-— 2018 ———— e ) =]
QUESTION 5 (5 marks) A company has three tasks to allocate to three contractors. Each of the contractors has a quote recorded for each task shown in the table. The quotes are in thousands of dollars ($°000s). Contractor‘ 1PN Q ‘ Task 2 ‘ Task 3 Use a matrix method to determine the minimum cost if each contractor is allocated one task.
QUESTION 6 (7 marks) A company needs to complete the following project as quickly as possible. Each task can only be completed by a single employee and must be completed before that employee can start the next task. The owner believes that this project can be completed in minimal time with only three employees. Evaluate the reasonableness of this belief.
QUESTION 7 (7 marks) A couple saved for their retirement by making the same monthly payments for 20 years into an account that earned 4.2% p.a. compounded monthly. At the age of 65 the couple retired and used all their savings to purchase a perpetuity with an interest rate of 5.76% p.a. compounded monthly paying $3600 each month. How much did they save each month to prepare for their retirement?
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 2 How many faces does this planar graph have? (A) 3 (B) 4 C) 5 (D) 7
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 5 The coach of a four-person relay team is deciding on the order of the runners. Use the bipartite graph to determine which statement 1s correct. Simon first runner Balal second runner Ivan third runner Linh fourth runner (A) Linh should be the first runner. (B) Simon should be the second runner. (C) Ivan should be the third runner. (D) Balal should be the fourth runner.
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 7 Which cut (C; C C5or Cy) could be used to determine the maximum flow from the source to the sink in this network? Cnl C Z C\\3 C4 90 | Source Sink Not to scale (55 (A) C B) G C) G (D) C4
QUESTION 8 A basketball competition has six teams that have completed three rounds of competition as shown. - - - [ | Bls | — | - | v | v | = Mo | v | v | = v = s — | v = v e | - - | v | = S| v = | = | v The graph to represent this information has (A) 6 edges. (B) 9 edges. (C) 15 edges. (D) 18 edges.
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 12 Which statement is correct? (A) A minimum spanning tree must contain a loop. (B) A minimum spanning tree must contain a cycle. (C) Every network has only one minimum spanning tree. (D) A minimum spanning tree has one more vertex than the number of edges.
QUESTION 13 Based on this project network what is the minimum number of days required to complete the project? (A) 16 (B) 17 (©) 19 (D) 31
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 15 Which of the following investment options gives the best return? (A) 5.93% p.a. compounding daily (B) 5.95% p.a. compounding monthly (C) 5.97% p.a. compounding quarterly (D) 5.99% p.a. compounding six-monthly
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 17 (4 marks) Determine the monthly repayment on a reducing balance loan of $720 000 at 4.8% p.a. over 25 years. Give your answer to the nearest dollar.
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 19 (5 marks) The activity table for a project is shown. Activity Prerequisite Time activity (days) a) b) ©) Use the activity table to construct a network diagram including earliest and latest starting times. [3 marks] Determine the critical path. [1 mark] Determine the shortest completion time for the project. [1 mark]
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 22 (4 marks) Rosa borrowed $32 000 as a reducing balance loan at 4.8% p.a. compounding monthly with monthly repayments of $278. How much will Rosa owe after 2 months to the nearest cent?
QUESTION 23 (4 marks) The network diagram shows the flow of water from the tank (source) to the kitchen tap (sink). L L L L Not to scale Tank ] D . 15 E a) Explain which dashed line (L L L; or L) 1s not a valid cut. [1 mark] b) Calculate the capacity of each dashed line that is a valid cut. [3 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 2 (4 marks) All buildings in a school are connected by underground electricity cables indicated by the network. All measurements are in metres. Admin Class 1 Sports shed Class 4 Tuckshop Not to scale 60 The electricity cables need replacing and will cost $1200 per metre. The school wants to minimise costs by replacing the shortest length of cable necessary to connect all buildings. If the school has a budget of $155 000 evaluate whether they can afford this project.
QUESTION 3 (5 marks) Jo contributes $2500 per quarter to an annuity earning 3.6% p.a. compounding quarterly. At the end of 4 years Jo makes a one-off extra contribution of $10 000 and continues with the regular quarterly contributions. Determine the value of the annuity at the end of 6 years to the nearest dollar.
QUESTION 4 (6 marks) The graph shows two investment models. Model 1 is compounding annually while Model 2 increases linearly by $126 per year. Model 1 2750 __- Model 2 Amount ($) 2020 2038 Year Determine the difference between the two investment strategies in 2030 to the nearest dollar.
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 6 (7 marks) A tow truck company has three tow trucks (A B and C) and receives calls from three motorists (P Q and R) who have broken down. The network shows the distances in kilometres (km) from each of the tow trucks to each of the motorists where x represents the distance between Tow Truck C and Motorist P. Not to scale The minimum total distance travelled by the three tow trucks in order for each tow truck to visit exactly one motorist 1s 32 km. Use the Hungarian algorithm to determine the distance between Tow Truck C and Motorist P.
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 1 The float time in minutes for the non-critical activity of this project network is Watch the news 10 min ‘Collect Turn on 'Prepare 'Cook qp Eat @b ingredients oven ingredients food food 3 min 5 min 8 min 17 min 5 min (A) 10 (B) 20 ) 23 (D) 30
QUESTION 2 The total number of vertices in this graph is (A) (B) ©) (D) ~N O WD W
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 6 This semi-Eulerian graph can be changed to an Eulerian graph by (A) adding a loop to vertex B. (B) removing the loop at vertex A. (C) adding an edge between vertices A and D. (D) removing the edge between vertices B and C.
QUESTION 7 This matrix was obtained after applying the Hungarian algorithm to determine the optimal allocation of three people Elandra (E) Farid (F) and Grace (G) to three tasks: legal (L) monitoring (M) and verification (V). L M V E|0 0 7 F|0 3 8 G|1 O O The optimal allocation is (A) EtoV FtoMand Gto L. (B) EtoV FtoLandGtoM. (C) EtoM FtoLand Gto V. (D) EtoM FtoVand GtoL.
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 9 Identify the graph that is a spanning tree. (A) o @) wn ~e ©) o &) = (B) (D) )—U w2 o 2 ( = ( =
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 17 (4 marks) An investment of $50 000 that compounds interest monthly is modelled by the recurrence relation A . 1=1.003754 where Ay =50 000. a) What would be the advertised interest rate per annum compounding monthly? [2 marks] b) How many months would it take for the value of the investment to exceed $51 000? [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 20 (4 marks) The table summarises the distances in kilometres (km) between three flower stores and three delivery locations: A B and C. Use the Hungarian algorithm to determine the minimum total distance needed to deliver flowers to all locations if each store delivers flowers to only one location. A B | C Store 1 24
QUESTION 21 (5 marks) The paths connecting various landmarks in a park are shown. D P Key B Bus stop C Coffee shop D Duck pond P Playground ¢ R Rose garden R W Water feature B a) Identify one cycle that passes through the rose garden and the playground. [1 mark] b) Identify whether the graph is Eulerian or semi-Eulerian. Justify your response. [2 marks] c) Construct an adjacency matrix from the graph using the vertex order listed in the key. [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 25 (5 marks) A couple borrow money to complete home renovations. Their bank has loaned the amount at 2.4% p.a. compounding monthly with repayments of $993.14 each month for 15 years. a) Determine the amount of money borrowed. [3 marks] b) Write a recurrence relation for the amount owing after n» months. [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 2 (5 marks) Tam deposits a fixed amount at the end of each month into an account paying 8.6% p.a. compounding monthly. From an initial zero balance she accumulates $51 343.85 in four years. A financial planner has advised Tam that she would have been at least $3000 better off if she had instead deposited half of the fixed amount at the end of each fortnight into an account paying 7.9% p.a. compounding fortnightly. Evaluate the reasonableness of this advice.
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 4 (5 marks) The table shows the current road length (in kilometres) between six towns. v [ vern [ o | e [ R | A T [ 6 s | [ % e | e | s e | e e | s w Cwew | T s e The government plans to build a direct road between Manon and Farra. Use a network diagram to determine the length of the direct road if it is to be 4 km shorter than the length of the current shortest road route between Manon and Farra.
QUESTION 5 (5 marks) The map details the length (in metres) of paths between nine key locations in a theme park. The annual cost to maintain the paths is $214 per metre. The theme park manager believes at least $138 000 can be saved each year if some paths are removed while still allowing visitors to access every key location using paths. Roller- coaster Ferris 170 Wheel Car park Eatlng area 05 T 6 60 Toilet Bumper Stunt 170 cars h show 185 165 65 Water slide Laser Not to scale show Evaluate the reasonableness of the manager’s belief.
QUESTION 6 (7 marks) The first three lines in a pattern have the equations given. Their slopes form the terms of one sequence and their y-intercepts form the terms of another sequence. Each sequence is either arithmetic or geometric. Line 1: y=-0.8x + 1.2 Line2: y=0.4x+2.7 Line3: y=-0.2x+ 4.2 Determine the coordinates of the point where Line 5 in the pattern intersects Line 1.
QUESTION 7 (7 marks) You live in Queensland and your friend is on a cruise ship holiday. As their ship departs from X to travel 1350 km due west to Tarawa your friend sends you a message saying ‘Local time 6:12 am Wednesday and enjoying the sunrise as our ship begins its trip to Tarawa’. Queensland Not to scale Key ==—=-International date line = «sseeeeee Time zone You plan to phone your friend as soon as they arrive in Tarawa. Assuming their ship is travelling at 50 km/h determine the time in Queensland when you will phone your friend.
QUESTION 1 A linear association with a correlation coefficient of 0.23 is best described as (A) weak positive. (B) weak negative. (C) strong positive. (D) strong negative.
QUESTION 2 A time series plot is shown. Profit ($’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 3 The duration in minutes of all activities in a project are shown. Activity pe yTefTe[s|;rpeyy The critical path for the project is PRSV. What is the earliest completion time for the project if it starts at 11:00 am? (A) 12:30 pm (B) 1:10pm (C) 1:30pm (D) 2:10 pm
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 8 Activities P and Q are the critical activities for a project. Activity Prerequisite activity
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 11 An annuity with an initial zero balance has $500 deposited at the end of every month. The annuity earns 4.8% p.a. interest compounding monthly. At the end of the fourth month the balance is closest to (A) $2002 (B) $2008 (C) $2012 (D) $2014
QUESTION 12 A reducing balance loan with an initial balance of $6000 is modelled by the recurrence relation Anal = [ + “) A — 400 where n is the number of months. The loan balance at the end of two months is closest to (A) $5100 (B) $5200 (C) $5215 (D) $5230
QUESTION 13 Four athletes Eoin (E) Fedir (F) Gede (G) and Hana (H) compete in three events: javelin (J) long jump (L) and sprints (S). Which bipartite graph represents this information? “ok J ok J F L F L G S G S H H (C) (D) oo o- - mraoantt n ron n
QUESTION 14 A calculator is used to determine the equation of the least-squares line for the plant growth data in the table. What is the correct equation? (A) d=0.6h+5.7 (B) h=0.6d+5.7 (C) d=5.7h+0.6 (D) h=5.7d+0.6
QUESTION 15 The resale value of a boat shows geometric decay. Resale value ($) 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 17 (4 marks) Terome paid a $50 000 deposit on a house valued at $570 000 and borrowed the remainder as a reducing balance loan at 6.6% p.a. compounding monthly. Determine the monthly repayment required to pay off the loan over 25 years.
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 19 (4 marks) Ngarra compares two investment options and decides option A will provide the better return. ¢ Option A: 5.60% p.a. compounding monthly ¢ Option B: 5.62% p.a. compounding quarterly Use the effective annual rate of interest formula to evaluate the reasonableness of Ngarra’s decision.
QUESTION 20 (4 marks) Graphs 1| and 2 are shown. | 2 a) Show that Euler’s formula applies to graph 1. b) What feature in the drawing should be changed to represent graph 2 as planar? c) Redraw graph 2 to represent it as a planar graph. [2 marks] [1 mark] [1 mark]
QUESTION 21 (4 marks) The road network shows the number of vehicles per hour travelling from the airport to the town centre. cut X _ College Airport Town centre \ Showground a) Determine the capacity of cut X. b) Determine the maximum flow from the airport to the town centre. [1 mark] [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 23 (5 marks) A network graph is shown. ec a) State the degree of vertex E. [1 mark] b) State the number of edges joining D and E. [1 mark] c) Construct an adjacency matrix from the graph with the vertices in alphabetical order. [3 marks]
QUESTION 24 (5 marks) Jed is preparing and serving a meal of curry and rice with naan bread. The table shows the duration and prerequisites for all the tasks they must complete. Task description Duration (minutes) Prerequisite Assemble equipment 2 — Boil rice 20 Prepare curry ingredients 6 Simmer curry 40 Fry naan bread + Serve meal 2 |B Do Make naan bread 8 a) Construct a network diagram to show the sequence of tasks from start to finish labelling all tasks and durations. Use forward and backward scanning to show the earliest and latest starting times for all tasks. [3 marks] b) Determine the critical activities and minimum completion time for preparing and serving the meal. [2 marks]
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 1 (5 marks) A triathlon relay has three sections: swim (S) cycle (C) and run (R). The matrix shows the average number of minutes for three athletes Jane (J) Knox (K) and Levi (L) to complete each section. S C R J|40 56 66 K/ 36 60 72 L/}25 48 78 Use the Hungarian algorithm to predict the minimum total relay time if assigning each athlete to completing one section.
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 3 (5 marks) The diagram represents a network of 10 ski stations connected by chairlift cables. The length (km) of each cable is shown except for cable C which is closed for maintenance. When cable C reopens the minimum total cable length required to connect all stations will decrease by | km. Determine the length of cable C and the minimum total cable length required to connect all stations when cable C reopens.
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 7 (5 marks) Five years ago a retiree invested $100 000 in a compound interest account earning 3.8% p.a. compounding monthly. They now intend to use the balance of the account to begin a perpetuity that will return 4% p.a. compounding annually and pay them $6000 each year. Provide advice to the retiree about whether their compound interest investment is large enough to finance the perpetuity.
QUESTION 1 Identify a minimum spanning tree from the diagrams below. (A) (B)
QUESTION 2 The graph below shows the relationship between the amount owed and time taken to repay a reducing balance loan. 140 000 120 000 o 000e 000 00 c ..... 100 000 T 80 000 60 000 Amount owed ($) 40 000 20 000 0 20 40 60 80 100 120 140 160 180 Time (months) The owed amount will be reduced to half the original amount borrowed in (A) 60 months. (B) 81 months. (C) 112 months. (D) 162 months.
QUESTION 3 The graph below has six vertices. The vertex with the smallest degree is A) 1 (B) 2 ©C) 3 (D) 4
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 8 Activities A B C D E F G H and J must be completed for the project shown in the network. Activity times are in minutes. G 7 Start Finish The earliest starting time in minutes for Activity J on the network diagram above is A) 16 (B) 15 C) 13 (D) 11
QUESTION 9 The edges J R M P P Q on the network diagram above make (A) apath. (B) acycle. (C) aclosed trail. (D) an open walk.
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 13 For a personal loan of $350 a payment of $60 is made after interest is added each month. The following recurrence relation shows the remaining balance at the end of consecutive months. The recurrence relation is Anv = 1.02434 - 60 The remaining balance after two months is (A) $191.73 (B) $242.81 (C) $245.76 (D) $298.51
QUESTION 14 Identify the planar graph that has four faces. (A) g (B) j (C) B (D) ;
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 16 Determine the value of the cut made on the network diagram below. B 70 E<—Cut (A) 160 (B) 170 (C) 180 (D) 240
QUESTION 17 A reducing balance loan of $12 000 was taken out at 10.5% per annum with interest calculated monthly for five years. Determine the monthly repayment required to pay off the loan. (A) $152.93 (B) $162.18 (C) $25793 (D) $267.18
QUESTION 18 Which adjacency matrix below represents the same information that is given in the network diagram? T & To (B) To (A) oo o = UOllO _ o —~ © @ — N — o o o n = =2 woI > © © — © Do -~ o o _ o © © - N — o o o n = =2 woI To (D) To ©) b o = = O UOlOl - © — @ — N — o o o N == woxL J S e —~ 8 o Do o © = _ o © —~ O N — ©o o o n == WOL]
QUESTION 19 An investment of $10 000 is made at an interest rate of 7.5% per annum compounding half yearly. The number of years it will take for the value of the investment to exceed $18 000 is (A) 7 (B) 8 C) 15 (D) 16
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 21 (4 marks) To provide herself with a regular income at retirement Mary invests in an annuity worth $270 000 at 3.5% per annum compounding monthly for 20 years. Calculate how much income she will receive each month.
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 25 (3 marks) The connected weighted graph below shows the time taken in minutes and seconds to walk between places in a park. Rose garden 1 min 55 sec 1 min 50 sec Butterfly house 3 min 10 sec 2 min 30 sec 2 min 20 sec 4 min 55 sec Tlayground Garden shed 2 min 20 sec Cafe a) Identify which two places are joined by a network bridge. [1 mark] b) Calculate the earliest time that a gardener could arrive at the butterfly house if they leave the garden shed at 8:55 am. [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 30 (4 marks) The network diagram below illustrates the time taken in days for 10 different activities labelled A—K involved in the completion of a task. H 10 E 2 a) Identify the critical path for the diagram above. [1 mark] b) Calculate the latest starting time for Activity G. [1 mark] c) Calculate the float time for Activity E. [2 marks]
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 2 (4 marks) A cable company is calculating the cost of laying cable between five houses (A B C D and E). The unit cost of laying the cable is $2.50 per metre. The shortest distances (in metres) between the houses are shown below. a) Construct a network diagram to represent the distances between the houses in the space provided below. [1 mark] b) Determine the minimum cost to connect all of the houses. [3 marks]
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 4 (3 marks) You have a savings account with an interest rate of 2.4% per annum paid quarterly. Your bank makes you a new offer. You are entitled to either an increase in the interest rate of 0.5% per annum or to your current interest paid monthly. Determine which option is the most profitable.
QUESTION 5 (8 marks) Kate Luca and Marcel are carpenters. Each carpenter needs to build one piece of furniture: a bookcase a chair or a desk. As each carpenter works at a different rate the table below shows the total cost for each carpenter to build each piece of furniture. a) Use the Hungarian algorithm to determine who should build each piece of furniture to minimise the total cost. [5 marks] b) Evaluate the reasonableness of your solution to 5a). [3 marks]
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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