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Data, 2UG 2005 HSC 27a

The area graph shows sales figures for Shoey’s shoe store.

2UG-2005-27a

  1. Approximately how many school shoes were sold in January?   (1 mark)
  2. For which month does the graph indicate that the same number of school shoes and business shoes was sold?   (1 mark)
  4. Identify ONE trend in this graph, and suggest a valid reason for this trend.   (2 marks)
Show Answers Only
  1. `15\ 000`
  2.  `text(April)`
  3. `text(Possible trends include)`
  4. `text(- Boot sales peak in the Winter months of Jun-Aug)`
  5. `\ \ text(because of the colder weather.)`
    `text(- School shoe sales peak in January as children prepare)`
    `\ \ text(to return to school for the new year.)`
Show Worked Solution

(i)   `text(School shoes sold)`

`≈ 18\ 000 − 3000`

`≈ 15\ 000`

 

(ii)  `text(April)`

 

(iii) `text(Possible trends include)`

`text(- Boot sales peak in the Winter months of Jun-Aug)`

`\ \ text(because of the colder weather.)`

`text(- School shoe sales peak in January as children prepare)`

`\ \ text(to return to school for the new year.)`

Statistics, STD2 S5 2005 HSC 26c

The weights of boxes of Brekky Bicks are normally distributed. The mean is 754 grams and the standard deviation is 2 grams.

  1. What is the `z`-score of a box of Brekky Bicks with a weight of 754 g?   (1 mark)

  2. What is the weight of a box that has a `z`-score of  –1?   (1 mark)

  3. Brekky Bicks boxes are labelled as having a weight of 750 g. What percentage of boxes will have a weight less than 750 g?   (2 marks)

Show Answers Only
  1. `0\ text{(mean)}`
  2.  `752\ text(grams)`
  3. `text(2.5%)`
Show Worked Solution

i.    `text{z-score (754 g) = 0}`

`text{(Noting that 754 g is the mean)}`

 

ii.   `ztext(-score)` `= (x − mu)/sigma`
`-1` `= (x − 754)/2`
 `x – 754` `= -2`
`x`  `= 752\ text(grams)`

 

iii. `text{z-score (750)}` `= (750 − 754)/2`
    `= -2`

 

 
  `:.\ text(Graph shows that 2.5% of boxes will weigh)`

`text(less than 750 g.)`

Financial Maths, STD2 F5 2005 HSC 26b

Rod is saving for a holiday. He deposits $3600 into an account at the end of every year for four years. The account pays 5% per annum interest, compounding annually.

The table shows future values of an annuity of $1.
 

2UG-2005-26b
 

  1. Use the table to find the value of Rod’s investment at the end of four years.   (2 marks)

  2. How much interest does Rod earn on his investment over the four years?   (2 marks)

Show Answers Only
  1. `$15\ 516.36`
  2. `$1116.36`
Show Worked Solution

i.   `text(Using the table),\ r =\ text(5% and)\ n = 4`

`text(Annuity factor = 4.3101)`

`:.\ text(Value of investment)`

`= 3600 xx 4.3101`

`= $15\ 516.36`

 

ii.  `text(Interest)` `= text(Value) − text(Contributions)`
  `= 15\ 516.36 − (4 xx 3600)`
  `= $1116.36`

Financial Maths, STD2 F4 2005 HSC 26a

A sports car worth $150 000 is bought in December 2005.

In December each year, beginning in 2006, the value of the sports car is depreciated by 10% using the declining balance method of depreciation.

In which year will the depreciated value first fall below $120 000?   (2 marks)

Show Answers Only

`text(The value falls below $120 000 in the third year)`

`text{which will be during 2008.}`

Show Worked Solution

`text(Using)\ \ S = V_0(1-r)^n`

`text(where)\ \ V_0 = 150\ 000, r = text(10%)`

`text(If)\ \ n = 2,`

`S` `= 150\ 000(1-0.1)^2`
  `= 121\ 500`

 
`text(If)\ \ n= 3,`

`S` `= 150\ 000(1-0.1)^3`
  `= 109\ 350`

 

`:.\ text(The value falls below $120 000 in the third year)`

`text{which will be during 2008.}`

Financial Maths, STD2 F4 2006* HSC 25b

In June, Ms Bigspender received a statement for her credit card account.

The account has no interest-free period. Compound interest is calculated daily and charged to her account on the statement date.
 

  1. For how many days is she charged interest on her purchase?  (1 mark)

  2. Calculate the interest charged to her account.  (2 marks)

Show Answers Only
  1.  `29`
  2.  `$8.98`
Show Worked Solution

i.  `text(# Days interest charged)`

`=\ text{9 (in May) + 20 (in June)}`

`= 29`

 

ii.   `text(Daily interest rate)\ (r) = 0.0498/100=0.000498`

`text(Closing Balance)\ (FV)` `= PV(1+r)^n`
  `= 617.72(1.000498)^29`
  `= $626.703`

 

`:.\ text(Interest charged)` `=626.70 – 617.72`  
  `=$8.98`  

Measurement, 2UG 2004 HSC 26b

The location of Sorong is `text(1°S 131°E)` and the location of Darwin is `text(12°S 131°E)`.

  1. What is the difference in the latitudes of Sorong and Darwin?  (1 mark)
  2. The radius of Earth is approximately `text(6400 km.)`

  3. Show that the great circle distance between Sorong and Darwin is approximately `text(1200 km)`.  (2 marks)

 

Show Answers Only
  1. `11°`
  2. `text(Proof)\ \ text{(See Worked Solutions)}`
Show Worked Solution

(i)  `text(Difference in latitudes)`

`= 12^@ – 1^@`

`= 11^@`

 

(ii)   `text(S)text(ince longitude is the same,)`

`text(Distance between Sarang and Darwin)`

`= 11/360 xx 2 pi r`

`= 11/360 xx 2 xx pi xx 6400`

`= 1228.7…\ text(km)`

`~~ 1200\ text(km … as required.)`

Probability, STD2 S2 2006 HSC 25a

Three cards labelled `C`, `J` and `M` can be arranged in any order.

  1. In how many different ways can the cards be arranged?  (1 mark)

  2. What is the probability that the second card in an arrangement is a `J`?  (1 mark)

  3. What is the probability that the last card in an arrangement is not a `C`?  (1 mark)

Show Answers Only
  1. `6`
  2. `1/3`
  3. `2/3`
Show Worked Solution
i.  `text(# Arrangements)` `= 3 xx 2 xx 1`
  `= 6`

 

ii.  `P\ text{(second card is J)}`

`= 1/3`

 

iii.  `P\ text{(last card is not a C)}`

`= 1 – P\ text{(last card is a C)}`

`= 1 – 1/3`

`= 2/3`

Measurement, STD2 M6 2006 HSC 24b

A 130 cm long garden rake leans against a fence. The end of the rake is 44 cm from the base of the fence.

  1. If the fence is vertical, find the value of `theta` to the nearest degree.  (2 marks)
      
          2UG-2006-24b-i

     

  2. The fence develops a lean and the rake is now at an angle of 53° to the ground. Calculate the new distance (`x` cm) from the base of the fence to the head of the rake. Give your answer to the nearest centimetre.  (2 marks)
     
          2UG-2006-24b-ii

Show Answers Only
  1. `text{70°  (nearest degree)}`
  2. `text{109 cm  (nearest cm)}`
Show Worked Solution
i.   

2UG-2006-24b1 Answer
`cos theta` `= 44/130`
  `= 70.216… ^@`
  `= 70^@\ \ \ text{(nearest degree)}`

 

ii.   

2UG-2006-24b2 Answer

`text(Using cosine rule)`

`x^2` `= 130^2 + 44^2-2 xx 130 xx 44 xx cos 53^@`
  `= 11\ 951.23…`
`x` `= 109.32…`
  `= 109\ text{cm  (nearest cm)}`

Data, 2UG 2006 HSC 23d

The graph shows the amounts charged by Company `A` and Company `B` to deliver parcels of various weights.

2UG-2006-23d

  1. How much does Company `A` charge to deliver a `3` kg parcel?  (1 mark)
  2. Give an example of the weight of a parcel for which both Company `A` and Company `B` charge the same amount.  (1 mark)
  4. For what weight(s) is it cheaper to use Company `A`?  (2 marks)
  5. What is the rate per kilogram charged by Company `B` for parcels up to `8` kg?  (1 mark)
Show Answers Only
  1. `$6`
  2. `text(4 kg or 7 kg)`
  3. `x > 7`
  4. `text($1.50 per kg)`
Show Worked Solution

(i)   `$6`

 

(ii)  `text(4 kg or 7 kg)`

 

(iii)  `text(Let)\ x = text(weights where Company)\ A`

`text{is cheaper (kg).}`

`4 < x <= 6`

`x > 7`

 

(iv)   `text(Company)\ B\ text(charges $12 for 8 kg)`

`:.\ text(Rate)` `= 12/8`
  `= $1.50\  text(per kg)`

Statistics, STD2 S1 2006 HSC 23c

Vicki wants to investigate the number of hours spent on homework by students at her high school.

  1. Briefly describe a valid method of randomly selecting 200 students for a sample.  (1 mark)

  2. Vicki chooses her sample and asks each student how many hours (to the nearest hour) they usually spend on homework during one week.

     

    The responses are shown in the frequency table.
     
         2UG-2006-23c

    What is the mean amount of time spent on homework?  (2 marks)

Show Answers Only
  1. `text(A valid method would be using a stratified sample.)`

     

    `text(The number of students sampled in each year is)`

     

    `text(proportional to the size of each year.)`

  2. `text(7.275 hours)`
Show Worked Solution

a.   `text(A valid method would be using a stratified sample.)`

`text(The number of students sampled in each year is)`

`text(proportional to the size of each year.)`

MARKER’S COMMENT: This “routine” exercise of finding a mean from grouped data was incorrectly answered by most students! The best responses copied the table and inserted a class-centre column (see solution).

 

b.    2UG-2006-23c Answer

 

`text(Mean)` `= text(Sum of Scores) / text(Total scores)`
  `= 1455/200`
  `= 7.275\ text(hours)`

Statistics, STD2 S1 2006 HSC 24a

2UG-2006-24a

List TWO ways in which this graph is misleading.  (2 marks)

Show Answers Only

`text(Reasons the graph is misleading include)`

`text(- the columns are a different widths/volumes)`

`text(- the vertical axis doesn’t start at zero)`

Show Worked Solution

`text(Reasons the graph is misleading include)`

`text(- the columns are a different widths/volumes)`

`text(- the vertical axis doesn’t start at zero)`

Probability, 2UG 2005 HSC 25c

Robyn plays a game in which she randomly chooses one of these five cards. She plays the game `60` times, replacing the card after each game.

2UG-2005-25c

  1. How many times would she expect to win `$4`?   (1 mark)
  3. What is the financial expectation of the game?   (2 marks)
  4. Another card is added to the game with ‘Win nothing $0’ written on it.
    Robyn claims that the financial expectation will not change.
  6. Do you agree? Justify your answer with suitable calculations.   (2 marks)
Show Answers Only
  1. `36`
  2. `text(Financial Expectation is to win)\ $0.80.`
  3. `text(The financial expectation will reduce)`
  4. `text(from win $0.80 to win $0.677…)`

 

Show Worked Solution

(i)   `Ptext{(win $4)}\ = 3/5`

`:.\ text(Expected times to win $4)`

`= 3/5 xx 60`

`= 36`

 

(ii)  `P($0) = 1/5`

`Ptext{(lose $8)}\ = 1/5`

`text(Financial Expectation)`

`= (3/5 xx 4) + (1/5 xx 0) − (1/5 xx 8)`

`= 12/5 + 0 − 8/5`

`= 4/5`

`:.\ text(Financial Expectation is to win $0.80)`

 

(iii)  `text(If an extra card to win $0 was added)`

`text(Financial expectation)`

`= (3/6 xx 4) + (2/6 xx 0) − (1/6 xx 8)`

`= 2 + 0 − 4/3`

`= 2/3`

`= $0.677…`

 

`:.\ text(The financial expectation will reduce from)`

`text(win $0.80 to win $0.677…)`

Measurement, STD2 M6 2005 HSC 25b

2UG-2005-25b

  1. Use Pythagoras’ theorem to show that `ΔABC` is a right-angled triangle.  (1 mark)

  2. Calculate the size of `∠ABC` to the nearest minute.  (2 marks)

Show Answers Only
  1. `text(Proof)`
  2. `67°23^{′}`
Show Worked Solution

i.   `ΔABC\ text(is right-angled if)\ \ a^2 + b^2 = c^2`

`a^2 + b^2` `= 5^2 + 12^2`
  `= 169`
  `= 13^2`
  `= c^2…\ text(as required.)`

MARKER’S COMMENT: Know your calculator process for producing an angle in minutes/seconds. Note >30 “seconds” rounds up to the higher “minute”.

 
ii.  `sin ∠ABC = 12/13`

`:.∠ABC` `= 67.38…°`
  `=67°22^{′}48^{″}`
  `= 67°23^{′}\ \ \ text{(nearest minute)}`

Statistics, STD2 S1 2005 HSC 24d

The sector graph shows the proportion of people, as a percentage, living in each region of Sumcity. There are 24 000 people living in the Eastern Suburbs.
 

2UG-2005-24d1
 

  1. Show that the total number of people living in Sumcity is  160 000.  (1 mark)

Jake used the information above to draw a column graph.
 

2UG-2005-24d2

  1. The column graph height is incorrect for one region.

     

    Identify this region and justify your answer.   (2 marks)

Show Answers Only
  1. `160\ 000`
  2. `text(Western Suburbs population)`
Show Worked Solution

a.   `text(Let the population of Sumcity =)\ P`

`text(15%)× P` `= 24\ 000`
`:.P`  `= (24\ 000)/0.15` 
  `= 160\ 000\ …\ text(as required)` 

 

b.  `text(Western Suburbs population)`

`= text(10%) × 160\ 000`

`= 16\ 000`

`text(The column graph has this population as)`

`text(12 000 people which is incorrect.)`

Algebra, STD2 A1 2005 HSC 24b

The formula  `D = (2A)/15`  is used to calculate the dosage of Hackalot cough medicine to be given to a child.

    • D is the dosage of Hackalot cough medicine in millilitres (mL).
    • A is the age of the child in months.
  1. If George is nine months old, what dosage of Hackalot cough medicine should he be given?  (1 mark)

The correct dosage of Hackalot cough medicine for Sam is 4 mL.

  1. What is the difference in the ages of Sam and George, in months?  (3 marks)

Show Answers Only
  1. `text(1.2 mL)`
  2. `30`
Show Worked Solution
a. `D` `= (2A)/15`
    `= (2 × 9)/15`
    `=1.2\ text(mL)`

 

`:.\ text(George should be given a dosage of 1.2 mL)`

 

b.   `text(Find)\ A\ text(when)\ D = text(4 mL)`

`4` `= (2 × A)/15`
 `2A` `= 60`
`A`  `= 30` 

 

`:.\ text(Sam is 30 months old and is 21 months)`

`text(older than George.)`

Statistics, STD2 S1 2005 HSC 24a

  1. Draw a stem-and-leaf plot for the following set of scores.

  2.  

     

    `21\ \ \ 45\ \ \ 29\ \ \ 27\ \ \ 19\ \ \ 35\ \ \ 23\ \ \ 58\ \ \ 34\ \ \ 27`  (2 marks)

  3. What is the median of the set of scores?   (1 mark)

  4. Comment on the skewness of the set of scores.   (1 mark)

Show Answers Only
  1.  
  2. `28`
  3. `text(The data has a tail that stretches to the right)`

  4.  

    `:.\ text(Data is positively Skewed.)`

Show Worked Solution
a.    HSC 2005 24a

 

b.   `text(10 scores)`

`:.\ text(Median)` `= text{(5th + 6th)}/2`
  `= (27 + 29)/2`
  `= 28`

 

c.   `text(The data has a tail that stretches to the right)`

`:.\ text(Data is positively skewed.)`

Probability, STD2 S2 2005 HSC 23c

Moheb owns five red and seven blue ties. He chooses a tie at random for himself and puts it on. He then chooses another tie at random, from the remaining ties, and gives it to his brother.

  1. What is the probability that Moheb chooses a red tie for himself?  (1 mark)

Copy the tree diagram into your writing booklet.
 

2UG-2005-23c
 

  1. Complete your tree diagram by writing the correct probability on each branch.  (2 marks)
  2. Calculate the probability that both of the ties are the same colour.  (2 marks)

Show Answers Only
  1. `5/12`
  2.  
  3. `31/66`
Show Worked Solution
i. `P(R)` `= (#\ text(red ties))/(#\ text(total ties))`
    `= 5/12`

 

ii.  

 

iii. `Ptext((same colour))`

`= P(text(RR)) + P(text(BB))`

`= 5/12 × 4/11\ \ +\ \ 7/12 × 6/11`

`= 20/132 + 42/132`

`= 31/66`

Financial Maths, STD2 F1 2004 HSC 27b

David is paid at these rates:
  

 

His time sheet for last week is:
  

  1. Calculate David’s gross pay for last week.  (3 marks)

  2. David decides not to work on Saturdays. He wants to keep his weekly gross pay the same. How many extra hours at the weekday rate must he work?  (1 mark)

Show Answers Only
  1. `$414.00`
  2. `text(9 extra hours)`
Show Worked Solution
a.   `text{Pay (Fri)}` `= text(4 hours) xx 18.00`
  `= $72.00`
`text{Pay (Sat)}` `= 6\ text(hours) xx 1.5 xx 18.00`
  `= $162.00`
`text{Pay (Sun)}` `= 5\ text(hours) xx 2 xx 18.00`
  `= $180.00`

 

`:.\ text(Gross pay)` `= 72 + 162 + 180`
  `= $414.00`

 

b.    `text(Pay on Sat) = $162.00`

`text(Weekly equivalent hours)`

`= 162/18`

`= 9\ text(hours)`

`:.\ text(He will have to work 9 extra hours on)`

`text(a weekday for the same gross pay)`

 

Financial Maths, STD2 F4 2004 HSC 27a

Aaron decides to borrow  $150 000  over a period of 20 years at a rate of 7.0% per annum.

2004 27a

  1. Using the Monthly Repayment Table, calculate Aaron’s monthly repayment.  (2 marks)

  2. How much interest does he pay over the 20 years?  (2 marks)

  3. Aaron calculates that if he repays the loan over 15 years, his total repayments would be `$242\ 730`.

     

    How much interest would he save by repaying the loan over 15 years instead of 20 years?  (2 marks)

Show Answers Only
  1. `$1162.50`
  2. `$129\ 000`
  3. `$36\ 270`
Show Worked Solution

i.   `text(Using the table:)`

`text(Monthly repayment on $1000 at 7.0% over 20 years = $7.75)`
 

`:.\ text(Monthly repayment on $150 000 loan)`

`= 150 xx 7.75`

`= $1162.50`

 

ii.  `text(Total repayments over 20 years)`

`= 20 xx 12 xx 1162.50`

`= $279\ 000`
 

`:.\ text(Interest paid over 20 years)`

`= 279\ 000 – 150\ 000`

`= $129\ 000`

 

iii.  `text(Savings)` `=\ text{Total paid (20 years) – Total paid (15 years)`
  `= 279\ 000 – 242\ 730`
  `= $36\ 270`

Algebra, STD2 A4 2004 HSC 26a

  1. The number of bacteria in a culture grows from 100 to 114 in one hour.

     

    What is the percentage increase in the number of bacteria?   (1 mark)

  2. The bacteria continue to grow according to the formula  `n = 100(1.14)^t`, where `n` is the number of bacteria after `t` hours.

     

    What is the number of bacteria after 15 hours?   (1 mark)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Time in hours $(t)$} \rule[-1ex]{0pt}{0pt} & \;\; 0 \;\;  &  \;\; 5 \;\;  & \;\; 10 \;\;  & \;\; 15 \;\; \\
\hline
\rule{0pt}{2.5ex} \text{Number of bacteria ( $n$ )} \rule[-1ex]{0pt}{0pt} & \;\; 100 \;\;  &  \;\; 193 \;\;  & \;\; 371 \;\;  & \;\; ? \;\; \\
\hline
\end{array}

  1. Use the values of `n` from  `t = 0`  to  `t = 15`  to draw a graph of  `n = 100(1.14)^t`.

     

    Use about half a page for your graph and mark a scale on each axis.   (4 marks)

  2. Using your graph or otherwise, estimate the time in hours for the number of bacteria to reach 300.   (1 mark)

Show Answers Only
  1. `text(14%)`
  2. `714`
  3. `text(Proof)\ \ text{(See Worked Solutions)}`
  4. `text(8.4 hours)`
Show Worked Solution

i.   `text(Percentage increase)`

COMMENT: Common ADV/STD2 content in new syllabus.

`= (114 -100)/100 xx 100`

`= 14text(%)`

 

ii.  `n = 100(1.14)^t`

`text(When)\ \ t = 15,`

`n` `= 100(1.14)^15`
  `= 713.793\ …`
  `= 714\ \ \ text{(nearest whole)}`

 

iii. 

 

iv.  `text(Using the graph)`

`text(The number of bacteria reaches 300 after)`

`text(approximately 8.4 hours.)`

Probability, 2UG 2004 HSC 25b

Joe sells three different flavours of ice-cream from three different tubs in a cabinet. The flavours are chocolate, strawberry and vanilla.

2004 25b

  1. In how many different ways can he arrange the tubs in a row? Show working to justify your answer.  (2 marks)
  3. Paul buys an ice-cream from Joe on two different days. He chooses the flavour at random. What is the probability that he chooses chocolate on both days?  (1 mark)
  5. Mei-Ling buys an ice-cream from Joe and chooses any two different flavours at random. What is the probability that she chooses chocolate first and then strawberry?  (2 marks)

 

Show Answers Only
  1. `6`
  3. `1/9`
  5. `1/6`
Show Worked Solution

(i)  `text{# Arrangements (order matters)}`

`= 3 xx 2 xx 1`

`= 6`

 

(ii)  `P(C, C)` `= 1/3 xx 1/3`
  `= 1/9`

 

(iii)  `P(C, S)` `= 1/3 xx 1/2`
  `= 1/6`

Data, 2UG 2004 HSC 24a

The following graphs have been constructed from data taken from the Bureau of Meteorology website. The information relates to a town in New South Wales.

The graphs show the mean 3 pm wind speed (in kilometres per hour) for each month of the year and the mean number of days of rain for each month (raindays).

2004 24a

  1. What is the mean 3 pm wind speed for September?  (1 mark)
  2. Which month has the lowest mean 3 pm wind speed?  (1 mark)
  3. In which three-month period does the town have the highest number of raindays?  (1 mark)
  4. Briefly describe the pattern relating wind speed with the number of raindays for this town. Refer to specific months.  (2 marks)

 

Show Answers Only
  1. `text(15 km/h)`
  2. `text(February)`
  3. `text(Jan – Mar)`
  4. `text(The mean number of rain days tends to be higher)`
    `text(when the wind speed is lower and vice versa.)`
    `text(For example, the highest number of mean rain)`
    `text(days is in Feb, which is also the month of the lowest)`
    `text(mean wind speed.)`

 

 

Show Worked Solution

(i)    `text(15 km/h)`

(ii)   `text(February)`

(iii)  `text(Jan – Mar)`

(iv)  `text(The mean number of rain days tends to be higher)`

`text(when the wind speed is lower and vice versa.)`

`text(For example, the highest number of mean rain)`

`text(days is in Feb, which is also the month of the lowest)`

`text(mean wind speed.)`

Measurement, STD2 M1 2005 HSC 23b

A clay brick is made in the shape of a rectangular prism with dimensions as shown.
 

  1. Calculate the volume of the clay brick.  (1 mark)

Three identical cylindrical holes are made through the brick as shown. Each hole has a radius of 1.4 cm.  
 

  1. What is the volume of clay remaining in the brick after the holes have been made? (Give your answer to the nearest cubic centimetre.)  (3 marks)

  2. What percentage of clay is removed by making the holes through the brick? (Give your answer correct to one decimal place.)  (1 mark)

Show Answers Only
  1. `text(1512 cm)^3`
  2. `text{1364 cm}^3`
  3. `text{9.8%}`
Show Worked Solution
a.    `V` `= l × b × h`
    `= 21 × 8 × 9`
    `= 1512\ text(cm)^3`

 

b.  `text(Volume of each hole)`

`= pir^2h`

`= pi × 1.4^2 × 8`

`= 49.260…\ text(cm)^3`

 

`:.\ text(Volume of clay still in brick)`

`= 1512 − (3 × 49.260…)`

`= 1364.219…`

`= 1364\ text{cm}^3\ text{(nearest whole)}`

 

c.  `text(Percentage of clay removed)`

`= ((3 × 49.260…))/1512 × 100`

`= 9.773…`

`= 9.8 text{%   (1 d.p.)}`

Probability, STD2 S2 2005 HSC 16 MC

On a television game show, viewers voted for their favourite contestant. The results were recorded in the two-way table.

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \rule[-1ex]{0pt}{0pt} & \textbf{Male viewers} & \textbf{Female viewers} \\
\hline
\rule{0pt}{2.5ex}\textbf{Contestant 1}\rule[-1ex]{0pt}{0pt} & 1372 & 3915\\
\hline
\rule{0pt}{2.5ex}\textbf{Contestant 2}\rule[-1ex]{0pt}{0pt} & 2054 & 3269\\
\hline
\end{array}

One male viewer was selected at random from all of the male viewers.

What is the probability that he voted for Contestant 1?

  1. `1372/(10\ 610)`
  2. `1372/5287`
  3. `1372/3426`
  4. `1372/2054`
Show Answers Only

`C`

Show Worked Solution

`text(Total male viewers)\ = 1372 + 2054= 3426`

  
`P\ text{(Male viewer chosen voted for C1)}`

`= text(Males who voted for C1)/text(Total male viewers)`

`= 1372/3426`
 

`=>  C`

Financial Maths, STD2 F4 2005 HSC 15 MC

A car bought for  $50 000  is depreciated using the declining balance method.

Which graph best represents the salvage value of the car over time?

 

2UG-2005-15abMC

2UG-2005-15cdMC

Show Answers Only

`D`

Show Worked Solution

`text(Declining Balance Method means that the salvage value)`

`text(of the car drops the most value in the 1st year and then)`

`text(drops less value each following year.)`

`=>  D`

Algebra, STD2 A1 2005 HSC 14 MC

Using the formula  `d = 5t^3 - 2`, Marcia tried to find the value of  `t`  when `d = 137`.

Here is her solution. She has made one mistake.
 

2UG-2005-14MC

Which line does NOT follow correctly from the previous line?

  1. `text(Line)\ A`
  2. `text(Line)\ B`
  3. `text(Line)\ C`
  4. `text(Line)\ D`
Show Answers Only

`B`

Show Worked Solution
`d` `= 5t^3 – 2`  
 `137` `= 5t^3 – 2 \ \ \ ` ` …text( Line A)`
 `139` `= 5t^3` `…text( Line B)`

 

`:.\ text(Line)\ B\ text(doesn’t follow on correctly.)`

`=>  B`

Probability, STD2 S2 2004 HSC 25c

Lie detector tests are not always accurate. A lie detector test was administered to 200 people.

The results were:

• 50 people lied. Of these, the test indicated that 40 had lied;
• 150 people did NOT lie. Of these, the test indicated that 20 had lied.

  1. Complete the table using the information above   (2 marks)
      
        

  2. For how many of the people tested was the lie detector test accurate?   (1 mark)

  3. For what percentage of the people tested was the test accurate?   (1 mark)

  4. What is the probability that the test indicated a lie for a person who did NOT lie?   (1 mark)

Show Answers Only
  1. `text(See Worked Solutions)`
  2. `170`
  3. `text(85%)`
  4. `2/15`
Show Worked Solution

i.

ii.  `text(# Accurate readings)`

`= 40 + 130`

`= 170`
 

iii.  `text(Percentage of people with accurate readings)`

`= text(# Accurate readings)/text(Total readings) xx 100`

`= 170/200`

`= 85 text(%)`
 

iv.  `text{P(lie detected when NOT a lie)}`

`= 20/150`

`= 2/15`

Financial Maths, STD2 F4 2004 HSC 25a

Tai uses the declining balance method of depreciation to calculate tax deductions for her business. Tai’s computer is valued at $6500 at the start of the 2003 financial year. The rate of depreciation is 40% per annum.

  1. Calculate the value of her tax deduction for the 2003 financial year.  (1 mark)

  2. What is the value of her computer at the start of the 2006 financial year?  (2 marks)

Show Answers Only
  1. `$2600`
  2. `$1404`
Show Worked Solution
i.  `text(Tax deduction)` `= 40 text(%) xx $6500`
  `= $2600`

 

ii. `text(Using)\  S = V_0(1 – r)^n,`

`text(Value at the start of 2006 FY)`

`= 6500(1 – 0.4)^3`

`= $1404`

Statistics, STD2 S5 2004 HSC 24c

The normal distribution shown has a mean of 170 and a standard deviation of 10.
 


 

  1. Roberto has a raw score in the shaded region. What could his `z`-score be?  (1 mark)

  2. What percentage of the data lies in the shaded region?  (2 marks)

Show Answers Only
  1. `1 <= text(z-score) <= 2`
  2. `text(13.5%)`
Show Worked Solution
i.  `ztext{-score(180)}` `= (x – mu)/sigma`
  `= (180 – 170) / 10`
  `= 1`

 

`ztext{-score(190)}` `= (190 -170)/10`
  `= 2`

 
`:. 1 <= ztext(-score) <= 2`

 

ii.   

`text(From the graph above,)`

`text(13.5% lies in the shaded area.)`

Measurement, STD2 M6 2004 HSC 24b

The diagram shows a radial survey of a piece of land.
 


 

  1. `Q` is south-east of `A`. What is the size of angle `PAQ`?  (1 mark)

  2. What is the bearing of `R` from `A`?  (1 mark)

  3. Find the size of angle `PAB` to the nearest degree.  (3 marks)

Show Answers Only
  1. `135°`
  2. `185°`
  3. `text{73° (nearest degree)}`
Show Worked Solution
i.   

`text(Let)\ E\ text(be directly east of)\ A`

`/_ EAQ = 45^@\ \ \ \ text{(given)}`

`:. /_ PAQ` `= 90^@ + 45^@`
  `= 135^@`

 

ii.   `text(Bearing of)\ R\ text(from)\ A`

`= 90^@ + 45^@ + 50^@`

`= 185^@\ \ \ text{(or  S 5°W)}`

 

iii.  `text(Using cosine rule in)\ Delta PAB`

` cos\ /_ PAB` `= (31^2 + 28^2 – 35^2) / (2 xx 31 xx 28)`
  `= 0.2995…`
`:. /_ PAB` `= 72.570…^@`
  `= 73^@\ \ \ \ text{(nearest degree)}`

Measurement, 2UG 2004 HSC 23c

Calculate the height  `(h\ text{metres})`  of the tree in the diagram. All measurements are
in metres.  (2 marks)

2004 23c

Show Answers Only

`text(6.75 m)`

Show Worked Solution

`text(Using similar triangles,)`

`h/5` `= 2.7/2`
`:.h` `= (5 xx 2.7)/2`
  `= 6.75\ text(m)`

Algebra, 2UG 2004 HSC 23b

Kirbee is shopping for computer software. Novirus costs `$115` more than
Funmaths. Let `x` dollars be the cost of Funmaths.

  1. Write an expression involving `x` for the cost of Novirus.  (1 mark)
  2. Novirus and Funmaths together cost `$415`. Write an equation involving
  3. `x` and solve it to find the cost of Funmaths.  (2 marks)
Show Answers Only
  1. `N = x + 115`
  2. `text(Funmaths costs $150)`
Show Worked Solution

(i)   `text(Let)\ \ N = text(cost of Novirus)`

`N = x + 115`

 

(ii)  `N + x = 415\ …\ (1)`

`text(Substitute)\ \ N = x + 115\ text{into (1) above}`

`x + 115 + x` `= 415`
`2x` `= 300`
`x` `= 150`

`:.\ text(Funmaths costs $150)`

Algebra, STD2 A4 2006 HSC 14 MC

In 2004 there were 13.5 million registered motor vehicles in Australia. The number of registered motor vehicles is increasing at a rate of 2.3% per year.

Which expression represents the number (in millions) of registered motor vehicles, if `y` represents the number of years after 2004?

  1. `13.5 xx (1.023)^y`
  2. `13.5 xx (0.023)^y`
  3. `13.5 xx (1.023) xx y`
  4. `13.5 xx (0.023) xx y`
Show Answers Only

`A`

Show Worked Solution

`text(In 2004, 13.5 million)`

`text(1 year later)` `= 13.5 xx (1.023)`
`text(2 years later)` `= 13.5 xx (1.023) xx (1.023)`
  `= 13.5 xx (1.023)^2`
`:. y\ text(years later)` `= 13.5 xx (1.023)^y`

`=>  A`

Linear Functions, 2UA 2004 HSC 2a

The diagram shows the points  `A(text(−1) , 3)`  and  `B(2, 0)`.

The line  `l`  is drawn perpendicular to the  `x`-axis through the point  `B`.
 

Linear Functions, 2UA 2004 HSC 2a 
 

  1. Calculate the length of the interval  `AB`.   (1 mark)
  2. Find the gradient of the line  `AB`.   (1 mark)
  3. What is the size of the acute angle between the line  `AB`  and the line  `l`?   (1 mark)
  4. Show that the equation of the line  `AB`  is  `x + y − 2 = 0`.    (1 mark)
  5. Copy the diagram into your writing booklet and shade the region defined by  `x + y − 2 <= 0`.   (1 mark)
  6. Write down the equation of the line  `l`.   (1 mark)
  7. The point  `C`  is on the line  `l`  such that  `AC`  is perpendicular to  `AB`. Find the coordinates of  `C`.   (2 marks)

 

Show Answers Only
  1. `3 sqrt2\ text(units)`
  2. `-1`
  3. `45^@`
  4. `text(Proof)\ \ text{(See Worked Solutions)}`
  5. Linear Functions, 2UA 2004 HSC 2a Answer
  6. `x = 2`
  7. `C\ (2, 6)`
Show Worked Solution
(i)    `A(-1,3)\ \ \ \ \ B(2,0)`
`AB` `= sqrt( (x_2 – x_1)^2 + (y_2 – y_1)^2 )`
  `= sqrt( (2+1)^2 + (0-3)^2 )`
  `= sqrt(9+9)`
  `= sqrt 18`
  `= 3 sqrt 2\ text(units)`

 

(ii)   `text(Gradient of)\ AB` `= (y_2 – y_1)/(x_2 – x_1)`
    `= (0 – 3)/(2 + 1)`
    `= – 1`

 

(iii)   `text(S) text(ince Gradient)\ AB = – 1`

`/_ABO = 45^@`

`:.\ text(Angle between)\ AB\ text(and)\ l`

`= 90 – 45`

`= 45^@`

 

(iv)   `text(Equation of)\ AB\ text(has)\ m = -1,\ text(through)\ \ (2,0)`
`y – y_1` `= m(x – x_1)`
`y – 0` `= -1 (x – 2)`
`y` `= -x + 2`

 

`:.\ x + y – 2 = 0\ \ \ …\ text(as required)`

 

(v)

Linear Functions, 2UA 2004 HSC 2a Answer

`text{Origin (0,0) satisfies the inequality}`

`:.\ text(Shaded area is below)\ x + y – 2 = 0`

 

(vi)   `text(Equation of)\ l`
  `x = 2`

 

(vii)   `m_(AC) xx m_(AB)` `= -1\ \ \ (AC⊥AB)`
  `m_(AC) xx -1` `= -1`
  `m_(AC)` `= + 1`

 

`text(Equation of)\ AC\ text(has)\ \ m = 1,\ text(through)\ (-1, 3),`

`y – y_1` `= m(x – x_1)`
`y – 3` `= 1 (x + 1)`
`y` `= x + 4`

 

`=>C\ text(lies on)\ y = x + 4`

`text(When)\ \ x = 2,\ \ y = 6`

`:. C\ (2, 6)`

Statistics, STD2 S1 2006 HSC 12 MC

The mean of a set of 5 scores is 62.

What is the new mean of the set of scores after a score of 14 is added?

  1.   38
  2.   54
  3.   62
  4.   76
Show Answers Only

`B`

Show Worked Solution

`text(Mean of 5 scores) = 62`

`:.\ text(Total of 5 scores) = 62 xx 5 = 310`

`text(Add a score of 14)`

`text(Total of 6 scores) = 310 + 14 = 324`

`:.\ text(New mean)` `= 324/6`
  `= 54`

`=>  B`

Measurement, STD2 M1 2006 HSC 11 MC

Peter rides his bike at a speed of 27 km/h.

What is this speed in m/s?

  1.  `7.5`
  2. `18.75`
  3. `97.2`
  4. `450`
Show Answers Only

`A`

Show Worked Solution
`text(27 km/h)` `= 27\ 000\ text(metres per hour)`
  `= (27\ 000)/60\ text(metres per minute)`
  `= (27\ 000)/(60 xx 60)\ text(metres per second)`
  `=7.5\ text(m/s)`

`=>  A`

Probability, STD2 S2 2006 HSC 10 MC

Kay randomly selected a marble from a bag of marbles, recorded its colour and returned it to the bag. She repeated this process a number of times.
  


  

Based on these results, what is the best estimate of the probability that Kay will choose a green marble on her next selection?

  1.   `5/24`
  2.   `1/24`
  3.   `1/6`
  4.   `1/5`
Show Answers Only

`C`

Show Worked Solution
`text{P(Green)}` `= text(# Green chosen) / text(Total Selections)`
  `= 4/24`
  `= 1/6`

`=>  C`

Algebra, STD2 A2 2006 HSC 7 MC

Which equation represents the relationship between `x` and `y` in this table?
 

2UG-2006-7MC
 

  1.  `y = 2x+1`
  2. `y = 2x-2` 
  3. `y = x/2-2` 
  4. `y = x/2+1`
Show Answers Only

`D`

Show Worked Solution

`text{By elimination (using the table)}`

`(0, 1)\ text(must satisfy)`

`:.\ text(NOT)\ B\ text(or)\ C`

`(2, 2)\ text(must satisfy)`

`:.\ text(NOT)\ A`

`=>  D`

Functions, 2ADV F1 2004 HSC 1d

 Find integers  `a`  and  `b`  by showing working to expand and simplify 

`(3-sqrt2)^2 = a-b sqrt2`.  (2 marks)

Show Answers Only

`a = 11,\ b = 6`

Show Worked Solution
`(3-sqrt2)^2` `= 9-6 sqrt2 + (sqrt2)^2`
  `= 9-6 sqrt2 + 2`
  `= 11-6 sqrt2`
   
`:.\ a = 11, \ \ b = 6`

Probability, STD2 S2 2006 HSC 6 MC

Marcella is planning to roll a standard six-sided die 60 times.

How many times would she expect to roll the number 4?

  1.   6
  2.   10
  3.   15
  4.   20
Show Answers Only

`B`

Show Worked Solution

`P(4) = 1/6`

`:.\ text(Expected times to roll 4)`

`= 1/6 xx text(number of rolls)`

`= 1/6 xx 60`

`= 10`

`=>  B`

Statistics, STD2 S1 2006 HSC 4 MC

A set of scores is displayed in a stem-and-leaf plot.
 

 2UG-2006-4MC

 
What is the median of this set of scores?

  1.   28
  2.   30
  3.   33
  4.   47
Show Answers Only

`C`

Show Worked Solution

`text(10 scores)`

`text(Median)` `= text{5th + 6th}/2`
  `= (28 + 38)/2`
  `= 33`

`=>  C`

Financial Maths, STD2 F1 2004 HSC 20 MC

Stan worked for 24 hours as shown on his pay slip.

What was his hourly rate of pay?

  1.   $11.20
  2.   $12.13
  3.   $14.56
  4.   $18.20
Show Answers Only

`A`

Show Worked Solution

`text(Let)\ X = text(normal time rate)`

`20X + (4 xx 1.5X)` `= $291.20`
 `26X` `= $291.20`
 `X` `= $11.20`

 
`:.\ text(Hourly rate of pay = $11.20)`

`=>  A`

Probability, STD2 S2 2005 HSC 23a

There are 100 tickets sold in a raffle. Justine sold all 100 tickets to five of her friends. The number of tickets she sold to each friend is shown in the table.
 

  1. Justine claims that each of her friends is equally likely to win first prize.

     

    Give a reason why Justine’s statement is NOT correct.   (1 mark)

  2. What is the probability that first prize is NOT won by Khalid or Herman?   (2 marks)

Show Answers Only
  1. `text(The claim is incorrect because each of her friends)`
    `text(bought a different number of tickets and therefore)`
    `text(their chances of winning are different.)`
  2. `69/100`
Show Worked Solution

i.    `text(The claim is incorrect because each of her friends bought)`

`text(a different number of tickets and therefore their chances of)`

`text(winning are different.)`

 

ii.  `text(Number of tickets not sold to K or H)`

`= 45 + 10 + 14`

`= 69`
 

`:.\ text(Probability 1st prize NOT won by K or H)`

`= 69/100`

Financial Maths, STD2 F1 2004 HSC 17 MC

Rita purchased a camera for $880 while on holidays in Australia. This price included 10% GST. When she left Australia she received a refund of the GST.

What was Rita’s refund?

  1.   $80
  2.   $88
  3.   $792
  4.   $800
Show Answers Only

`A`

Show Worked Solution

`text(Let)\ C = text(cost before GST)`

`880` `= C + text(10%) C`
`1.1C` `= 880`
`C` `= $800`
   
`:.\ text(GST)` `=10 text(%) xx 800`
  `= $80`

 
`=>  A`

Measurement, STD2 M1 2004 HSC 23a

The diagram shows the shape of Carmel’s garden bed. All measurements are in
metres.

  1. Show that the area of the garden bed is 57 square metres.   (2 marks)

  2. Carmel decides to add a 5 cm layer of straw to the garden bed.

     

    Calculate the volume of straw required. Give your answer in cubic metres.   (2 marks)

  3. Each bag holds 0.25 cubic metres of straw.

     

    How many bags does she need to buy?   (2 marks)

  4. A straight fence is to be constructed joining point A to point B.

     

    Find the length of this fence to the nearest metre.   (2 marks)

Show Answers Only
  1. `text(Proof)\ \ text{(See Worked Solutions)}`
  2. `text(2.85 m³)`
  3. `text(She needs to buy 12 bags)`
  4. `8\ text{m  (nearest metre)}`
Show Worked Solution
a.    `text(Area of)\ Delta ABC` `= 1/2 xx b xx h`
  `= 1/2 xx 10 xx 5.1`
  `= 25.5\ text(m²)`
`text(Area of)\ Delta ACD` `= 1/2 xx 10 xx 6.3`
  `= 31.5\ text(m²)`

 

`:.\ text(Total Area)` `= 25.5 + 31.5`
  `= 57\ text(m² … as required)`

 

b.    `V` `= Ah`
  `= 57 xx 0.05`
  `= 2.85\ text(m³)`

 

c.    `text(Bags to buy)` `= 2.85/0.25`
  `= 11.4`

 
`:.\ text(She needs to buy 12 bags.)`

 

d.   `text(Using Pythagoras,)`

`AB^2` `= 6.0^2 + 5.1^2`
  `= 36 + 26.01`
  `= 62.01`
`AB` `= 7.874…`
  `=8\ text{m  (nearest metre)}`

Financial Maths, STD2 F4 2005 HSC 10 MC

The table is used to calculate monthly loan repayments.
 

2UG-2005-10MC
 

Samantha has borrowed  $70 000  at 8% per annum for 15 years.

What is her monthly loan repayment?

  1.    $143.40
  2.    $669.20
  3.    $8030.40
  4.    $10 038.00
Show Answers Only

`B`

Show Worked Solution

`text(Monthly repayment of $1000 at 8% for 15 years)`

`= $9.56`
 

`:.\ text(Monthly repayment of $70 000)`

`= 70 × $9.56`

`= $669.20`

`=>  B`

Measurement, STD2 M1 2004 HSC 13 MC

During a ten-minute period, Kath is exercising and Jim is resting.

How much more air would Kath breathe than Jim during this time?

  1.  40 Litres
  2. 94 Litres
  3. 940 Litres
  4. 1060 Litres
Show Answers Only

`C`

Show Worked Solution

`text(Kath’s air volume)`

`= 10 xx 100`

`=1000\ text(L)`

`text(Jim’s air volume)`

`= 10 xx 6`

`= 60\text(L)`
 

`:.\ text(Extra air that Kath breathes)`

`= 1000 – 60`

`= 940\ text(L)`

`=>  C`

Financial Maths, STD2 F1 2005 HSC 6 MC

Janet’s gross income last year was $60 000. She had allowable tax deductions of $5000. Janet paid 1.5% of her taxable income for the Medicare levy.

How much was Janet’s Medicare levy?

  1.    $750
  2.    $825
  3.    $900
  4.    $975
Show Answers Only

`B`

Show Worked Solution
`text(Taxable income)` `=\ text(Gross income) − text(Deductions)`
  `= 60\ 000 − 5000`
  `= $55\ 000`
   
`:.\ text(Medicare Levy)` `=\ text(1.5%) × $55\ 000`
  `= $825`

 
`=> B`

Measurement, STD2 M6 2005 HSC 5 MC

Which formula should be used to calculate the distance between Toby and Frankie?

  1. `a/(sin A) = b/(sin B)`
  2. `c^2 = a^2 + b^2`
  3. `A = 1/2 ab\ sinC`
  4. `c^2 = a^2 + b^2 − 2ab\ cosC`
Show Answers Only

`A`

Show Worked Solution

`text(The triangle is not a right-angled triangle,)`

`:.\ text(Not)\ B`

`text(Given the information on the diagram provides)`

`text(2 angles and 1 side, the sine rule will work best.)`

`a/sinA = b/sinB`

`=> A`

Probability, STD2 S2 2005 HSC 3 MC

Four radio stations reported the probability of rain as shown in the table.
 

Which radio station reported the highest probability of rain?

  1.    `text(2AT)`
  2.    `text(2BW)`
  3.    `text(2CZ)`
  4.    `text(2DL)`
Show Answers Only

`D`

Show Worked Solution

`text(Converting all probabilities to decimals)`

`2AT` `= 0.53`
`2BW` `= 0.17`
`2CZ` `= 0.52`
`2DL` `= 0.60`

`=> D`

Algebra, STD2 A1 2004 HSC 11 MC

If  `d = 6t^2`, what is a possible value of `t` when  `d = 2400`?

  1. `0.05`
  2. `20`
  3. `120`
  4. `400`
Show Answers Only

`B`

Show Worked Solution
`d` `= 6t^2`
`t^2` `= d/6`
`t` `= +- sqrt(d/6)`

 
`text(When)\ \ d = 2400:`

`t` `= +- sqrt(2400/6)`
  `= +- 20`

 
`=> B`

Financial Maths, STD2 F1 2004 HSC 10 MC

Using the tax table, determine the tax payable on a taxable income of $47 000.

     

  1.   $8310.40
  2.   $9 109.60
  3.   $9 110.00
  4.   $10 310.40
Show Answers Only

`C`

Show Worked Solution

`text(Tax on $47 000)`

`= 8310 + 0.40 xx (47\ 000 – 45\ 000)`

`= 8310 + 800`

`= $9110`

`=> C`

Statistics, STD2 S1 2004 HSC 6-7 MC

Use the set of scores  1, 3, 3, 3, 4, 5, 7, 7, 12  to answer Questions 6 and 7.
 

Question 6

What is the range of the set of scores?

  1. 6
  2. 9
  3. 11
  4. 12

 

Question 7

What are the median and the mode of the set of scores?

  1. Median 3, mode 5
  2. Median 3, mode 3
  3. Median 4, mode 5
  4. Median 4, mode 3
Show Answers Only

`text(Question 6:)\ C`

`text(Question 7:)\ D`

Show Worked Solution

`text(Question 6)`

`text(Range)` `= text(High) – text(Low)`
  `= 12 – 1`
  `= 11`

`=> C`

 

`text(Question 7)`

`text(9 scores)`

`:.\ text(Median)` `= (9 + 1) / 2`
  `=5 text(th score)`
  `= 4`

`text(Mode) = 3`

`=> D`

CORE*, FUR1 2009 VCAA 6 MC

In 2005, Peter’s annual salary was $35 000.

At the start of each subsequent year, his annual salary increases by 4.75%.

In 2010 his salary will be closest to

A.   $36 663

B.   $42 140

C.   $43 310

D.   $44 140

E.   $55 670

Show Answers Only

`D`

Show Worked Solution

`P = 35\ 000, \ R = 1.0475, \ n = 5`

`text(Using)\ \ \ A` `= PR^n`
  `= 35\ 000 xx 1.0475^5`
  `= $44\ 140.597…`

`=>  D`

CORE, FUR1 2009 VCAA 5 MC

A new air-conditioning unit was purchased for $5000 on 1 January 2009.

On 1 January of each year after 2009 its value is depreciated by 20% using the reducing balance method.

The value of the air conditioner will be below $1500 for the first time on 1 January

A.   2012

B.   2013

C.   2014

D.   2015

E.   2016

Show Answers Only

`D`

Show Worked Solution
`text{Value (Jan12)}` `= 5000(1-\frac{20}{100))^3`
  `= 5000 xx 0.8^3`
  `= 2560`
`text{Value (Jan14)}` `=5000 xx 0.8^5`
  `=1638.40`
`text{Value (Jan15)}` `=5000 xx 0.8^6`
  `= 1310.72`

  
`=>  D`

CORE*, FUR1 2008 VCAA 6 MC

Sam and Charlie each invest $5000 for three years.

Sam’s investment earns simple interest at the rate of 7.5% per annum.

Charlie’s investment earns interest at the rate of 7.5% per annum compounding annually.

At the conclusion of three years, correct to the nearest cent, Sam will have

A.   $86.48 less than Charlie.

B.   $86.48 more than Charlie.

C.   $132.23 less than Charlie.

D.   $132.23 more than Charlie.

E.   the same as Charlie.

Show Answers Only

 `A`

Show Worked Solution

`text(Sam’s Investment,)`

`I` `= (PrT)/100`
  `= ((5000)(7.5)(3))/100`
  `= 1125`

 

`:.\ text(Total amount)` `= 5000 + 1125`
  `= $6125`

 
`text(Charlie’s Investment,)`

`A` `= PR^n`
  `= (5000)(1.075)^3`
  `= $6211.48`

 

`text(Difference)` `= 6211.48-6125`
  `= $86.48`

`=>  A`