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v1 Financial Maths, STD2 F1 2004 HSC 27b

Jack is paid at these rates:

\begin{array}{|l|} \hline \text{Weekday rate} & \text{\(\$\)15 per hour}\\ \text{Saturday rate} & \text{Time-and-a-half}\\ \text{Sunday rate} & \text{Double time}\\ \hline \end{array}

His time sheet for last week is:

\begin{array}{|l|l|l|l|} \hline & \textit{Start} & \textit{Finish} & \textit{Unpaid break}\\ \hline \text{Friday} & \text{9.00 am} & \text{4.00 pm} & \text{1 hour} \\ \text{Saturday} & \text{9.00 am} & \text{4.00 pm} & \text{1 hour} \\ \text{Sunday} & \text{9.00 am} & \text{1.00 pm} & \text{30 minutes} \\ \hline \end{array}

  1. Calculate Jack's gross pay for last week.  (3 marks)
  2. Jack decides not to work on Sundays. 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. \(\$330\)
  2. \(\text{7 extra hours}\)
Show Worked Solution
i.     \(\text{Pay(Fri)}\) \(=6 \ \text {hours } \times 15.00\)
    \(=\$90.00\)
  \(\text{Pay(Sat)}\) \(=6 \ \text {hours } \times 1.5 \times 15.00\)
    \(=\$135.00\)
  \(\text{Pay(Sun)}\) \(=3.5 \ \text {hours } \times 2 \times 15.00 \)
    \(=\$105.00\)

\(\therefore \text{Gross pay }\) \(=90+135+105\)
  \(=\$330\)

 

ii.     \(\text{Pay on Sun}=\$105\)

\(\text{Weekly equivalent hours}\) \(=\dfrac{105}{15}\)
  \(=7 \ \text{hours}\)

 

\(\therefore \ \text{He will have to work 7 extra hours on a weekday}\)

v1 Financial Maths, STD2 F1 2022 HSC 21

A real estate agent's commission for selling houses is 2% for the first $900 000 of the sale price and 1.5% for any amount over $900 000.

Calculate the commission earned in selling a house for $1 200 000.  (2 marks)

Show Answers Only

`$22\ 500`

Show Worked Solution
`text{Commission}` `=900\ 000 xx 2text{%} + (1\ 200\ 000-900\ 000) xx 1.5text{%}`
  `=900\ 000 xx 0.02 + 300\ 000 xx 0.015`
  `=18\ 000 + 4\ 500`
  `=$22\ 500`

v1 Financial Maths, STD2 F1 2013 HSC 11 MC

An enterprise agreement has the following annual salary arrangements:
 

Rowan's employer pays 5% more than the enterprise agreement. He is on Step 2 and receives an allowance for Leader 1.

What is Rowan's gross monthly pay?

  1. $3575.50
  2. $3730.00
  3. $3937.50
  4. $4150.00
Show Answers Only

`C`

Show Worked Solution
♦ Mean mark 46%
`text(Gross annual pay)` `=(40\ 000+5000)xx1.05`
  `=$47\ 250`

 

`:.\ text(Gross monthly pay)` `=(47\ 250)/12`
  `=$3937.50`

 
`=>\ C`

v1 Financial Maths, STD2 F1 2007 HSC 3 MC

Dan is about to go on holidays for four weeks. His weekly salary is $375  and his holiday loading is 20% of four weeks pay.

What is Dan's total pay for the four weeks holiday?

  1. $400
  2. $1250
  3. $1800
  4. $2150
Show Answers Only

`C`

Show Worked Solution
`text(Salary)\ text{(4 weeks)}` `= 4 xx 375`
  `= $1500`

 

`text(Holiday loading)` `= 1500 xx 20%`
  `= $300`

 

`:.\ text(Total pay)` `= 1500+300`
  `= $1800`

 
`=>  C`

v1 Financial Maths, STD2 F1 2008 HSC 7 MC

Maya’s regular wage is $20 per hour. One week, she worked 9 hours at double time.

How many hours would Maya need to work at time-and-a-half to earn the same amount?

  1. 10
  2. 11
  3. 12
  4. 13
Show Answers Only

`C`

Show Worked Solution

`text(Amount earned at double time)`

`= 9 xx 2 xx 20`

`= $360`

`text(Time-and-a-half rate)` `= 1.5 xx 20`
  `= $30 text(/hr)`

 
`:.\ text(# Hours at time-and-a-half)`

`= 360 / 30`

`= 12\ text(hrs)`

`=>  C`

v1 Financial Maths, STD2 F1 2014 HSC 13 MC

Mark works as a car salesperson. His commission is based on a sliding scale of 5% on the first $3000 of his sales, 3% on the next $1500, and 1.5% thereafter.

What is Mark’s commission when his total sales are $6,250? 

  1. $202.75
  2. $210.50
  3. $216.25
  4. $221.25
Show Answers Only

`D`

Show Worked Solution

`text(Commission)`

`= (3000 xx text(5%)) + (1500 xx text(3%)) + (6250 – 4500) xx text(1.5%)`

`= (3000 xx 0.05) + (1500 xx 0.03) + (1750 xx 0.015)`

`= 150 + 45 + 26.25`

`= 221.25`

`=> D`

v1 Financial Maths, STD2 F1 2006 HSC 22 MC

This income tax table is used to calculate Daniel’s tax payable.

Taxable income Tax payable
$0 − $11 000 Nil
$11 001 − $42 400 20 cents for each $1 over $11 000
$42 401 − $78 800 $6280 plus 33 cents for each $1 over $42 400
$78 801 − $108 400 $18 292 plus 37 cents for each $1 over $78 800
$108 401 and over $31 316 plus 48 cents for each $1 over $108 400

Daniel’s taxable income increases from $45 000 to $80 000.

What percentage of his increase will he pay in additional tax?

  1. `text(22.7%)`
  2. `text(25.5%)`
  3. `text(33.1%)`
  4. `text(40.6%)`
Show Answers Only

`C`

Show Worked Solution
`text(Tax on $45 000)` `= 6280 + 0.33 xx (45\ 000-42\ 400)`
  `= 6280 + 0.33 xx 2600`
  `= 6280 + 858`
  `= $7138`
`text(Tax on $80 000)` `= 18\ 292 + 0.37 xx (80\ 000-78\ 800)`
  `= 18\ 292 + 0.37 xx 1200`
  `= 18\ 292 + 444`
  `= $18\ 736`
`:.\ text(Extra tax)` `= 18\ 7360-7138`
  `= $11\ 598`

`:.\ \text{% of income increase paid in tax}`

`= (11\ 598) / (35\ 000) xx 100`

`=33.14%`

`=> C`

v1 Financial Maths, STD2 F1 2013 HSC 13 MC

Jared borrowed $9 000. He repaid the loan in full at the end of three years with a lump sum of $10 350.

What annual simple interest rate was he charged?

  1. 6%
  2. 5.25%
  3. 5%
  4. 4.5%
Show Answers Only

`C`

Show Worked Solution

`text(Total interest paid) = 10\ 350-9000 = $1350`

`I` `=Prn`
`1350` `=9000 xx r xx 3`
`r` `=1350/(27\ 000)`
  `=5 text(%)`

 
`=> C`

v1 Financial Maths, STD2 F1 2010 HSC 5 MC

Lina invests $2500 for 1 year and 2 months. The simple interest is calculated at a rate of 5% per annum.

What is the total value of the investment at the end of this period?

  1. $2700
  2. $2650
  3. $2630
  4. $2800 
Show Answers Only

`C`

Show Worked Solution
`text(Interest)` `=Prn`
  `=2500 xx \text(5%)\ xx 14/12`
  `=$130`

 

`:.\ text(Value of Investment)` `=2500+130`
  `=$2630`

`=>  C`

EXAMCOPY Algebra, STD1 A1 2019 HSC 34

Given the formula  `C = (A(y + 1))/24`, calculate the value of  `y`  when  `C = 120`  and  `A = 500`.  (3 marks)

Show Answers Only

`4.76`

Show Worked Solution

`text(Make)\ \ y\ \ text(the subject:)`

`C` `= (A(y + 1))/24`
`24C` `= A(y + 1)`
`y + 1` `= (24C)/A`
`y` `= (24C)/A-1`
  `= (24 xx 120)/500-1`
  `= 4.76`

Standard Deviation, SM-Bank 011

Mr Ralph has a History class that has completed two separate exams during the term.

The results of each exam are summarised in the histograms below.
 

Without using calculations, explain which test will have the highest standard deviation.  (2 marks)

Show Answers Only

\(\text{By inspection, Test B has a higher range than Test A.}\)

\(\text{Test A results look to have a tighter spread of data points}\)

\(\text{about its expected mean, when compared to Test B.}\)

\(\text{Test B will therefore have a higher standard deviation.}\) 

Show Worked Solution

\(\text{By inspection, Test B has a higher range than Test A.}\)

\(\text{Test A results look to have a tighter spread of data points}\)

\(\text{about its expected mean, when compared to Test B.}\)

\(\text{Test B will therefore have a higher standard deviation.}\) 

Standard Deviation, SM-Bank 017

Dataset 1 has mean \(\bar x_1\) and standard deviation \(\sigma_1\).

Dataset 2 has mean \(\bar x_2\) and standard deviation \(\sigma_2\).

Consider the following statement:  If  \(\bar x_1 < \bar x_2\), then  \(\sigma_1 < \sigma_2\).

Is this statement correct? Explain your answer.   (2 marks)

Show Answers Only

\(\text{Standard deviation is a measure of how much members}\)

\(\text{of a data group differ from the mean value of the group.}\)

\(\text{It follows that the relative standard deviation between two}\)

\(\text{datasets is not affected if}\ \ \bar x_1 < \bar x_2\).

\(\text{Therefore, the statement is incorrect.}\)

Show Worked Solution

\(\text{Standard deviation is a measure of how much members}\)

\(\text{of a data group differ from the mean value of the group.}\)

\(\text{It follows that the relative standard deviation between two}\)

\(\text{datasets is not affected if}\ \ \bar x_1 < \bar x_2\).

\(\text{Therefore, the statement is incorrect.}\)

Standard Deviation, SM-Bank 015

Rhonda and her friends were surveyed about the number of concerts they have been to in the last 12 months.

Their responses are as follows:

\(3, \ 4, \ 8, \ 10, \ 12, \ 13\)

  1. Determine the median number of concerts from this data set.   (1 mark)

  2. Calculate the standard deviation of this data set, giving your answer to one decimal place.   (1 mark)

Show Answers Only

i.    \(\text{Median}\ = 9\)

ii.   \(\text{Std Dev}\ = 3.8\)

Show Worked Solution

i.    \(3, \ 4, \ 8, \ 10, \ 12, \ 13\)

\(\text{6 data points}\)

\(\text{Median}\ = \dfrac{\text{3rd + 4th}}{2} = \dfrac{8+10}{2} = 9 \)
 

ii.    \(\text{By calculator (using Statistics mode):} \)

\(\text{Std Dev}\ = 3.771… = 3.8\ \text{(1 d.p.)} \)

Standard Deviation, SM-Bank 014

Albert teaches Physics and sets his class a mid-term exam.

The results are summarised in the Stem and Leaf plot drawn below.
 

  1. Determine the median test score of the data set.   (1 mark)

  2. Calculate the standard deviation of this data set, giving your answer to two decimal places.   (1 mark)

Show Answers Only

i.    \(\text{Median}\ = 83\)

ii.   \(\text{Std Dev}\ = 12.14\)

Show Worked Solution

i.    \(\text{Dataset values:}\ 62, 65, 78, 79, 83, 89, 94, 96, 97 \)

\(\text{9 data points}\ \ \Rightarrow\ \ \text{Median = 5th value} \)

\(\text{Median}\ = 83\)
 

ii.    \(\text{By calculator (using Statistics mode):} \)

\(\text{Std Dev}\ = 12.139… = 12.14\ \text{(2 d.p.)} \)

Standard Deviation, SM-Bank 012

Seven 40-year old males are asked how many children they have in a survey.

The results are summarised in the histogram drawn below.
 

  1. Determine the mean number of children of the group surveyed, giving your answer to two decimal places.   (1 mark)

  2. Calculate the standard deviation of this data set, giving your answer to two decimal places.   (1 mark)

Show Answers Only

i.    \(\text{Mean}\ = 2.57\)

ii.   \(\text{Std Dev}\ = 1.05\)

Show Worked Solution

i.    \(\text{Dataset values:}\ 1, 2, 2, 2, 3, 4, 4 \)

\(\text{Mean}\ = \dfrac{1+2+2+2+3+4+4}{7} = \dfrac{18}{7} = 2.571… = 2.57\ \text{(2 d.p.)} \)
 

ii.    \(\text{By calculator (using Statistics mode):} \)

\(\text{Std Dev}\ = 1.049… = 1.05\ \text{(2 d.p.)} \)

Standard Deviation, SM-Bank 010

A dataset is represented by the dot plot drawn below.
 

Determine the standard deviation of the dataset, giving your answer correct to two decimal places.   (2 marks)

Show Answers Only

\(\text{Std Dev}\ = 1.25\)

Show Worked Solution

\(\text{Dataset values:}\ 0, 1, 1, 2, 2, 3, 4 \)

\(\text{By calculator (using Statistics mode):}\)

\(\text{Std Dev}\ = 1.245… = 1.25\ \text{(2 d.p.)} \)

Standard Deviation, SM-Bank 009

Isa Guha recorded the number of sixes hit in the first nine games of the Women's Big Bash Cricket League over two seasons.

The results are recorded in the two dot plots below.
  

  1. Determine the standard deviation of the results in Season 1, giving your answer correct to one decimal place.   (2 marks)

  2. Without using calculations, explain which data set will have the highest standard deviation.  (2 marks)

Show Answers Only

i.    \(\text{Std Dev}\ = 1.9\ \text{(1 d.p.)} \)

ii.    \(\text{By inspection, season 1 has a slightly higher range}\)

\(\text{(5 vs 4) and its data points can be seen to be much}\)

\(\text{wider spread about the expected mean value.}\)

\(\text{Season 1 will therefore have a higher standard deviation.}\) 

Show Worked Solution

i.    \(\text{Season 1 dataset:}\ 6, 6, 7, 8, 10, 10, 10, 11, 11\)

\(\text{By calculator (using Statistics mode):}\)

\(\text{Std Dev}\ = 1.930… = 1.9\ \text{(1 d.p.)} \)
 

ii.    \(\text{By inspection, season 1 has a slightly higher range}\)

\(\text{(5 vs 4) and its data points can be seen to be much}\)

\(\text{wider spread about the expected mean value.}\)

\(\text{Season 1 will therefore have a higher standard deviation.}\) 

Standard Deviation, SM-Bank 008

In a cricket test match, a scorebook recorded the number of runs scored by England's top six batsman.

The scores are summarised in the Stem and Leaf plot below.
 

Determine the standard deviation of the scores, giving your answer correct to one decimal place.   (2 marks)

Show Answers Only

\(\text{Std Dev}\ = 6.6\)

Show Worked Solution

\(\text{Runs scored dataset:}\ 8, 12, 15, 21, 23, 27 \)

\(\text{By calculator (using Statistics mode):}\)

\(\text{Std Dev}\ = 6.574… = 6.6\ \text{(1 d.p.)} \)

Standard Deviation, SM-Bank 007

Ms Arnott has seven students in her Ethics class. The results of the most recent exam, completed by the whole class, is summarised in the Stem and Leaf plot below.
 

Determine the standard deviation of the exam results, giving your answer correct to one decimal place.   (2 marks)

Show Answers Only

\(\text{Std Dev}\ = 8.8\)

Show Worked Solution

\(\text{Exam result dataset:}\ 56, 63, 69, 72, 77, 78, 84 \)

\(\text{By calculator (using Statistics mode):}\)

\(\text{Std Dev}\ = 8.84… = 8.8\ \text{(1 d.p.)} \)

Standard Deviation, SM-Bank 006

Seven players in two basketball teams, the Swifties and the Chiefs, recorded how many 3-point baskets they had shot in the last season.

The results are recorded in the two Stem and Leaf plots below.
 

  1. Determine the standard deviation of the Swifties' results, giving your answer correct to one decimal place.   (2 marks)

  2. Without using calculations, explain which data set will have the smallest standard deviation.  (2 marks)

Show Answers Only

i.     \(\text{Std Dev}\ = 13.4 \)

ii.    \(\text{The results of the Chiefs have a much smaller range (18 vs 38)}\)

\(\text{and are a much tighter fit around the expected mean.}\)

\(\text{The Chiefs’ results will therefore have a smaller standard deviation.}\) 

Show Worked Solution

i.    \(\text{Swifties’ dataset:}\ 1, 2, 17, 22, 26, 33, 39 \)

\(\text{By calculator (using Statistics mode):}\)

\(\text{Std Dev}\ = 13.43… = 13.4\ \text{(1 d.p.)} \)
 

ii.    \(\text{The results of the Chiefs have a much smaller range (18 vs 38)}\)

\(\text{and are a much tighter fit around the expected mean.}\)

\(\text{The Chiefs’ results will therefore have a smaller standard deviation.}\) 

Standard Deviation, SM-Bank 005

9 students completed two quizzes and the results were summarised in the dot plot diagrams below.
 

  1. Determine the median value of the results of Quiz A.   (1 mark)

  2. Calculate the standard deviation of Quiz A and Quiz B, giving your answers correct to one decimal place.  (2 marks)

Show Answers Only

i.     \(\text{Median}\ = 7\)

ii.    \(\text{Std Dev (Quiz A)}\ = 1.3 \)

\(\text{Std Dev (Quiz B)}\ = 0.8\)

Show Worked Solution

i.    \(\text{9 data points}\ \ \Rightarrow \ \ \text{Median = 5th data point}\)

\(\text{Median}\ = 7 \)
 

ii.    \(\text{By calculator (using Statistics mode):}\)

\(\text{Quiz A dataset:}\ 5, 5, 6, 7, 7, 8, 8, 8, 9 \)

\(\text{Std Dev (Quiz A)}\ = 1.33… = 1.3\ \text{(1 d.p.)} \)
 

\(\text{Quiz B dataset:}\ 6, 6, 7, 7, 7, 8, 8, 8, 8 \)

\(\text{Std Dev (Quiz B)}\ = 0.78… = 0.8\ \text{(1 d.p.)} \)

Standard Deviation, SM-Bank 004

Two data sets are represented in the dot plot diagrams below.
 

  1. Calculate the standard deviation of Data Set B, giving your answer correct to one decimal place.   (1 mark)

  2. Without using calculations, explain which data set has the highest standard deviation.  (2 marks)

Show Answers Only

i.    \(\text{Std Dev}\ = 1.79… = 1.8\ \text{(1 d.p.)} \)

ii.   \(\text{By inspection, Data Set A has a smaller range and a tighter}\)

\(\text{spread against its expected mean value.}\)

\(\text{Data Set B will therefore have a higher standard deviation.}\) 

Show Worked Solution

i.    \(\text{Data points:}\ 4, 4, 5, 5, 6, 6, 7, 8, 9, 9\)

\(\text{By calculator (using Statistics mode):} \)

\(\text{Std Dev}\ = 1.79... = 1.8\ \text{(1 d.p.)} \)
 

ii.   \(\text{By inspection, Data Set A has a smaller range and a tighter}\)

\(\text{spread against its expected mean value.}\)

\(\text{Data Set B will therefore have a higher standard deviation.}\) 

Standard Deviation, SM-Bank 003

In a small business, the seven employees earn the following wages per week:

\(\$300, \ \$490, \ \$520, \ \$590, \ \$660, \ \$680, \ \$970\)

  1.  Calculate the standard deviation for this set of data, giving your answer to one decimal place.  (1 mark)

  2.  Each employee receives a $20 pay increase.

     

     Explain the effect that this increase will this have on the standard deviation?  (2 marks)

Show Answers Only

i.    \(191.0\)

ii.    \(\text{All values increase by \$20, but so too does the mean.} \)

\(\text{Therefore the spread about the new mean will not change} \)

\(\text{and therefore the standard deviation will remain the same.} \)

Show Worked Solution

i.    \(\text{By calculator (in Statistics mode:}\)

\(\text{Std Dev}\ = 191.044...  =191.0\ \text{(1 d.p.)} \)


ii.    \(\text{All values increase by \$20, but so too does the mean.} \)

\(\text{Therefore the spread about the new mean will not change} \)

\(\text{and therefore the standard deviation will remain the same.} \)

Standard Deviation, SM-Bank 002

Ali’s class sits a Geography test and the results are recorded below.

\(58,\ \ 74,\ \ 65,\ \ 66,\ \ 73,\ \ 71,\ \ 72,\ \ 74,\ \ 62,\ \ 70\)

The mean for the test was 68.5. 

  1. Calculate the standard deviation for the test. Give your answer correct to one decimal place.    (2 marks)

  2. Explain whether the mean of the test is greater than or less than the median of the test.    (1 mark)

Show Answers Only

i.    \(5.2\ \ \text{(to 1 d.p.)} \)

ii.    \(\text{Median}\ = \dfrac{70+71}{2} = 70.5 \)

\(\Rightarrow\ \text{Median > Mean  (70.5 > 68.5)} \)

Show Worked Solution

i.    \(\text{By calculator (in Statistics mode):}\)

\(\text{Std Dev}\ = 5.220… = 5.2\ \text{(1 d.p.)} \)

♦ Mean mark (a) 39%.

 
ii.    \(\text{Reorder test results in ascending order:}\)

\(58,\ \ 62,\ \ 65,\ \ 66,\ \ 70, \ \ 71,\ \ 72,\ \ 73,\ \ 74,\ \ 74\)

\(\text{Median}\ = \dfrac{70+71}{2} = 70.5 \)

\(\Rightarrow\ \text{Median > Mean  (70.5 > 68.5)} \)

Standard Deviation, SM-Bank 001

The ages of nine students were recorded in the table below.
 

 

  1. What is the standard deviation, correct to two decimal places?   (2 marks)

  2. Briefly explain what is meant by the term standard deviation.   (1 mark)

Show Answers Only

i.    \(\text{By calculator (in Statistics mode):} \)

\(\text{Std Dev}\ = 1.5947… = 1.59\ \ \text{(to 2 d.p.)} \)

 

ii.   \(\text{Standard deviation is a measure of how much members}\)

\(\text{of a data group differ from the mean value of the group.}\)

Show Worked Solution

i.    \(\text{By calculator (in Statistics mode):} \)

\(\text{Std Dev}\ = 1.5947… = 1.59\ \ \text{(to 2 d.p.)} \)

 

ii.   \(\text{Standard deviation is a measure of how much members}\)

\(\text{of a data group differ from the mean value of the group.}\)

Box-Plots and 5-Number Summary, SM-Bank 016

Ellyse recorded the number of wickets she took in the first seven games of the cricket season, which are as follows:

\(3, \ 5, \ 0, \ 8, \ 1, \ 2, \ 2 \)

  1. Complete the 5-number summary table of Ellyse's results below.   (2 marks)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}   \rule[-1ex]{0pt}{0pt} &  &  &  &  \\
\hline
\end{array}

  1. Draw a box plot, using the number line below for reference, that displays Ellyse's results.   (2 marks)
     

  1. Describe the skew of Ellyse's results.   (1 mark)

Show Answers Only

i.    \(\text{Ordering the data:}\ 0, \ 1, \ 2, \ 2, \ 3, \ 5, \ 8\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex} 0  \rule[-1ex]{0pt}{0pt} & 1 & 2 & 5 & 8 \\
\hline
\end{array}

ii.   
     

iii.   \(\text{Positively skewed}\)

Show Worked Solution

i.    \(\text{Ordering the data:}\ 0, \ 1, \ 2, \ 2, \ 3, \ 5, \ 8\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex} 0  \rule[-1ex]{0pt}{0pt} & 1 & 2 & 5 & 8 \\
\hline
\end{array}

ii.   
     

iii.   \(\text{Positively skewed}\)

Box Plots and 5-Number Summary, SM-Bank 015

Eli sat 22 Maths quizzes throughout year 8 and her results were recorded in the 5-number summary below.

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  30 \rule[-1ex]{0pt}{0pt} & 50 & 60 & 70 & 80 \\
\hline
\end{array}

  1. Using the number line below as reference, draw a box plot that displays Eli's results.   (2 marks)
     

  1. Describe the skew of Eli's results.   (1 mark)

Show Answers Only

i.    
       

ii.    \(\text{Negatively skewed (slightly)}\)

Show Worked Solution

i.    
       

ii.    \(\text{Negatively skewed (slightly)}\)

Box Plots and 5-Number Summary, SM-Bank 014

The test results in English and Mathematics for a class were recorded and displayed in the box plots.
 

  1. What is the interquartile range for English?   (1 mark)

  2. Compare and contrast the two data sets by referring to the skewness of the distributions and the measures of their centres and spread.   (3 marks)

Show Answers Only

i.    `text{IQR}_text{(English)}\ = 80-50=30`

ii.  `text(Skewness)`

  • `text(English has greater negative skew)`
  • `text(Maths is more normally distributed)`

`text(Location and Spread)`

  • `text(English has a range of 85, Maths has 40.)`
  • `text{English has larger IQR than Maths (30 vs 15)}`
  • `text{Maths’ median (75) is higher than English (70)}`
  • `text{Same upper quartile marks (80)}`
  • `text(English has highest and lowest individual mark)`
Show Worked Solution

i.    `text{IQR}_text{(English)}\ = 80-50=30`

 

♦ Mean mark (ii) 35%
COMMENT: The best answers use the correct language of location and spread such as mean, median, interquartile range, standard deviation and skewness.

ii.  `text(Skewness)`

  • `text(English has greater negative skew)`
  • `text(Maths is more normally distributed)`

`text(Location and Spread)`

  • `text(English has a range of 85, Maths has 40.)`
  • `text{English has larger IQR than Maths (30 vs 15)}`
  • `text{Maths’ median (75) is higher than English (70)}`
  • `text{Same upper quartile marks (80)}`
  • `text(English has highest and lowest individual mark)`

Box Plots and 5-Number Summary, SM-Bank 013

Terry and Kim each sat twenty class tests. Terry’s results on the tests are displayed in the box plot shown in part (i).

  1. Kim’s  5-number summary for the tests is  67,  69,  71,  73,  75.

     

    Draw a box plot to display Kim’s results below that of Terry’s results.   (1 mark)
     
       

  2. What percentage of Terry’s results were below 69?     (1 mark)

  3. Describe the skew of Kim's results.   (1 mark)

Show Answers Only
i.    

ii.  `text(50%)`
 

iii.  `text{By inspection of box plot: Evenly skewed}`

Show Worked Solution
i. 

 
ii.  `text(50%)`
 

iii.  `text{By inspection of box plot: Evenly skewed}`

Box Plots and 5-Number, SM-Bank 011

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.   \(\text{Range}\ = 7 \)

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 6-1=5 \)

Show Worked Solution

i.   \(\text{Range}\ = 7-0=7 \)
  

ii.   
         

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  0 \rule[-1ex]{0pt}{0pt} & 1 & 4 & 6 & 7 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 6-1=5 \)

Box Plots and 5-Number, SM-Bank 010

Using a 5-number summary of the data represented in this graph, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.   \(\text{Median}\ = 2 \)

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-1=4 \)

Show Worked Solution

i.   \(\text{15 data points}\ \Rightarrow \ \text{Median = 8th data point}\)

\(\text{Median}\ = 2 \)
  

ii.   
           

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  0 \rule[-1ex]{0pt}{0pt} & 1 & 2 & 5 & 7 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-1=4 \)

Box Plots and 5-Number, SM-Bank 009

Yoyo was practicing his cello for an orchestra audition and the data set below records the number of hours he practiced each day over a 10-day period.

\(7.6, \ 12.2, \ 8.4, \ 7.8, \ 8.8, \ 9.3, \ 11.9, \ 7.0, \ 8.2, \ 10.4\)

Using a 5-number summary of this dataset, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Range}\ = 12.2-7.0 = 5.2 \)
 

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 10.4-7.8=2.6 \)

Show Worked Solution

i.    \(\text{Placing data values in order:}\)

\(7.0, \ 7.6, \ 7.8, \ 8.2, \ 8.4, \ 8.8, \ 9.3, \ 10.4, \ 11.9, \ 12.2\)

\(\text{Range}\ = 12.2-7.0 = 5.2 \)
 

ii.    \(\underbrace{7.0}_{\text{min}}, \ 7.7, \ \underbrace{7.8}_{Q1}, \ 8.2, \ \underbrace{8.4, \ 8.8}_{Q2}, \ 9.3, \ \underbrace{10.4}_{Q3}, \ 11.9, \ \underbrace{12.2}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  7.0 \rule[-1ex]{0pt}{0pt} & 7.8 & 8.6 & 10.4 & 12.2 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 10.4-7.8=2.6 \)

Box Plots and 5-Number, SM-Bank 008

Matt records the number of times he takes his dog Max for a walk each month. The data set below records the months January to August.

\(21, \ 24, \ 28, \ 22, \ 15, \ 12, \ 13, \ 17\)

Using a 5-number summary of this dataset, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Median}\ = \dfrac{17+21}{2} = 19 \)
 

ii.    \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 23-14=9 \)

Show Worked Solution

i.    \(\text{Placing data values in order:}\)

\(12, \ 13, \ 15, \ 17, \ 21, \ 22, \ 24, \ 28 \)

\(\text{Median}\ = \dfrac{17+21}{2} = 19 \)
 

ii.    \(\underbrace{12}_{\text{min}}, \underbrace{13+15}_{Q1}, \ \underbrace{17+21}_{Q2}, \ \underbrace{22, \ 24}_{Q3}, \ \underbrace{28}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  12 \rule[-1ex]{0pt}{0pt} & 14 & 19 & 23 & 28 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 23-14=9 \)

Box Plots and 5-Number, SM-Bank 007

The data set below consists of 8 data points.

\(7.0, \ 7.4, \ 8.1, \ 9.3, \ 9.5, \ 10.7, \ 11.1, \ 12.9 \)

Complete the 5-number summary table of the data set below.   (2 marks)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} & \ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \ \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}   \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

Show Answers Only

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  7.0 \rule[-1ex]{0pt}{0pt} & 7.75 & 9.4 & 10.9 & 12.9 \\
\hline
\end{array}

Show Worked Solution

\(\underbrace{7.0}_{\text{min}}, \underbrace{7.4,\ 8.1}_{Q1}, \ \underbrace{9.3, \ 9.5}_{Q2}, \ \underbrace{10.7, \ 11.1}_{Q3}, \ \underbrace{12.9}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  7.0 \rule[-1ex]{0pt}{0pt} & 7.75 & 9.4 & 10.9 & 12.9 \\
\hline
\end{array}

Box Plots and 5-Number, SM-Bank 006

Rocket Reddy played 10 full seasons of first grade rugby league and recorded the number of tries he scored each season.

\(13, \ 5, \ 11, \ 2, \ 10, \ 13, \ 5, \ 7, \ 8, \ 3\)

Complete the 5-number summary table of Rocket Reddy's data below.   (2 marks)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} & \ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \ \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}   \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

Show Answers Only

\(\underbrace{2}_{\text{min}}, \ 3, \underbrace{5}_{Q1}, \ 5, \ \underbrace{7, \ 8}_{Q2}, \ 10, \ \underbrace{11}_{Q3}, \ 13, \ \underbrace{13}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  2 \rule[-1ex]{0pt}{0pt} & 5 & 7.5 & 11 & 13 \\
\hline
\end{array}

Show Worked Solution

\(\text{Place data points in order:}\)

\(2, \ 3, \ 5, \ 5, \ 7, \ 8, \ 10, \ 11, \ 13, \ 13\)

\(\underbrace{2}_{\text{min}}, \ 3, \underbrace{5}_{Q1}, \ 5, \ \underbrace{7, \ 8}_{Q2}, \ 10, \ \underbrace{11}_{Q3}, \ 13, \ \underbrace{13}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  2 \rule[-1ex]{0pt}{0pt} & 5 & 7.5 & 11 & 13 \\
\hline
\end{array}

Box Plots and 5-Number, SM-Bank 005

Le Bron plays basketball and records the number of free throws he shoots in the first nine games of the season.

\(12, \ 8, \ 4, \ 15, \ 13, \ 7, \ 8, \ 3, \ 10\)

Using a 5-number summary of this dataset, or otherwise, determine

  1. the median   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Median}\ = 8\)

ii.    \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-2 =3\)

Show Worked Solution

i.    \(\text{Ordering the data values:}\)

\(3, \ 4, \ 7, \ 8, \ 8, \ 10, \ 12, \ 13, \ 15\)

\(\text{Median}\ = 8\)
 

ii.    \(\underbrace{3}_{\text{min}}, \ \underbrace{4, \ 7}_{Q1}, \ 8, \ \underbrace{8}_{Q2}, \ 10, \ \underbrace{12, \ 13}_{Q3}, \ \underbrace{15}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  3 \rule[-1ex]{0pt}{0pt} & 5.5 & 8 & 12.5 & 15 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 12.5-5.5 =7\)

Box Plots and 5-Number, SM-Bank 004

Robert records the total goals scored in each of the first 11 matches of his favourite soccer team.

\(3, \ 5, \ 1, \ 2, \ 2, \ 7, \ 6, \ 4, \ 1, \ 5, \ 3\)

Using a 5-number summary of this dataset, or otherwise, determine

  1. the range   (1 mark)

  2. the interquartile range   (2 marks)

Show Answers Only

i.    \(\text{Range}\ = 7-1=6\)

ii.   \(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-2 =3\)

Show Worked Solution

i.    \(\text{Ordering the data values:}\)

\(1, \ 1, \ 2, \ 2, \ 3, \ 3, \ 4, \ 5, \ 5, \ 6, \ 7\)

\(\text{Range}\ = 7-1=6\)
 

ii.   \(\underbrace{1}_{\text{min}}, 1, \ \underbrace{2}_{Q1}, \ 2, \ 3, \ \underbrace{3}_{Q2}, \ 4, \ 5, \ \underbrace{5}_{Q3}, \ 6, \ \underbrace{7}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  1 \rule[-1ex]{0pt}{0pt} & 2 & 3 & 5 & 7 \\
\hline
\end{array}

\(\text{IQR}\ = \text{Q}_3-\text{Q}_1 = 5-2 =3\)

Box Plots and 5-Number, SM-Bank 003

The numerical data set below is made up of 9 data points.

\(1.1, \ 1.3, \ 1.3, \ 1.3, \ 1.6, \ 1.7, \ 1.9, \ 2.1, \ 2.1\)

Complete 5-number summary table below.   (2 marks)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} & \ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \ \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}   \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

Show Answers Only

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  1.1 \rule[-1ex]{0pt}{0pt} & 1.3 & 1.6 & 2.0 & 2.1 \\
\hline
\end{array}

Show Worked Solution

\(\underbrace{1.1}_{\text{min}}, \ \underbrace{1.3, \ 1.3}_{Q1}, \ 1.3, \ \underbrace{1.6}_{Q2}, \ 13, \ \underbrace{1.9, \ 2.1}_{Q3}, \ \underbrace{2.1}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  1.1 \rule[-1ex]{0pt}{0pt} & 1.3 & 1.6 & 2.0 & 2.1 \\
\hline
\end{array}

Box Plots and 5-Number, SM-Bank 002

The numerical data set below is made up of 7 data points.

\(5, \ 7, \ 7, \ 10, \ 13, \ 15, \ 19\)

Complete 5-number summary table below.   (2 marks)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} & \ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \ \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}   \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

Show Answers Only

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  5 \rule[-1ex]{0pt}{0pt} & 7 & 10 & 15 & 19 \\
\hline
\end{array}

Show Worked Solution

\(\underbrace{5}_{\text{min}}, \ \underbrace{7}_{Q1}, \ 7, \ \underbrace{10}_{Q2}, \ 13, \ \underbrace{15}_{Q3}, \ \underbrace{19}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  5 \rule[-1ex]{0pt}{0pt} & 7 & 10 & 15 & 19 \\
\hline
\end{array}

Box Plots and 5-Number, SM-Bank 001

The numerical data set below is made up of 11 data points.

\(2, \ 3, \ 3, \ 5, \ 8, \ 10, \ 11, \ 11, \ 12, \ 14, \ 16\)

Complete 5-number summary table below.   (2 marks)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} & \ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \ \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}   \rule[-1ex]{0pt}{0pt} &  \\
\hline
\end{array}

Show Answers Only

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  2 \rule[-1ex]{0pt}{0pt} & 3 & 10 & 12 & 16 \\
\hline
\end{array}

Show Worked Solution

\(\underbrace{2}_{\text{min}}, \ 3, \ \underbrace{3}_{Q1}, \ 5, \ 8, \ \underbrace{10}_{Q2}, \ 11, \ 11, \ \underbrace{12}_{Q3}, \ 14, \ \underbrace{16}_{\text{max}}\)

\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \text{Min} \ \rule[-1ex]{0pt}{0pt} &\ \ \text{Q}_1 \ \ \ &\ \ \text{Q}_2 \ \ \ &\ \ \text{Q}_3 \ \ \ & \  \text{Max} \ \\
\hline
\rule{0pt}{2.5ex}  2 \rule[-1ex]{0pt}{0pt} & 3 & 10 & 12 & 16 \\
\hline
\end{array}

Simple Interest, SMB-023

Jevin has a bank account that pays him simple interest.

The bank statement below shows the transactions on Jevin’s account for the month of July.
  

  1. What amount, in dollars, did Jevin deposit in cash on 11 July?  (1 mark)

Interest for this account is calculated on the minimum monthly balance at a rate of 3.0% per annum.

  1. Calculate the interest for July, correct to the nearest cent.  (2 marks)

Show Answers Only
  1. `$620`
  2. `$15.30`
Show Worked Solution
a.    `text(Deposit)` `= 6870.67-6250.67`
    `= $620`

 

b.   `text(Minimum Balance) = $6120.86`

`I` `=Prn`
  `= 6120.86 xx 3/100 xx 1/12`
  `= 15.302…`
  `= $15.30`

Simple Interest, SMB-022

The transaction details for a savings account for the month of August 2014 are shown in the table below.

The table is incomplete.
  

 

Simple interest is calculated and paid monthly on the minimum balance for that month.

Calculate the annual simple interest rate paid on this account, correct to two decimal places.   (4 marks)

Show Answers Only

`text{3.75%}`

Show Worked Solution

`text(Minimum balance for month) = $4870.50`

`text{Interest paid}\ = 5885.72-5870.50= $15.22`

`I` `=Prn`
`15.22` `= 4870.50 xx r xx 1/12`
`:. r`  `=(15.22 xx 12)/4870.50`
  `= 0.03749…`
  `= 3.75text{%   (2 d.p.)}`

Simple Interest, SMB-021

The graph below shows the growth in value of a $1000 investment over a period of four years.
 

A different amount of money is invested under the same investment conditions for eight years.

In total, the amount of interest earned on this investment is $600.

Calculate the amount of money invested.   (3 marks)

Show Answers Only

`$1500`

Show Worked Solution

`text(The linear graph shows a simple interest rate is applied.)`

`text{Simple interest rate} = 50/1000 xx 100=5text(% p.a.)`

`I = 600,\ \ r = 5/100,\ \ n=8`

`600` `= P xx 5/100 xx 8`
`:.P` `= 600/0.4`
  `= $1500`

Simple Interest, SMB-020

Chardie invests a sum of money in an account paying simple interest at a rate of 5.25% per annum.

No withdrawals or deposits are made into the account and over 4 years and the total value of Chardie's investment grows to `$22\ 385`.

Calculate the sum of money Chardie originally invested.   (3 marks)

Show Answers Only

`$18\ 500`

Show Worked Solution

`text{Interest earned}\ = 22\ 385-18\ 500=$3885`

`I = 3885, \ \ r = 5.25/100, \ \ n = 4`

`I` `= Prn`
`3885` `= P xx 5.25/100 xx 4`
`P`  `= 3885/0.21`
  `= $18\ 500`

Simple Interest, SMB-019

A sum of money is invested in an account paying simple interest at a rate of 5.0% per annum.

No withdrawals or deposits are made into the account and over 3 years, with the total interest earned on the investment being $120.

Calculate the sum of money originally invested. (2 marks)

Show Answers Only

`$800`

Show Worked Solution

`I = 120, \ \ r = 5/100, \ \ n = 3`

`I` `= Prn`
`120` `= P xx 5/100 xx 3`
`P`  `= 120/0.15`
  `= $800`

Simple Interest, SMB-018

Wilbur invests a sum of money into an account paying simple interest at a rate of 4.25% per annum.

The total interest earned on Wilbur's investment over 4 years is $6800.

Calculate the sum of money Wilbur originally invested.   (2 marks)

Show Answers Only

`$40\ 000`

Show Worked Solution

`I = 6800, \ \ r = 4.25/100, \ \ n = 4`

`I` `= Prn`
`6800` `= P xx 4.25/100 xx 4`
`P`  `= 6800/0.17`
  `= $40\ 000`

Simple Interest, SMB-017 MC

A sum of money is invested in an account paying simple interest at a rate of 8% per annum.

The total interest earned on this investment over 6 years is $27 000.

The sum of money invested is

  1. `$12\ 960`
  2. `$45\ 000`
  3. `$56\ 250`
  4. `$202\ 500`
Show Answers Only

`C`

Show Worked Solution

`I = 27 \ 000, \ \ r = 8/100, \ \ n = 6`

`I` `= Prn`
`27 \ 000` `= (P xx 8 xx 6)/100`
`P`  `= (2\ 700\ 000)/48`
  `= $56\ 250`

 
`=>  C`

Simple Interest, SMB-016

Kate and Amberley are Swifties and want to travel to Melbourne to go to a Tay-Tay concert.

It will cost them a total of $13 000 for tickets, accommodation and transport.

They currently have $12 500 and can invest this amount for 9 months.

What is the minimum simple interest rate, correct to 1 decimal place, at which they can invest their money to reach their goal of $13 000?   (3 marks)

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`5.4\text{%}`

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`n = \frac {9}{12} = 0.75`

`text{Interest required to reach goal} =13\ 000-12\ 500=$500`

`I` `=Prn`
`500` `=12\ 500 xx r xx 0.75`
`r` `=500/9375`
  `=0.05333…`
  `=5.333…\text{%}`

 
`:.\ text{Minimum interest rate = 5.4%}`

Simple Interest, SMB-015

Carissa borrowed $4000 to buy new surfboards.

She did not make any monthly repayments and repaid the loan in full 2 years later with a lump sum of $4400.

Determine the annual simple interest rate that Carissa was charged.   (2 marks)

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`5.0\text{%}`

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`text(Total interest paid)=4400-4000=$400`

`I` `=Prn`
`400` `=4000 xx r xx 2`
`r` `=400/8000`
  `=0.05`
  `=5.0\text{%}`

Simple Interest, SMB-014

Steffi borrowed $8600 to buy a new car.

She did not make any monthly repayments but instead repaid the loan in full 2 years later with a lump sum of $10 062.

Determine the annual simple interest rate that Steffi was charged.   (2 marks)

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`8.50\text{%}`

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`text(Total interest paid)=10\ 062-8600=$1462`

`I` `=Prn`
`1462` `=8600 xx r xx 2`
`r` `=1462/(17\ 200)`
  `=0.0850`
  `=8.50\text{%}`

Simple Interest, SMB-013

$2800 is invested in an account that earns simple interest at the rate of 4.0% per annum.

Calculate the total interest earned in the first six months.   (2 marks)

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`$56`

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`P = 2800,\ \ r = 4.0text(%),\ \ n = \frac{6}{12}=0.5`

`I` `= Prn`
  `= 2800 xx 4.0/100 xx 0.5`
  `= $56`

Simple Interest, SMB-012

$5000 is invested in an account that earns simple interest at the rate of 3.0% per annum.

Calculate the total interest earned in the first two years.   (2 marks)

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`$300`

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`P = 5000,\ \ r = 3.0text(%),\ \ n = 2`

`I` `= Prn`
  `= 5000 xx 3.0/100 xx 2`
  `= $300`

Simple Interest, SMB-011

Find an expression for the total value of an investment, in dollars, if $24 000 is invested for `x` months at a simple interest rate of 4.75% per annum?   (2 marks)

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`$(24\ 000 + 95x)`

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`text(Interest)` `= 24\ 000 xx x/12 xx 4.75/100`
  `= 95x`

 
`:.\ \text{Investment value}\ =$(24\ 000 + 95x)`

Simple Interest, SMB-009 MC

Albert borrowed $2000 off his brother Sid so he could attend the rugby league Magic Round in Brisbane.

He did not make any monthly repayments but instead repaid the loan in full 12 months later with a lump sum of $2350.

What was the annual simple interest rate Sid charged Albert?

  1. 3.5%
  2. 17.5%
  3. 23.5%
  4. 35.0%
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`B`

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`text(Total interest paid)=2350-2000=$350`

`I` `=Prn`
`350` `=2000 xx r xx 1`
`r` `=350/2000`
  `=0.1750`
  `=17.50\text{%}`

 
`=> B`

Simple Interest, SMB-008

Sandy borrowed $7 000 for an overseas trip.

She did not make any monthly repayments but instead repaid the loan in full at the end of three years with a lump sum of $8800.

Calculate the annual simple interest rate was she charged?   (2 marks)

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`8.57\text{%}`

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`text(Total interest paid)=8800-7000=$1800`

`I` `=Prn`
`1800` `=7000 xx r xx 3`
`r` `=1800/(21\ 000)`
  `=0.08571…`
  `=8.57\text{%}`