num-title-ct-corea

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)

--- 6 WORK AREA LINES (style=lined) ---

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)

--- 4 WORK AREA LINES (style=lined) ---

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)

--- 4 WORK AREA LINES (style=lined) ---

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 016

Determine the standard deviation of the following dataset, giving your answer correct to one decimal place. (1 mark)

$13, \ 14, \ 18, \ 18, \ 23, \ 27, \ 31$

Show Answers Only

$\text{Std Dev}\ = 6.2$

Show Worked Solution

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

$\text{Std Dev}\ = 6.207… = 6.2\ \text{(1 d.p.)} $

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:

$3, \ 4, \ 8, \ 10, \ 12, \ 13$

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

--- 2 WORK AREA LINES (style=lined) ---
Calculate the standard deviation of this data set, giving your answer to one decimal place. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

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.

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

--- 2 WORK AREA LINES (style=lined) ---
Calculate the standard deviation of this data set, giving your answer to two decimal places. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

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.

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

--- 2 WORK AREA LINES (style=lined) ---
Calculate the standard deviation of this data set, giving your answer to two decimal places. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

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)

--- 4 WORK AREA LINES (style=lined) ---

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.

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

--- 2 WORK AREA LINES (style=lined) ---
Without using calculations, explain which data set will have the highest standard deviation. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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)

--- 4 WORK AREA LINES (style=lined) ---

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)

--- 4 WORK AREA LINES (style=lined) ---

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.

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

--- 2 WORK AREA LINES (style=lined) ---
Without using calculations, explain which data set will have the smallest standard deviation. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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.

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

--- 2 WORK AREA LINES (style=lined) ---
Calculate the standard deviation of Quiz A and Quiz B, giving your answers correct to one decimal place. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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.

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

--- 2 WORK AREA LINES (style=lined) ---
Without using calculations, explain which data set has the highest standard deviation. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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:

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

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

--- 6 WORK AREA LINES (style=lined) ---
Each employee receives a $20 pay increase.

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

--- 2 WORK AREA LINES (style=lined) ---

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.

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

--- 1 WORK AREA LINES (style=lined) ---
Explain whether the mean of the test is greater than or less than the median of the test. (1 mark)

--- 3 WORK AREA LINES (style=lined) ---

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.

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

--- 4 WORK AREA LINES (style=lined) ---
Briefly explain what is meant by the term standard deviation. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

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 $

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}

--- 0 WORK AREA LINES (style=lined) ---

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

--- 0 WORK AREA LINES (style=lined) ---

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

--- 1 WORK AREA LINES (style=lined) ---

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}

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

--- 0 WORK AREA LINES (style=lined) ---

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

--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

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

Show Worked Solution

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.

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

--- 1 WORK AREA LINES (style=lined) ---
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)

--- 6 WORK AREA LINES (style=lined) ---

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).

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

--- 1 WORK AREA LINES (style=lined) ---
Describe the skew of Kim's results. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

ii. `text(50%)`

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

Show Worked Solution

ii. `text(50%)`

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

Box Plots and 5-Number Summary, SM-Bank 012 MC

This box plot represents a set of scores.

What is the interquartile range of this set of scores?

Show Answers Only

`C`

Show Worked Solution

`text{Q}_1 = 8, \ text{Q}_3 = 11`

`text{IQR}`	`= text{Q}_3-text{Q}_1`
	`= 11-8`
	`= 3`

`=> C`

Box Plots and 5-Number, SM-Bank 011

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

the range (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
the interquartile range (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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

the median (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
the interquartile range (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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

the range (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
the interquartile range (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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

the median (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
the interquartile range (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

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

the median (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
the interquartile range (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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

the range (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
the interquartile range (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

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.

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

--- 1 WORK AREA LINES (style=lined) ---

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

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

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`$620`
`$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)

--- 5 WORK AREA LINES (style=lined) ---

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)

--- 5 WORK AREA LINES (style=lined) ---

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)

--- 5 WORK AREA LINES (style=lined) ---

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)

--- 4 WORK AREA LINES (style=lined) ---

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)

--- 4 WORK AREA LINES (style=lined) ---

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

`$12\ 960`
`$45\ 000`
`$56\ 250`
`$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)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`5.4\text{%}`

Show Worked Solution

`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)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`5.0\text{%}`

Show Worked Solution

`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)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`8.50\text{%}`

Show Worked Solution

`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)

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

`$56`

Show Worked Solution

`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)

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

`$300`

Show Worked Solution

`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)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`$(24\ 000 + 95x)`

Show Worked Solution

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

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

Simple Interest, SMB-010 MC

What is the interest earned, in dollars, if $4800 is invested for `x` months at a simple interest rate of 2.25% per annum?

`9x`
`10.8x`
`108x`
`900x`

Show Answers Only

`A`

Show Worked Solution

`text(Interest)`	`= 4800 xx x/12 xx 2.25/100`
	`= 9x`

`=> A`

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?

3.5%
17.5%
23.5%
35.0%

Show Answers Only

`B`

Show Worked Solution

`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)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`8.57\text{%}`

Show Worked Solution

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

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

Simple Interest, SMB-007 MC

Jackie invests $4350 for 3 years. The simple interest is calculated at a rate of 4.5% per annum.

What is the total value of the investment at the end of this period, to the nearest dollar?

$4395
$4546
$4722
$4937

Show Answers Only

`D`

Show Worked Solution

`text(Interest)`	`=Prn`
	`=4350 xx \frac{4.5}{100} xx 3`
	`=$587.25`

`:.\ text(Value of Investment)=4350 + 587 =$4937`

`=> D`

Simple Interest, SMB-006 MC

Gutho invests $10 000 for 1 year and 8 months. The simple interest is calculated at a rate of 4.25% per annum.

What is the total value of the investment at the end of this period, to the nearest dollar?

$10 425
$10 571
$10 708
$14 562

Show Answers Only

`C`

Show Worked Solution

`text{1 year 8 months = 12 + 8 = 20 months}`

`text(Interest)`	`=Prn`
	`=10\ 000 xx \frac{4.25}{100} xx \frac{20}{12}`
	`=$708`

`:.\ text(Value of Investment)=10\ 000+708=$10\ 708`

`=> C`

Simple Interest, SMB-005

Johnno lives overseas and needs $6000 for his planned trip to Parramatta Stadium to watch Junior Paolo play.

If he invests $5600 for 15 months at a simple interest rate of 6.5% per annum, determine if will get to see the big fella play. Show your working. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`text(Interest)`	`=Prn`
	`=5600 xx \frac{6.5}{100} xx \frac{15}{12}`
	`=$455`

`text(Value of Investment)`	`=5600+455`
	`=$6055>$6000`

`:.\ \text{Johnno will get to see Junior play}.`

Show Worked Solution

`text(Interest)`	`=Prn`
	`=5600 xx \frac{6.5}{100} xx \frac{15}{12}`
	`=$455`

`text(Value of Investment)`	`=5600+455`
	`=$6055`

`:.\ \text{Johnno will get to see Junior play}.`

Simple Interest, SMB-004

Clancy estimates that he will need $7800 for his planned trip to visit the The Stockman's Hall of Fame in Longreach.

If he invests $7000 for 18 months at a simple interest rate of 6% per annum, will he reach his goal of $7800? Show your working. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`A`

Show Worked Solution

`text(Interest)`	`=Prn`
	`=7000 xx \frac{6}{100} xx \frac{18}{12}`
	`=$630`

`text(Value of Investment)`	`=7000+630`
	`=$7630`

`:.\ \text{Clancy won’t reach his goal of $7800}.`

Simple Interest, SMB-003

Min Woo invests $8000 for 3 years. The simple interest is calculated at a rate of 4% per annum.

Calculate the total value of the investment at the end of this period. (2 marks)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

`$8960`

Show Worked Solution

`text(Interest)`	`=Prn`
	`=8000 xx \frac{4}{100} xx 3`
	`=$960`

`:.\ text(Value of Investment)`	`=8000+960`
	`=$8960`

Simple Interest, SMB-002 MC

$2500 is invested in an account that earns simple interest at the rate of 3.0% per annum.

The total interest earned in the first two years is

$55
$75
$150
$833

Show Answers Only

`C`

Show Worked Solution

`P = 2500,\ \ r = 3.0text(%),\ \ n = 2`

`I`	`= Prn`
	`= 2500 xx 3.0/100 xx 2`
	`= $150`

`=> C`

Simple Interest, SMB-001

$14 000 is invested in an account that earns simple interest at the rate of 2.5% per annum.

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

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

`$1050`

Show Worked Solution

`P = 14\ 000,\ \ r = 2.5text(%),\ \ n = 3`

`I`	`= Prn`
	`= 14\ 000 xx 2.5/100 xx 3`
	`= $1050`

Financial Maths, SMB-027

The cash price of a large refrigerator is $2000.

A customer buys the refrigerator under a hire-purchase agreement.

She does not pay a deposit and will pay $55 per month for four years.

Calculate the total amount, in dollars, the customer will pay. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
Find the total interest the customer will pay over four years. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

`$2640`
`$640`

Show Worked Solution

i. `text{Total amount paid} = 55 xx 4 xx 12 = $2640`

ii. `text{Total interest} = 2640-2000= $640`

Financial Maths, SMB-026

Shaun decides to buy a new sound system on a hire-purchase plan.

The sound system is priced at $3500.

Shaun pays a 15% deposit and monthly repayments for five years.

If Shaun's total purchase price after paying the last instalment is $4425, calculate his monthly repayment. (3 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`$65`

Show Worked Solution

`text{Deposit} = \frac{15}{100} xx 3500 = $525`

`text{Balance due after deposit} = 4425-525= $3900`

`text{Number of repayments} = 5 xx 12 = 60`

`text{Monthly repayment} = \frac{3900}{60} = $65`

Financial Maths, SMB-025

Brad investigated the cost of buying a $720 washing machine under a hire purchase agreement.

A 25% deposit is required and the balance will be paid in 24 equal monthly repayments of $27.90.

Calculate the amount of interest Brad pays on this purchase. (3 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`$129.60`

Show Worked Solution

`text{Deposit} = \dfrac{25}{100} xx 720 = $180`

`text{Total instalments} = 24 xx 27.90 = $669.60`

`text{Total purchase price} = 180+669.60 = $849.60`

`text{Interest paid} = 849.60-720= $129.60`

Financial Maths, SMB-024

A $2000 lounge suite was sold under a hire-purchase agreement.

A deposit of $200 was paid.

The balance was to be paid in 36 equal monthly instalments of $68.

Calculate the total interest paid in the purchase. (3 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`$648`

Show Worked Solution

`text{Deposit} = $200`

`text(Total instalments) = 36 xx 68 = $2448`

`text{Total price paid} = 200 + 2448 = $2648`

`text{Interest paid} = 2648-2000 = $648`