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Indices, SMB-004 MC

Which expression is equal to  `6^3 xx 36^2`?

  1. `6 xx 3 xx 36 xx 2`
  2. `6 xx 6 xx 6 xx 6 xx 6`
  3. `6 xx 6 xx 6 xx 36 xx 6`
  4. `6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`
Show Answers Only

`D`

Show Worked Solution
`6^3 xx 36^2` `= (6xx6xx6) xx (6xx6)^2`
  `= (6xx6xx6) xx (6xx6) xx (6 xx6)`
  `=6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`

 
`=>D`

Financial Maths, SMB-013

The table shows the income tax rates for the 2022-23 financial year.

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex}\textit{    Taxable income}\rule[-1ex]{0pt}{0pt} & \textit{    Tax payable}\\
\hline
\rule{0pt}{2.5ex}\text{\$0 – \$18 200}\rule[-1ex]{0pt}{0pt} & \text{Nil}\\
\hline
\rule{0pt}{2.5ex}\text{\$18 201 – \$45 000}\rule[-1ex]{0pt}{0pt} & \text{19 cents for each \$1 over \$18 200}\\
\hline
\rule{0pt}{2.5ex}\text{\$45 001 – \$120 000}\rule[-1ex]{0pt}{0pt} & \text{\$5092 plus 32.5 cents for each \$1 over \$45 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$120 001 – \$180 000}\rule[-1ex]{0pt}{0pt} & \text{\$29 467 plus 37 cents for each \$1 over \$120 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$180 001 and over}\rule[-1ex]{0pt}{0pt} & \text{\$51 667 plus 45 cents for each \$1 over \$180 000}\\
\hline
\end{array}

Boonie is a professional cricketer and has a gross income of $145 000. During the financial year, he has allowable tax deductions of $1300 for cricket bats and pads.

What is Boonie's total amount of tax payable for the financial year?  (3 marks)

Show Answers Only

`$38\ 236`

Show Worked Solution

`text(Taxable income)\ =145\ 000-1300=$143\ 700`

`text{Tax payable}`

`= 29\ 467 + 0.37 (143\ 700-120\ 000)`

`= 29\ 467 + 8769`

`= $38\ 236`

Financial Maths, SMB-012 MC

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex}\textit{    Taxable income}\rule[-1ex]{0pt}{0pt} & \textit{    Tax payable}\\
\hline
\rule{0pt}{2.5ex}\text{\$0 – \$18 200}\rule[-1ex]{0pt}{0pt} & \text{Nil}\\
\hline
\rule{0pt}{2.5ex}\text{\$18 201 – \$45 000}\rule[-1ex]{0pt}{0pt} & \text{19 cents for each \$1 over \$18 200}\\
\hline
\rule{0pt}{2.5ex}\text{\$45 001 – \$120 000}\rule[-1ex]{0pt}{0pt} & \text{\$5092 plus 32.5 cents for each \$1 over \$45 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$120 001 – \$180 000}\rule[-1ex]{0pt}{0pt} & \text{\$29 467 plus 37 cents for each \$1 over \$120 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$180 001 and over}\rule[-1ex]{0pt}{0pt} & \text{\$51 667 plus 45 cents for each \$1 over \$180 000}\\
\hline
\end{array}

Using the tax table, what is the tax payable on $47 580?

  1. $5721.20
  2. $5930.50
  3. $15 463.50
  4. $20 555.50
Show Answers Only

`B`

Show Worked Solution

`text(Tax Payable)`

`= 5092 + 0.325 (47\ 580-45\ 000)`

`= 5092 + 838.50`

`= 5930.50`
 

`=>  B`

Financial Maths, SMB-011

George makes a single deposit of $9000 into an account that pays simple interest.

After 4 years, George's account has a balance of $10 350.

What simple interest rate did George receive on his investment?   (2 marks)

Show Answers Only

`3.75text(%)`

Show Worked Solution
`text(Interest earned)` `= 10\ 350-9000`
  `= $1350`

 

`text(Using)\ \ I = Prn,`

`1350` `= 9000 xx r xx 4`
`:. r` `= 1350/(4 xx 9000)`
  `= 0.0375`
  `= 3.75text(%)`

Financial Maths, SMB-009

Pamela deposits $2000 into a savings account which earns simple interest at the rate of 2.5% per annum.

No deposits or withdrawals are made from this account.

After 2 years, how much is in Pamela's savings account?  (2 marks)

Show Answers Only

`$2100`

Show Worked Solution
`text(Interest earned)` `= Prn`
  `= 2000 xx 2.5/100 xx 2`
  `= $100`

 

`:.\ text{Account balance}` `= 2000 + 100`
  `= $2100`

Financial Maths, SMB-008

Dante deposits $5000 into a savings account which earns simple interest.

No deposits or withdrawals are made from this account.

After 4 years, Dante notices there is $5600 in the account.

What is the annual rate of interest for the account?   (2 marks)

Show Answers Only

`3text(%)`

Show Worked Solution
`text(Interest per year)` `= (5600-5000)÷4`
  `= 600 ÷ 4`
  `= $150`

 

`:.\ text{Interest rate (p.a.)}` `= 150/5000 xx 100`
  `= 3 text(%)`

Financial Maths, SMB-007

Mr. Soros put $500 into a simple interest account for a year.

He did not take any money out or add any money to the account.

At the end of the year he had $530 in the account.

What was the annual percentage interest rate?   (2 marks)

Show Answers Only

`text(6%)`

Show Worked Solution
`text(Interest earned)` `= 530-500`
  `= $30`

 

`:.\ text{Interest rate (annual)}`

`= 30/500`

`= 0.06`

`= 6text(%)`

Financial Maths, SMB-006

Cassie opens a savings account and deposits $900 into it.

She makes no more deposits and earns simple interest on her original deposit at 3.5% each year.

How much interest will Cassie earn after 4 years?  (2 marks)

Show Answers Only

`$126`

Show Worked Solution
`text(Interest earned)` `=Prn`
  `= 900 xx 3.5/100 xx 4`
  `= $126`

Financial Maths, SMB-005

On a weekend, Abbey works 8 hours at her normal pay rate and 12 hours at time and a half of her normal pay.

Abbey was paid $707.20 in total for this work.

What is her normal pay rate per hour?  (2 marks)

Show Answers Only

`$27.20\ text(per hour)`

Show Worked Solution

`text(Total normal hours)`

`= 8 + 1.5 xx 12`

`= 26`

 

`:.\ text(Abbey’s normal pay rate)`

`= 707.20/26`

`= $ 27.20\ text(per hour.)`

Financial Maths, SMB-004

John, Olivia and Louis are picking grapes to earn money.

Their pay is based on the number of tonnes of grapes they pick.
 

  Tonnes picked
John 4
Olivia 3
Louis 1

 

Their total pay is  $640.

How much does Olivia earn?  (2 marks)

Show Answers Only

`$240`

Show Worked Solution

`text(Payment per tonne)`

`= 640/8`

`= $80`
 

`:.\ text(Olivia earns)` `= 3 xx 80`
  `= $240`

Financial Maths, SMB-003 MC

David has a job selling mobile phone plans. His weekly salary, `W` dollars, is calculated using the rule below:

`W = 300 + 0.05 P`

where `P` is the total value in dollars of the mobile phone plans he sells that week.

David sold $32 000 worth of mobile phone plans in a given week.

What was David's salary in the week?

  1. `$640`
  2. `$1280`
  3. `$1900`
  4. `$3230`
Show Answers Only

`C`

Show Worked Solution
`W` `= 300 + 0.05 xx 32\ 000`
  `= 300 + 1600`
  `= 1900`

 
`=>C`

Financial Maths, SMB-002

Bella is an electrician.

She charges $150 to attend a job and then a fixed price for each minute she spends on the job.

The graph below shows Bella's charge based on the number of minutes she spends at the job.
 

How much will Bella charge for a job that takes 60 minutes?  (2 marks)

Show Answers Only

`$330`

Show Worked Solution

`text(Charge to attend = $150)`

`text(From the graph,)`

`=>\ text(50 minute job costs $300)`

`:.\ text(C)text(ost per minute)` `= (300-150)/50 = $3`

 

`:.\ text(C)text(ost of 60 minute job)`

`= 150 + 60 xx 3`

`= $330`

Financial Maths, SMB-001

Olivia earned $17.24 per hour working at a pizza store.

This week she worked for  `8 1/4` hours.

She used the money she earned this week to buy concert tickets for herself and her friends.

Each concert ticket cost $14.15.

Calculate the maximum number of concert tickets Olivia could have bought?  (2 marks)

Show Answers Only

`10`

Show Worked Solution
`text(Money earned)` `= 8 1/4 xx 17.24`
  `= $142.23`

 

`:.\ text(Maximum tickets)` `= 142.23/14.15`
  `= 10.05…`
  `= 10`

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`

Measurement, STD1 M5 2022 HSC 5 MC

Two similar figures are shown.
 

What is the value of `x` ?

  1. 6
  2. 8
  3. 18
  4. 27
Show Answers Only

`C`

Show Worked Solution

`text{Scale factor}\ =3/2 =1.5`

`:.\ x = 1.5 xx 12 = 18`
  

`text{Alternate solution}`

`text{Using sides of similar figures in the same ratio:}`

`x/12` `=3/2`  
`x` `=12 xx (3/2)`  
`x` `=18`  

   
`=> C`

Measurement, STD2 M1 2022 HSC 28

A dam is in the shape of a triangular prism which is 50 m long, as shown.

Both ends of the dam, `A B C` and `D E F`, are isosceles triangles with equal sides of length 25 metres. The included angles `B A C` and `E D F` are each `150^@`.

 
     

Calculate the number of litres of water the dam will hold when full.  (4 marks)

Show Answers Only

`7\ 812\ 500\ text{L}`

Show Worked Solution

`V=Ah`

`text{Use sine rule to find}\ A:`

`A` `=1/2 ab\ sinC`  
  `=1/2 xx 25 xx 25 xx sin150^@`  
  `=156.25\ text{m}^2`  

 

`:.V` `=156.25 xx 50`  
  `=7812.5\ text{m}^3`  

 

`text{S}text{ince 1 m³ = 1000 litres:}`

`text{Dam capacity}` `=7812.5 xx 1000`  
  `=7\ 812\ 500\ text{L}`  

♦♦ Mean mark 33%.

Financial Maths, STD2 F1 2022 HSC 21

A real estate agent's commission for selling houses is 2% for the first $800 000 of the sale price and 1.5% for any amount over $800 000.

Calculate the commission earned in selling a house for $1 500 000.  (2 marks)

Show Answers Only

`$26\ 500`

Show Worked Solution
`text{Commission}` `=800\ 000 xx 2text{%} + (1\ 500\ 000-800\ 000) xx 1.5text{%}`  
  `=800\ 000 xx 0.02 + 700\ 000 xx 0.015`  
  `=16\ 000 + 10\ 500`  
  `=$26\ 500`  

Financial Maths, STD2 F1 2022 HSC 7 MC

Tian is paid $20.45 per hour, as well as a meal allowance of $16.20 per day.

What are Tian's total earnings if she works 9 hours per day for 5 days?

  1. `$329.85`
  2. `$936.45`
  3. `$1001.25`
  4. `$1649.25`
Show Answers Only

`C`

Show Worked Solution
`text{Earnings (5 days)}` `=5 xx [(9 xx 20.45) + 16.20]`  
  `=5 xx 200.25`  
  `=$1001.25`  

 
`=>C`

Measurement, STD2 M1 2021 HSC 6 MC

Suppose  `a=b/7`, where  `b=22.`

What is the value of  `a`, correct to three significant figures?

  1. 3.14
  2. 3.15
  3. 3.142
  4. 3.143
Show Answers Only

`A`

Show Worked Solution

`a=b/7=22/7=3.1428…`

`3.1428 = 3.14\ text{(to 3 sig fig)}`

`=>  A`

Statistics, STD1 S1 2020 HSC 24

  1. The ages in years, of ten people at the local cinema last Saturday afternoon are shown.

\(38 \ \ 25 \ \ 38 \ \ 46 \ \ 55 \ \ 68 \ \ 72 \ \ 55 \ \ 36 \ \ 38\)

  1. The mean of this dataset is 47.1 years.
  2. How many of the ten people were aged between the mean age and the median age?  (2 marks)

  3. On Wednesday, ten people all aged 70 went to this same cinema.
  4. Would the standard deviation of the age dataset from Wednesday be larger than, smaller than or equal to the standard deviation of the age dataset given in part (a)? Briefly explain your answer without performing any calculations.  (2 marks)

Show Answers Only

a.     \(1\)

b.    \(\text{Standard deviation is a measure of how much the}\)

\(\text{ages of individuals differ from the mean age of the group.}\)
 

\(\Rightarrow\ \text{Standard deviation of Wednesday’s group would be}\)

\(\text{less as the mean is 70 and everyone’s age is 70.}\)

Show Worked Solution

a.     \(\text{Reorder ages in ascending order:}\)

    \(25, 36, 38, 38, 38, 46, 55 , 55, 68, 72\)

\(\text{Median} = \dfrac{\text{5th + 6th}}{2} = \dfrac{38 + 46}{2} = 42\)

\(\therefore\ \text{People with age between 42 − 47.1 = 1}\)

♦ Mean mark (a) 39%.

 
b.    \(\text{Standard deviation is a measure of how much the}\)

\(\text{ages of individuals differ from the mean age of the group.}\)
 

\(\Rightarrow\ \text{Standard deviation of Wednesday’s group would be}\)

\(\text{less as the mean is 70 and everyone’s age is 70.}\)

♦♦♦ Mean mark (b) 20%.

Measurement, STD2 M1 2020 HSC 25

A composite solid consists of a triangular prism which fits exactly on top of a cube, as shown.
 

Find the surface area of the composite solid.   (3 marks)

Show Answers Only

`424 \ text{cm}^2`

Show Worked Solution

`text{S.A. of 1 face of cube} = 8 xx 8 = 64 \ text{cm}^2`

`text{Height of triangle} = 11 – 8 = 3 \ text{cm}`

`therefore \ text{S.A. (triangular prism)}` `= 2 xx ( frac{1}{2} xx 8 xx 3 ) + 2 xx (5 xx 8)`
  `= 24 + 80`
  `= 104 \ text{cm}^2`

 

`therefore \ text{Total S.A.}` `= 5 xx 64 + 104`
  `= 424 \ text{cm}^2`

Financial Maths, STD2 F1 2020 HSC 20

The table shows the income tax rates for the 2019 – 2020 financial year.

\begin{array} {|l|l|}
\hline
\rule{0pt}{2.5ex}\textit{    Taxable income}\rule[-1ex]{0pt}{0pt} & \textit{    Tax payable}\\
\hline
\rule{0pt}{2.5ex}\text{\$0 – \$18 200}\rule[-1ex]{0pt}{0pt} & \text{Nil}\\
\hline
\rule{0pt}{2.5ex}\text{\$18 201 – \$37 000}\rule[-1ex]{0pt}{0pt} & \text{19 cents for each \$1 over \$18 200}\\
\hline
\rule{0pt}{2.5ex}\text{\$37 001 – \$90 000}\rule[-1ex]{0pt}{0pt} & \text{\$3572 plus 32.5 cents for each \$1 over \$37 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$90 001 – \$180 000}\rule[-1ex]{0pt}{0pt} & \text{\$20 797 plus 37 cents for each \$1 over \$90 000}\\
\hline
\rule{0pt}{2.5ex}\text{\$180 001 and over}\rule[-1ex]{0pt}{0pt} & \text{\$54 097 plus 45 cents for each \$1 over \$180 000}\\
\hline
\end{array}

For the 2019 – 2020 financial year, Wally had a taxable income of $122 680. During the year, he paid $3000 per month in Pay As You Go (PAYG) tax.

Calculate Wally's tax refund, ignoring the Medicare levy.   (3 marks)

Show Answers Only

`$3111.40`

Show Worked Solution
`text(Tax paid)` `=12 xx 3000`
  `=$36\ 000`

 
`text(Tax payable on $122 680)`

`=20\ 797 + 0.37(122\ 680-90\ 000)`

`=20\ 797 + 0.37(32\ 680)`

`=$32\ 888.60`
 

`:.\ text(Tax refund)` `=36\ 000-32\ 888.60`  
  `=$3111.40`  

Measurement, STD2 M6 2020 HSC 16

Consider the triangle shown.
 


 

  1. Find the value of `theta`, correct to the nearest degree.   (2 marks)

  2. Find the value of `x`, correct to one decimal place.   (2 marks)

Show Answers Only
  1. `39^@`
  2. `12.1 \ text{(to 1 d.p.)}`
Show Worked Solution
a.      `tan theta` `= frac{8}{10}`
  `theta` `= tan ^(-1) frac{8}{10}`
    `= 38.659…`
    `= 39^@ \ text{(nearest degree)}`

 

b.     `text{Using Pythagoras:}`

`x` `= sqrt{8^2 + 10^2}`
  `= 12.806…`
  `= 12.8 \ \ text{(to 1 d.p.)}`

Measurement, STD2 M1 2020 HSC 5 MC

A plant stem is measured to be 16.0 cm, correct to one decimal place.

What is the percentage error in this measurement?

  1.  0.3125%
  2.  0.625%
  3.  3.125%
  4.  6.25%
Show Answers Only

`A`

Show Worked Solution

♦ Mean mark 41%.

`text{Absolute error} = 1/2 xx \text{precision} = 1/2 xx 0.1 = 0.05\ text{cm}`

`%  text(error)` `= frac(0.05)(16.0) xx 100`
  `= 0.3125%`

 
`=> \ A`

Probability, STD2 S2 2019 HSC 25

A bowl of fruit contains 17 apples of which 9 are red and 8 are green.

Dennis takes one apple at random and eats it. Margaret also takes an apple at random and eats it.

By drawing a probability tree diagram, or otherwise, find the probability that Dennis and Margaret eat apples of the same colour.  (3 marks)

Show Answers Only

`8/17`

Show Worked Solution

`P(text(same colour))` `= P(R R) + P(GG)`
  `= 9/17 xx 8/16 + 8/17 xx 7/16`
  `= 72/272 + 56/272`
  `= 8/17`
♦♦ Mean mark 35%.

Financial Maths, STD2 F1 2019 HSC 9 MC

What is the interest earned, in dollars, if $800 is invested for `x` months at a simple interest rate of 3% per annum?

  1. `2x`
  2. `24x`
  3. `200x`
  4. `2400x`
Show Answers Only

`A`

Show Worked Solution

♦♦♦ Mean mark 20%!

`text(Interest)` `= 800 xx x/12 xx 3/100`
  `= 2x`

 
`=> A`

Measurement, STD2 M1 2019 HSC 8 MC

A person's weight is measured as 79.3 kg.

What is the absolute error of this measurement?

  1. 10 grams
  2. 50 grams
  3. 100 grams
  4. 500 grams
Show Answers Only

`B`

Show Worked Solution

♦ Mean mark 46%.

`text(A)text(bsolute error)` `= 1/2 xx\ text(precision)`
  `= 1/2 xx 0.1\ text(kg)`
  `= 1/2 xx 100\ text(grams)`
  `= 50\ text(grams)`

 
`=> B`

Financial Maths, STD2 F1 2019 HSC 7 MC

Julia earns $28 per hour. Her hourly pay rate increases by 2%.

How much will she earn for a 4-hour shift with this increase?

  1. $2.24
  2. $28.56
  3. $112
  4. $114.24
Show Answers Only

`D`

Show Worked Solution
`text(Hourly rate)` `= 28 xx 1.02`
  `= $28.56`

 

`:.\ text(Shift earnings)` `= 4 xx 28.56`
  `= $114.24`

`=> D`