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Financial Maths, STD2 EQ-Bank 01 MC

Jacinta buys several items at the supermarket. The docket for her purchases is shown below.

What is the amount of GST included in the total? 

  1. $1.15
  2. $1.27
  3. $1.55
  4. $1.71
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Total price of taxable items}\ +\ 10\%\ \text{ GST}\ =1.29+7.23+4.13=$12.65\)

\(\therefore\ 110\%\ \text{of original price}\) \(=$12.65\)
\(\therefore\ \text{GST}\) \(=$12.65\times\dfrac{100}{110}\)
  \(=$1.15\)

\(\Rightarrow A\)

Financial Maths, STD2 F1 2024 HSC 8 MC

A bill for servicing a car is made up of:

    • $242 for parts, which includes 10% GST
    • $100 for labour, excluding GST.

The mechanic needs to add 10% GST onto the labour charge.

How much GST does the customer pay in total?

  1. $22.00
  2. $24.20
  3. $32.00
  4. $34.20
Show Answers Only

\(C\)

Show Worked Solution

\(\text {Let}\ \ X=\text{ parts cost ex-GST}\)

  \(X+X \times 0.1\) \(=242\)
  \(1.1X\) \(=242\)
  \(X\) \(=220\)

 
\(\text{Total GST}=0.1(220+100)=\$ 32.00\)

\(\Rightarrow C\)

♦ Mean mark 43%.

Financial Maths, STD2 F1 2023 HSC 30

A receipt from a supermarket shows a total of $124.87. The GST shown on the receipt is $3.86.

GST, at a rate of 10%, is only charged on some items.

What was the value of the items which did NOT have GST charged?  (3 marks)

Show Answers Only

`$82.41`

Show Worked Solution

`text{Let}\ X=\ text{cost of goods that attract GST (before GST added)}`

`10% xx X` `=3.86`  
`X` `=$38.60\ \ text{(before GST added)}`  

 

`text{Items with no GST}` `=124.87-38.60-3.86`  
  `=$82.41`  
♦ Mean mark 46%.

Financial Maths, STD2 F1 2023 HSC 13 MC

An item is discounted by 30% and then a further discount of 20% is applied to the reduced price.

What is the total percentage discount?

  1. 25%
  2. 44%
  3. 50%
  4. 56%
Show Answers Only

`=>B`

Show Worked Solution

`text{Method 1}`

`text{Let original price}\ =x`

`text{1st discount}\ =0.7x`

`text{2nd discount}\ = 0.7x xx 0.8=0.56x`

`text{Total discount}\ = 1-0.56=0.44`
 

♦♦ Mean mark 47%.

`text{Method 2}`

`text{$100 less 30% = $70}`

`text{$70 less 20%} = 70-0.2xx70=$56`

`text{Total discount $100 ↓ $56 = 44%}`

`=>B`

Financial Maths, STD2 F1 2023 HSC 6 MC

An item was purchased for a price of $880, including 10% GST.

What is the amount of GST included in the price?

  1. $8.00
  2. $8.80
  3. $80.00
  4. $88.00
Show Answers Only

`=>C`

Show Worked Solution

`text{Let}\ C =\ text{Original cost}`

`C+0.1 xx C` `=880`  
`1.1C` `=880`  
`C` `=880/1.1`  
  `=$800`  

 
`:.\ text{GST}\ =800xx0.1=$80`

`=>C`

♦ Mean mark 41%.

Financial Maths, STD1 F1 2021 HSC 12

A dance school runs a holiday program and charges $150 per student.

The costs of running the program are:

Dance teacher: $110 per hour

Room hire: $52 per hour plus 10% GST.

The program goes for two hours a day for five days.

What profit does the dance school make if 20 students pay for the program?  (3 marks)

Show Answers Only

`$1328`

Show Worked Solution

`text(Revenue) = 20 xx 150 = $3000`

`text(C)text(ost per hour)` `= 110 + (52 + \text{GST})`
  `= 110 + 52 xx 1.1`
  `= $167.20`
`text(Total cost)` `= 2 xx 5 xx 167.20`
  `= $1672`

 

`:.\ text(Profit)` `= 3000 – 1672`
  `= $1328`

Financial Maths, STD2 F1 2019 HSC 29

Part of a supermarket receipt is shown.

Determine the missing values, `A` and `B`, to complete the receipt.  (2 marks)

Show Answers Only

`$9.00`

Show Worked Solution

`text(Chocolate is the only item where GST applies.)`

♦♦ Mean mark 25%.

`text(GST on chocolate = 0.70`

`=> text(C)text(ost of chocolate) = $7.00`

`:. A = 7.00 + 0.70 = $7.70`

`:. B` `= 36.25 – (7.70 + 5.00 + 8.50 + 3.20 + 2.85)`
  `= $9.00`

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`

Financial Maths, STD2 F1 2019 HSC 6 MC

Mary is 18 years old and has just purchased comprehensive motor vehicle insurance. The following excesses apply to claims for at-fault motor vehicle accidents.

 
How much would Mary be required to pay as excess if she made a claim as the driver at fault in a car accident?

  1. $1600
  2. $850 + $400
  3. $850 + $1600
  4. $850 + $1600 + $400
Show Answers Only

`C`

Show Worked Solution

`text(Mary’s excess = 850 + 1600)`

`text{($400 does not apply as Mary is under 25.)}`

`=> C`

Financial Maths, STD2 F1 2018 HSC 15 MC

Sam is the driver at fault in a car accident.

Which of the following is covered by Sam's compulsory third-party (CTP) insurance?

  1. Repairs to Sam's car
  2. Injury to the other driver
  3. Damage to the other driver's car
  4. Cost of repairing a building damaged in the accident
Show Answers Only

`B`

Show Worked Solution

`text(CTP insurance covers liability for death or injury)`

♦♦ Mean mark 34%.

`text(to other people, but does not cover property damage.)`

`=>B`

Financial Maths, STD2 F1 2018 HSC 14 MC

To determine the retail price of an item, a shop owner increases its cost price by 30%. In a sale, the retails price is reduced by 30% to give the sale price.

How does the sale price compare to the cost price?

  1. The sale price is less than the cost price.
  2. The sale price is the same as the cost price.
  3. The sale price is more than the cost price.
  4. It is impossible to compare without knowing the cost price.
Show Answers Only

`text(A)`

Show Worked Solution

`text{Take an item that costs $100 (for example):}`

♦ Mean mark 50%.

`=>\ text(Original price) = 100 xx 1.3 = $130`

`=>\ text(Sale Price) = 130 xx 0.7 = $91`

`:.\ text(Sale price < cost price)`

`=>\ text(A)`

Financial Maths, STD2 F1 SM-Bank 5

Alex is buying a used car which has a sale price of  $13 380. In addition to the sale price there are the following costs:

2014 27a1

  1. Stamp Duty for this car is calculated at $3 for every $100, or part thereof, of the sale price.  
    Calculate the Stamp Duty payable.   (1 mark)

  2. Alex wishes to take out comprehensive insurance for the car for 12 months.

     

    The cost of comprehensive insurance is calculated using the following:
     
          2014 27a2
    Find the total amount that Alex will need to pay for comprehensive insurance.   (3 marks)

  3. Alex has decided he will take out the comprehensive car insurance rather than the less expensive non-compulsory third-party car insurance.

  4.  

    What extra cover is provided by the comprehensive car insurance?   (1 mark)

Show Answers Only
  1. `$402`
  2. `$985.74`
  3. `text(Comprehensive insurance covers Alex)`
  4. `text(for damage done to his own car as well.)`
Show Worked Solution
♦♦♦ Mean mark 12%
IMPORTANT: “or part thereof ..” in the question requires students to round up to 134 to get the right multiple of $3 for their calculation.
i.    `($13\ 380)/100 = 133.8`
`:.\ text(Stamp duty)` `= 134 xx $3`
  `= $402`

 

ii.   `text(Base rate) = $845`

 
`text(FSL) =\ text(1%) xx 845 = $8.45`
 

`text(Stamp)` `=\ text(5.5%) xx(845 + 8.45)`
  `= 46.9397…`
  `= $46.94\ text{(nearest cent)}`

 

`text(GST)` `= 10 text(%) xx(845 + 8.45)`
  `= 85.345`
  `= $85.35`

 

`:.\ text(Total cost)` `= 845 + 8.45 + 46.94 + 85.35`
  `= $985.74`

 

♦ Mean mark 34%.
iii.   `text(Comprehensive insurance covers Alex)`
  `text(for damage done to his own car as well.)`

Financial Maths, STD2 F1 SM-Bank 7

A dress was on sale with 25% discount.

As a regular customer, Kate received a further 10% on the already discounted price.

What was the overall percentage discount Kate received?  (2 marks)

Show Answers Only

`text(32.5%)`

Show Worked Solution

`text{Solution 1 (efficient method)}`

`text(Overall discount)` `=1-(0.75 xx 0.90)`
  `=1-0.675`
  `=0.325`
  `=32.5text(%)`

 

`text(Solution 2)`

`text(Let the dress cost) = $100`

`text(C) text(ost after 25% discount) = $75`

 

`text(C) text(ost after another 10% discount)`

`= 75 – (10 text{%} xx 75)`

`= $67.50`
 

`:.\ text(Overall discount) = 32.5text(%)`

Financial Maths, STD2 F1 SM-Bank 12

A golf shop is having a Boxing Day sale.

  1. What is the percentage discount on a putter which is reduced from $120.00 to $102.00?  (1 mark)

  2. The same discount applies storewide. What discount amount is applicable to a box of golf balls whose original price was $25.00?  (1 mark)

  3. What is the sale price of a golf bag which originally cost $160.00  (1 mark)

Show Answers Only
  1. `15 text(%)`
  2. `$3.75`
  3. `$136.00`
Show Worked Solution
i.     `text(Percentage Discount)` `=(120-102)/120 xx 100`
    `=18/120 xx 100`
    `=15 text(%)`

 

ii.    `text(Discounted Amount)` `=15 text(%) xx 25`
    `=$3.75`

 

iii.    `text(Sale Price)` `= 160 – 15 text(%) xx 160`
    `=0.85 xx 160`
    `=$136.00`

Financial Maths, STD2 F1 SM-Bank 1

Ralph buys a utility vehicle with a market value of $63 500.

Stamp duty is calculated on the vehicle as follows:

  • 3% of market value up to $45 000
  • 5% of market value over $45 000

Calculate the amount of stamp duty payable by Ralph.  (2 marks)

Show Answers Only

`$2275`

Show Worked Solution
`text(Stamp Duty)` `= 3text(%) xx 45\ 000 + 5text(%) xx (63\ 500 – 45\ 000)`
  `= 3text(%) xx 45\ 000 + 5text(%) xx 18\ 500`
  `= $2275`

Financial Maths, STD2 F1 2016 HSC 27a

Alice intends to buy a car and insure it.

Briefly describe what each of these types of insurance covers: 

    • Compulsory third-party insurance (CTP)

    • Non-compulsory third-party property insurance.  (2 marks)

Show Answers Only

`text(CTP Insurance:)`

`text(This insures a driver against liability)`

`text(if their car injures or kills a person)`

`text(in an accident.)`

`text(Non-compulsory TP Insurance:)`

`text(This insurance covers damage to)`

`text(other people’s property in an accident,)`

`text(but does not cover the driver’s own vehicle.)`

Show Worked Solution

`text(CTP Insurance:)`

♦♦♦ Mean mark 13%.
MARKER’S COMMENT: Again, car insurance causes major issues for students.

`text(This insures a driver against liability)`

`text(if their car injures or kills a person)`

`text(in an accident.)`

`text(Non-compulsory TP Insurance:)`

`text(This insurance covers damage to)`

`text(other people’s property in an accident,)`

`text(but does not cover the driver’s own vehicle.)`

Financial Maths, STD2 F1 2015 HSC 25 MC

An insurance company offers customers the following discounts on the basic annual premium for car insurance.

2015 25 mc

If a customer is eligible for more than one discount, subsequent discounts are applied to the already discounted premium. The combined compulsory third party (CTP) and comprehensive insurance discount is always applied last.

Jamie has three insurance policies, including combined CTP and comprehensive insurance, with this company. He has used this company for 8 years and he has never made a claim.

The basic annual premium for his car insurance is $870.

How much will Jamie need to pay after the discounts are applied?

  1.    $482.44
  2.    $515.50
  3.    $541.60
  4.    $557.60
Show Answers Only

`C`

Show Worked Solution

`text(Multi-policy discount)`

`text(New premium)` `= 870 − (text(15%) xx 870)`
  `= $739.50`

 
`text(No claim bonus)`

`text(New premium)` `= 739.50 − (text(20%) xx 739.50)`
  `= $591.60`

 
`text(Combined CTP bonus)`

`text(New premium)` `= 591.60 − 50`
  `= $541.60`

`⇒ C`

Financial Maths, STD2 F1 2015 HSC 15 MC

A camera costs $449, including 12% GST.

What is the price of the camera without GST, correct to the nearest dollar?

  1.    `$395`
  2.    `$401`
  3.    `$437`
  4.    `$503`
Show Answers Only

`B`

Show Worked Solution

`text(Let)\ C\ text(= cost of camera ex-GST)`

♦ Mean mark 36%.
`C + text(12%)C` `= $449`
`1.12C` `= 449`
`:. C` `= 449/1.12`
  `= $400.89…`

`⇒ B`

Financial Maths, STD2 F1 2004 HSC 17 MC

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

What was Rita’s refund?

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

`A`

Show Worked Solution

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

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

 
`=>  A`

Financial Maths, STD2 F1 2007 HSC 6 MC

The price of a CD is $22.00, which includes 10% GST.

What is the amount of GST included in this price?

  1.    $2.00
  2.    $2.20
  3.    $19.80
  4.    $20.00
Show Answers Only

`A`

Show Worked Solution

`text(CD costs $22.00 incl. GST`

`text(Let)\ C = text(original cost)`

`C + text(10%) xx C` `= 22`
`1.1C` `= 22`
`C` `= 20`

 

`:.\ text(GST)` `= 22.00 – 20.00`
  `= $2.00`

 
`=>  A`

Financial Maths, STD2 F1 2007 HSC 3 MC

Joe is about to go on holidays for four weeks. His weekly salary is $280 and his holiday loading is 17.5% of four weeks pay.

What is Joe’s total pay for the four weeks holiday?

  1. $196
  2. $329
  3. $1169 
  4. $1316 
Show Answers Only

`D`

Show Worked Solution
`text(Salary)\ text{(4 weeks)}` `= 4 xx 280`
  `= $1120`

 

`text(Holiday loading)` `= 1120 xx 17.5%`
  `= $196`

 

`:.\ text(Total pay)` `= 1120 + 196`
  `= $1316`

 
`=>  D`

Financial Maths, STD2 F1 2014 HSC 18 MC

The average NSW annual water consumption from the residential sector is equal to  90 340  litres per person per year. The Building Sustainability Index (BASIX) uses this as the benchmark to set a target for reducing water consumption by up to 40%.

A new building, planned to house 50 people, has been designed to meet a 25% reduction on this water consumption benchmark.

How much water per year, to the nearest kilolitre, is this building designed to save when fully occupied?

  1.    1129
  2.    1807
  3.    2710
  4.    3388
Show Answers Only

`A`

Show Worked Solution

`text(Benchmark) = 90\ 340\ text(L)`

`text(Water saved if usage)\ darr text(25%)`

`= 90\ 340 xx text(25%)`

`= 22\ 585\ text(L per person)`

 
`:.\ text(Water saved for 50 people)`

`= 50 xx 22\ 585`

`= 1\ 129\ 250\ text(L)`

`~~ 1129\ text(kL)`

`=>  A`

Financial Maths, STD2 F1 2010 HSC 23a

This advertisement appeared in a newspaper

2010 23a 

 What is the maximum possible salary per annum for this civil engineer, correct to the nearest dollar?   (2 marks)

Show Answers Only

`$86\ 396`

Show Worked Solution

`text(Base wage)=1586.70\ text(pw)`

`text(Max weekly base)` `=$1586.70+(text{3.5%}\ xx 1586.70)`
  `=1586.70+55.53`
  `=1642.23\ text((nearest cent))`
`:.\ text(Max annual base)` `=1642.23xx52`
  `=85\ 395.96`
  `=$85\ 396\ text{(nearest dollar)}`

Financial Maths, STD2 F1 2010 HSC 2 MC

A new phone was purchase for $725 which included 10% GST.

What was the price of the phone without GST, correct to the nearest cent? 

  1.    $65.91
  2.    $72.50
  3.    $652.50
  4.    $659.09
Show Answers Only

`D`

Show Worked Solution
♦ Mean mark 44%.
COMMENT: A surprise this was so poorly answered. Ensure you understand this tax!
`text(Price phone)\ +\ text(10% GST)` `=725`
`text(110%)\ xx\ text(Phone price)` `=725`
`:.\ text(Phone price)` `=725/1.1`
  `=$659.09`

`=>  D`