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CORE*, FUR2 2009 VCAA 1

The recommended retail price of a golf bag is $500. Rebecca sees the bag discounted by $120 at a sale.

  1. What is the price of the golf bag after the $120 discount has been applied?   (1 mark)

  2. Find the discount as a percentage of the recommended retail price.   ( 1 mark)

Show Answers Only
  1. `$380`
  2. `text(24%)`
Show Worked Solution
a.    `text(Price)` `= 500-120`
    `= $380`

 

b.    `text(Discount)` `= 120/500 xx 100text(%)`
    `= 24text(%)`

 

CORE*, FUR1 2015 VCAA 3 MC

The closing price of a share on Wednesday was $160.

The closing price of the same share on Thursday was 3% less than its closing price on Wednesday.

The closing price of the same share on Friday was 4.5% more than its closing price on Thursday.

The closing price of the share on Friday is closest to

A.   $157.38

B.   $161.98

C.   $162.18

D.   $162.40

E.   $172.22

Show Answers Only

`C`

Show Worked Solution
`text{Closing price (Fri)}` `= 160 xx 0.97 xx 1.045`
  `=$162.184`

`=> C`

CORE*, FUR1 2015 VCAA 2 MC

An investment property was purchased for $600 000.

Over a 10-year period, its value increased to $850 000.

The increase in value, as a percentage of the purchase price, is closest to

A.     `text(4.2%)`

B.   `text(25.0%)`

C.   `text(29.4%)`

D.   `text(41.7%)`

E.   `text(70.6%)`

Show Answers Only

`D`

Show Worked Solution
`text{Increase (%)}` `=(850\ 000 – 600\ 000)/(600\ 000)`
  `=0.4166…`
  `=41.66…text(%)`

 
`=> D`

CORE*, FUR1 2010 VCAA 4 MC

The price of a one-way airfare between two cities varies each day according to demand.

• On Monday the price is $160.
• The price on Tuesday is 25% greater than the price on Monday.
• The price on Wednesday is 10% less than the price on Tuesday.
• The price on Thursday is 25% less than the price on Wednesday.
• The price on Friday is 20% greater than the price on Thursday.
• The Saturday price is the same as the Friday price.

The price on Saturday is

A.   $150

B.   $162

C.   $176

D.   $288

E.   $330

Show Answers Only

`B`

Show Worked Solution
`text{Price (Tue)}` `= 160 xx text(125%)`
  `= 200`
`text{Price (Wed)}` `= 200 xx 90text(%)`
  `= 180`
`text{Price (Thu)}` `= 180 xx 75text(%)`
  `=135`
`text{Price (Fri)}` `= 135 xx 120 text(%)`
  `= 162`

 

`text(Saturday price is same as Friday.)`

`=> B`

CORE*, FUR2 2014 VCAA 1

The adult membership fee for a cricket club is $150.

Junior members are offered a discount of $30 off the adult membership fee.

  1. Write down the discount for junior members as a percentage of the adult membership fee.   (1 mark)

Adult members of the cricket club pay $15 per match in addition to the membership fee of $150.

  1. If an adult member played 12 matches, what is the total this member would pay to the cricket club?   (1 mark)

If a member does not pay the membership fee by the due date, the club will charge simple interest at the rate of 5% per month until the fee is paid.

Michael paid the $150 membership fee exactly two months after the due date.

  1. Calculate, in dollars, the interest that Michael will be charged.   (1 mark)

The cricket club received a statement of the transactions in its savings account for the month of January 2014.

The statement is shown below.

     BUSINESS, FUR2 2014 VCAA 1

    1. Calculate the amount of the withdrawal on 17 January 2014.   (1 mark)

    2. Interest for this account is calculated on the minimum balance for the month and added to the account on the last day of the month.
    3. What is the annual rate of interest for this account?  Write your answer, correct to one decimal place.   (1 mark)

  1.  

Show Answers Only

  1. `text(20%)`
  2. `$330`
  3. `$15`
    1. `$17\ 000`
    2. `3.5`

Show Worked Solution

a.   `text(Discount for junior members)`

`= 30/150 xx 100text(%)`

`= 20text(%)`

  
b.   `text(Match Payments)= 12 xx 15=$180`

`:.\ text(Total paid to the club)` `= 150 + 180`
  `= $330`

 

c.    `I` `= (PrT)/100`
    `= (150 xx 5 xx 2)/100`
    `= $15`

 

d.i.   `text(Withdrawal on 17 Jan)`

`= 59\ 700-42\ 700`

`= $17\ 000`
    

d.ii.   `text(Minimum Jan balance) = $42\ 700`

`47\ 200 xx r xx 1/12` `= 125.12`
`:. r` `= (125.12 xx 12)/(42\ 700)`
  `= 0.0351…`

  
`:.\ text(Annual interest rate) = 3.5text(%)`

CORE*, FUR1 2007 VCAA 7 MC

At the start of each year Joe's salary increases to take inflation into account.

Inflation averaged 2% per annum last year and 3% per annum the year before that.

Joe's salary this year is $42 000.

Joe's salary two years ago, correct to the nearest dollar, would have been

A.   `$39\ 900`

B.   `$39\ 925`

C.   `$39\ 926`

D.   `$39\ 976`

E.   `$39\ 977`

Show Answers Only

`E`

Show Worked Solution

`text(Let last year’s salary)\ = x`

♦♦ Mean mark 23%.
MARKERS’ COMMENT: Depreciating this year’s salary of $42 000 by 3% and then 2% to get ($42 000 x 0.97 x 0.98) is an incorrect strategy used by almost half of students. Make sure you understand why!
`x xx 1.03` `= 42 \ 000`
`x` `= (42\ 000)/1.03`
  `= $40 \ 776.70`

 

`text(Let salary 2 years ago)\ = y`

`y xx 1.02` `= $40 \ 776.70`
 `:. y` `=$39 \ 977.15`

 
`=>  E`

CORE*, FUR1 2006 VCAA 7 MC

Mervyn bought a new lawn mower at a sale.

First, there was a 20% discount from the original price.

Then, an $80 trade-in for his old mower was subtracted from this reduced price.

This left Mervyn with $368 to pay for the new lawn mower.

The original price of the new lawn mower was

A.   $468.00

B.   $537.50

C.   $540.00

D.   $560.00

E.   $580.00

Show Answers Only

`D`

Show Worked Solution

 `text(Let original price) = P`

`:.\ text(Original price less 20% discount) = 0.8P`

 

`text($80 trade-in for old mower subtracted)`

`text{from discounted price = $368 (given)}`

`:.\ 0.8P − 80` `= $368`
`0.8P` `= 448`
`P` `= $560`

`=>  D`

CORE*, FUR1 2005 VCAA 8 MC

On Monday, a clock has a certain price.

In a crazy week of sales the price goes up and down as follows.

Tuesday – the price of the clock is increased by 10%.
Wednesday – Tuesday’s price is reduced by 10%.
Thursday – Wednesday’s price is increased by 20%.
Friday – Thursday’s price is reduced by 20%.

When compared with Monday’s price, the price on Friday is closest to

A.   the same as Monday’s price.

B.   4% lower than Monday’s price.

C.   4% higher than Monday’s price.

D.   5% lower than Monday’s price.

E.   5% higher than Monday’s price.

Show Answers Only

`D`

Show Worked Solution

`text(Let Monday price be)\ $x.`

`text(Tuesday price)` `= x xx text(110%)`
  `= 1.1x`
`text(Wednesday price)` `= 1.1x × text(90%)`
  `= 0.99x`
`text(Thursday price)`  `= 0.99x xx text(120%)`
  `= 1.188x`
`text(Friday price)` `= 1.188x xx text(80%)`
  `= 0.9504x`

 

`:.\ text(Friday’s price is around 95% of Monday’s)`

`text(price, or 5% lower compared to Monday.)`

`=>  D`

CORE*, FUR1 2012 VCAA 4 MC

Mei’s starting salary is $65 000 per annum.

After the first year her salary will increase by 2.8%.

After the second year her salary will increase by a further 3.5%.

After this second increase, her salary will be closest to

A.   $66 820

B.   $68 690

C.   $69 030

D.   $69 160

E.   $69 630

Show Answers Only

`D`

Show Worked Solution

`text(Salary after 1st year)`

`= 65\ 000 + 2.8text(%) xx 65\ 000`

`= $66\ 820`

`text(Salary after 2nd year)`

`= $66\ 820 + 3.5text(%) xx 66\ 820`

`= $69\ 158.70`

`=> D`

CORE*, FUR1 2012 VCAA 1 MC

The selling price of a large tin of paint is $215.

After a 25% discount, the selling price of the tin of paint will become

A.     $43.00

B.     $53.75

C.   $161.25

D.   $190.00

E.   $195.00

Show Answers Only

`C`

Show Worked Solution
`text(Price after discount)` `= 215 – 25text(%) xx 215`
  `= $215 -53.75`
  `= $161.25`

`=>   C`

CORE*, FUR1 2013 VCAA 6 MC

A worker has received an annual salary increase of 3% for the past two years.

This year, the worker’s annual salary is $46 500.

Two years ago, her salary was closest to

A.   `$42\ 315`

B.   `$43\ 750`

C.   `$43\ 830`

D.   `$45\ 140`

E.   `$49\ 330`

Show Answers Only

`C`

Show Worked Solution

`text(Let)\ x\ text(be the worker’s salary 2 years ago)`

♦♦ Mean mark 30%.
`x xx 1.03 xx 1.03` `= 46\ 500`
`x (1.03)^2` `= 46\ 500`
`:. x` `= (46\ 500) / 1.03^2`
  `= 43\ 830.70…`

 
`=>  C`

CORE*, FUR1 2013 VCAA 2 MC

The closing price of a share on Monday was $30.

The closing price of the share on Tuesday was 5% more than its closing price on Monday.

The closing price of the share on Wednesday was 5% less than its closing price on Tuesday.

Which one of the following calculations will give the closing price of the share, in dollars, on Wednesday?

A.   `30 xx 1.05 xx 0.95`  

B.   `30 xx 1.05 xx –0.05`  

C.   `30 + 1.05 xx 0.95`

D.   `30 + 0.05 xx 30 - 0.05 xx 30`

E.   `30 + 1.05 - 0.95`

Show Answers Only

`A`

Show Worked Solution

`text(On Tuesday,)`

`text(Closing price)` `= 30 xx text(105%)`
  `= 30 xx 1.05`

`text(On Wednesday,)`

`text(Closing price)` `= (30 xx 1.05) xx text(95%)`
  `= 30 xx 1.05 xx 0.95`

`=>  A`

CORE*, FUR1 2014 VCAA 2 MC

An internet car market site charges $120 to advertise a car for sale.

The car is sold for $15 000.

The $120 charge as a percentage of the selling price of the car is

A.   0.008%

B.   0.08%

C.   0.80%

D.   1.20%

E.   1.25%

Show Answers Only

`C`

Show Worked Solution
`text(Charge %)` `= 120 / (15\ 000) xx 100`
  `= 0.8text(%)`

`=>  C` 

CORE*, FUR1 2014 VCAA 1 MC

This month, a business charges $1500 to install a water tank.

Next month, the charge will increase by 3.5%.

The charge next month will be

A.       `$45.00`

B.       `$52.50`

C.   `$1545.00`

D.   `$1552.50`

E.   `$1950.00` 

Show Answers Only

`D`

Show Worked Solution

`text(Next month’s charge)`

`= 1500 + 3.5text(%) xx 1500`

`= 1500 + 52.5`

`= $1552.5`

`=>  D`