SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Financial Maths, 2ADV M1 2022 HSC 17

Cards are stacked to build a 'house of cards'. A house of cards with 3 rows is shown.

A house of cards requires 3 cards in the top row, 6 cards in the next row, and each successive row has 3 more cards than the previous row.

  1. Show that a house of cards with 12 rows has a total of 234 cards.  (2 marks)

  2. Another house of cards has a total of 828 cards.
  3. How many rows are in this house of cards?  (3 marks)

Show Answers Only
Show Worked Solution

a.   

 
 
   
   

 
b.   

 
 
   

 

 
 
 

 

Financial Maths, 2ADV M1 2018 HSC 14d

An artist posted a song online. Each day there were    downloads, where  is the number of days after the song was posted.

  1. Find the number of downloads on each of the first 3 days after the song was posted.  (1 mark)

  2. What is the total number of times the song was downloaded in the first 20 days after it was posted?  (2 marks)

Show Answers Only


Show Worked Solution

i.   

 

ii. 

♦ Mean mark 38%.

Financial Maths, 2ADV M1 SM-Bank 8 MC

There are 3000 tickets available for a concert.

On the first day of ticket sales, 200 tickets are sold.

On the second day, 250 tickets are sold.

On the third day, 300 tickets are sold.

This pattern of ticket sales continues until all 3000 tickets are sold.

How many days does it take for all of the tickets to be sold?

Show Answers Only

Show Worked Solution

 

 

 

 
 

Financial Maths, 2ADV M1 2004 HSC 5a

Clare is learning to drive. Her first lesson is 30 minutes long. Her second lesson is 35 minutes long. Each subsequent lesson is 5 minutes longer than the lesson before.

  1. How long will Clare’s twenty-first lesson be?  (1 mark)

  2. How many hours of lessons will Clare have completed after her twenty-first lesson?  (2 marks)

  3. During which lesson will Clare have completed a total of 50 hours of driving lessons?  (2 marks)

Show Answers Only
Show Worked Solution

i.   

 
 

 

 

ii. 

 
 
 
 

 

(iii) 
 

 
 
 
 

 

Financial Maths, 2ADV M1 2007 HSC 3b

Heather decides to swim every day to improve her fitness level.

On the first day she swims 750 metres, and on each day after that she swims metres more than the previous day. That is, she swims 850 metres on the second day, 950 metres on the third day and so on.

  1. Write down a formula for the distance she swims on the th day.  (1 mark)

  2. How far does she swim on the 10th day?  (1 mark)

  3. What is the total distance she swims in the first 10 days?  (1 mark)

  4. After how many days does the total distance she has swum equal the width of the English Channel, a distance of 34 kilometres?  (2 marks)

Show Answers Only
Show Worked Solution
i. 

 
 
 

 

ii. 
 

 

 

iii. 

 
 

 

 

iv. 

 

 
 
 
 
 

 

Financial Maths, 2ADV M1 2006 HSC 3c

On the first day of the harvest, an orchard produces 560 kg of fruit. On the next day, the orchard produces 543 kg, and the amount produced continues to decrease by the same amount each day.

  1. How much fruit is produced on the fourteenth day of the harvest?  (2 marks)

  2. What is the total amount of fruit that is produced in the first 14 days of the harvest?  (1 mark)

  3. On what day does the daily production first fall below 60 kg?  (2 marks)

Show Answers Only
  3. `text(On the 31st day, production will first drop below 60 kg.)`
Show Worked Solution

i.   

 
 

 

 

ii. 

 
 
 

 

 

iii. 

 

Financial Maths, 2ADV M1 2005 HSC 7a

Anne and Kay are employed by an accounting firm.

Anne accepts employment with an initial annual salary of  $50 000. In each of the following years her annual salary is increased by $2500.

Kay accepts employment with an initial annual salary of  $50 000. In each of the following years her annual salary is increased by 4%.

  1. What is Anne’s annual salary in her thirteenth year?  (2 marks)

  2. What is Kay’s annual salary in her thirteenth year?  (2 marks)

  3. By what amount does the total amount paid to Kay in her first twenty years exceed that paid to Anne in her first twenty years?  (3 marks)

Show Answers Only
Show Worked Solution

i.   

 

 

 

ii. 

 
 
 

 

iii. 

 
 
 

 

 
 

 

 

Financial Maths, 2ADV M1 2010 HSC 4a

Susanna is training for a fun run by running every week for 26 weeks. She runs 1 km  in the first week and each week after that she runs 750 m more than the previous week, until she reaches 10 km in a week. She then continues to run 10 km each week.

  1. How far does Susannah run in the 9th week?     (1 mark)

  2. In which week does she first run 10 km?     (1 mark)

  3. What is the total distance that Susannah runs in 26 weeks?     (2 marks)

Show Answers Only
Show Worked Solutions

i.    

 
 

 

 

ii. 

MARKER’S COMMENT: Better responses wrote the formula for the term before clearly substituting in known values and .
 

 

 

iii. 

MARKER’S COMMENT: Many students incorrectly calculated , not taking into account the AP stopped at the 13th term.
 
 
 
 

 

Financial Maths, 2ADV M1 2011 HSC 3a

A skyscraper of 110 floors is to be built. The first floor to be built will cost $3 million. The cost of building each subsequent floor will be $0.5 million more than the floor immediately below.

  1. What will be the cost of building the 25th floor?     (2 marks)

  2. What will be the cost of building all 110 floors of the skyscraper?     (2 marks)

Show Answers Only
Show Worked Solutions
i.     

 
 

MARKER’S COMMENT: Better responses listed the sequence of terms in the series as illustrated.
 
 

 
 

MARKER’S COMMENT: Better responses stated the formula BEFORE any calculations were performed. This allows markers to allocate part marks to students who had errors in calculation.

 

ii.     
   
 
 
 

 

Financial Maths, 2ADV M1 2012 HSC 12c

Jay is making a pattern using triangular tiles. The pattern has 3 tiles in the first row, 5 tiles in the second row, and each successive row has 2 more tiles than the previous row.

2012 12c

  1. How many tiles would Jay use in row 20?     (2 marks)

  2. How many tiles would Jay use altogether to make the first 20 rows?     (1 mark)

  3. Jay has only 200 tiles. How many complete rows of the pattern can Jay make?     (2 marks)

Show Answers Only
Show Worked Solutions
i.   
 
 

 

 
 

 

 

MARKER’S COMMENT: Better responses stated the formula BEFORE any calculations were performed. This enabled students to get some marks if they made an error in their working.
ii.   
 
 

 

 

 iii.   

NOTE: Examiners often ask questions requiring to be found using the formula as this requires the solving of a quadratic, and interpretation of the answer.
 
 
 

 

Financial Maths, 2ADV M1 2013 HSC 12c

Kim and Alex start jobs at the beginning of the same year. Kim's annual salary in the first year is $30,000 and increases by 5% at the beginning of each subsequent year. Alex's annual salary in the first year is $33,000, and increases by $1,500 at the beginning of each subsequent year.

  1. Show that in the 10th year, Kim's annual salary is higher than Alex's annual salary.     (2 marks)

  2. In the first 10 years how much, in total, does Kim earn?     (2 marks)

  3. Every year, Alex saves of her annual salary. How many years does it take her to save $87,500?     (3 marks)

Show Answers Only
Show Worked Solutions

i.    

 


 

 

ii.   

 
 

 

 

iii.   


 

♦ Mean mark 45%.
IMPORTANT: Using the AP sum formula to create and then solve a quadratic in is challenging and often examined. Students need to solve and interpret the solutions.