SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Algebra, STD2 A4 2022 HSC 22

The formula    is used to calculate the cost of producing laptops, where is the cost in dollars, is the number of laptops produced and is the fixed cost in dollars.

  1. Find the cost when 1943 laptops are produced and the fixed cost is $20 180.  (1 mark)

  2. Some laptops have some extra features added. The formula to calculate the production cost for these is
  3.      
  4. where is the additional cost in dollars per laptop produced.
  5. Find the number of laptops produced if the additional cost is $26 per laptop and the total production cost is $97 040.  (2 marks)

Show Answers Only
Show Worked Solution

a.   

 
   

 

b.   

 
 
 
 
   

Algebra, STD2 A2 2022 HSC 16

Tom is 25 years old, and likes to keep fit by exercising.

  1. Use this formula to find his maximum heart rate (bpm).
  2.      Maximum heart rate = 220 – age in years
  3. Tom's maximum heart rate is ........................... bpm.   (1 mark)
  4. Tom will get the most benefit from this exercise if his heart rate is between 50% and 85% of his maximum heart rate.
  5. Between what two heart rates should Tom be aiming for to get the most benefit from his exercise?  (2 marks)

Show Answers Only
Show Worked Solution
a.   
   

 

b.   

Algebra, STD1 A3 2021 HSC 25

The diagram shows a container which consists of a small cylinder on top of a larger
cylinder.
 


 

The container is filled with water at a constant rate to the top of the smaller cylinder. It takes 5 minutes to fill the larger cylinder.

Draw a possible graph of the water level in the container against time.  (2 marks)
 

Show Answers Only

Show Worked Solution
♦ Mean mark 38%.

Algebra, STD2 A2 2019 HSC 14 MC

Last Saturday, Luke had 165 followers on social media. Rhys had 537 followers. On average, Luke gains another 3 followers per day and Rhys loses 2 followers per day.

If    represents the number of days since last Saturday and    represents the number of followers, which pair of equations model this situation?

A. 

 
B.

 
C.

 
D.

 
Show Answers Only

Show Worked Solution

Algebra, STD2 A2 SM-Bank 3

The average height, , in centimetres, of a girl between the ages of 6 years and 11 years can be represented by a line with equation

where is the age in years. For this line, the gradient is 6.

  1. What does this indicate about the heights of girls aged 6 to 11?   (1 mark)

  2. Give ONE reason why this equation is not suitable for predicting heights of girls older than 12.   (1 mark)

Show Answers Only
Show Worked Solution

i. 


 

ii. 

Algebra, STD2 A2 SM-Bank 2

The weight of a steel beam, , varies directly with its length, .

A 1200 mm steel beam weighs 144 kg.

Calculate the weight of a 750 mm steel beam.  (2 marks)

Show Answers Only

Show Worked Solution

 

 

 

Algebra, STD2 A2 2017 HSC 20 MC

A pentagon is created using matches.

By adding more matches, a row of two pentagons is formed.

Continuing to add matches, a row of three pentagons can be formed.

Continuing this pattern, what is the maximum number of complete pentagons that can be formed if 100 matches in total are available?

A.    

B.    

C.    

D.    

Show Answers Only

Show Worked Solution

 

Algebra, STD2 A2 2017 HSC 3 MC

The graph shows the relationship between infant mortality rate (deaths per 1000 live births) and life expectancy at birth (in years) for different countries.
 

What is the life expectancy at birth in a country which has an infant mortality rate of 60?

  1. 68 years
  2. 69 years
  3. 86 years
  4. 88 years
Show Answers Only

Show Worked Solution


 

Algebra, STD2 A2 2016 HSC 29e

The graph shows the life expectancy of people born between 1900 and 2000.
 


  1. According to the graph, what is the life expectancy of a person born in 1932?  (1 mark)

  2. With reference to the value of the gradient, explain the meaning of the gradient in this context.  (2 marks)

Show Answers Only
Show Worked Solution

i.   

ii.   

 
 

 

♦♦ Mean mark (ii) 33%.

Algebra, STD2 A2 2007 HSC 27b

A clubhouse uses four long-life light globes for five hours every night of the year. The purchase price of each light globe is $6.00 and they each cost    per hour to run.

  1. Write an equation for the total cost () of purchasing and running these four light globes for one year in terms of  .    (2 marks)

  2. Find the value of    (correct to three decimal places) if the total cost of running these four light globes for one year is $250.   (1 mark)

  3. If the use of the light globes increases to ten hours per night every night of the year, does the total cost double? Justify your answer with appropriate calculations.   (1 mark)

  4. The manufacturer’s specifications state that the expected life of the light globes is normally distributed with a standard deviation of 170 hours.

     

    What is the mean life, in hours, of these light globes if 97.5% will last up to 5000 hours?   (1 mark)

Show Answers Only
Show Worked Solution

i. 

 
 
 

 

ii. 

 
 

 

iii. 

 
   

 

iv. 

 

Algebra, STD2 A2 2014 HSC 26f

The weight of an object on the moon varies directly with its weight on Earth.  An astronaut who weighs 84 kg on Earth weighs only 14 kg on the moon.

A lunar landing craft weighs 2449 kg when on the moon. Calculate the weight of this landing craft when on Earth.   (2 marks)

Show Answers Only

 

Show Worked Solution

 

 

Algebra, STD2 A2 2010 HSC 27c

The graph shows tax payable against taxable income, in thousands of dollars.

2010 27c

  1. Use the graph to find the tax payable on a taxable income of $21 000.  (1 mark)

  2. Use suitable points from the graph to show that the gradient of the section of the graph marked    is  .    (1 mark)

  3. How much of each dollar earned between  $21 000  and  $39 000  is payable in tax?   (1 mark)

  4. Write an equation that could be used to calculate the tax payable, , in terms of the taxable income, , for taxable incomes between  $21 000  and  $39 000.   (2 marks)

Show Answers Only
Show Worked Solution
i.

 

 

ii. 

♦♦ Mean mark 25%
 
 
 

 

iii. 

♦♦♦ Mean mark 12%!
MARKER’S COMMENT: Interpreting gradients is an examiner favourite, so make sure you are confident in this area.
 

 

iv. 

♦♦♦ Mean mark 15%.
STRATEGY: The earlier parts of this question direct students to the most efficient way to solve this question. Make sure earlier parts of a question are front and centre of your mind when devising strategy.

 
 

Algebra, STD2 A2 2009 HSC 24d

A factory makes boots and sandals. In any week

• the total number of pairs of boots and sandals that are made is 200
• the maximum number of pairs of boots made is 120
• the maximum number of pairs of sandals made is 150.

The factory manager has drawn a graph to show the numbers of pairs of boots () and sandals () that can be made.
 

 

  1. Find the equation of the line .   (1 mark)

  2. Explain why this line is only relevant between and for this factory.     (1 mark)

  3. The profit per week, , can be found by using the equation  .

     

    Compare the profits at and .     (2 marks)

Show Answers Only

  2.  

     

     

     

Show Worked Solution

i.    

♦♦♦ Mean mark part (i) 14%. 
Using is a less efficient but equally valid method, using    and  (-intercept).

 

ii. 

♦ Mean mark 49%

 

iii. 

♦ Mean mark 40%.
 
 

 
 

 

Algebra, STD2 A2 2009 HSC 13 MC

The volume of water in a tank changes over six months, as shown in the graph.
 

 2UG-2010-13MC

 
Consider the overall decrease in the volume of water.

What is the average percentage decrease in the volume of water per month over this time, to the nearest percent?

  1.  6%
  2. 11%
  3. 32%
  4. 64%
Show Answers Only

Show Worked Solution
♦ Mean mark 48%
COMMENT: Remember that % decrease requires the decrease in volume to be divided by the original volume (50,000L).