SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

NETWORKS, FUR1 2017 VCAA 2 MC

Two graphs, labelled Graph 1 and Graph 2, are shown below.
 

 
The sum of the degrees of the vertices of Graph 1 is

  1. two less than the sum of the degrees of the vertices of Graph 2.
  2. one less than the sum of the degrees of the vertices of Graph 2.
  3. equal to the sum of the degrees of the vertices of Graph 2.
  4. one more than the sum of the degrees of the vertices of Graph 2.
  5. two more than the sum of the degrees of the vertices of Graph 2.
Show Answers Only

Show Worked Solution

Algebra, STD2 A1 SM-Bank 5

Fried's formula is used to calculate the medicine dosages for children aged 1-2 years.
 


 

Ben is 1.5 years old and receives a daily dosage of 450 mg of a medicine.

According to Fried's formula, what would the appropriate adult daily dosage of the medicine be?  (2 marks)

Show Answers Only

Show Worked Solution

 

GEOMETRY, FUR1 2017 VCAA 1 MC

A wheel has five spokes equally spaced around a central hub, as shown in the diagram below.
 


 

The angle between two spokes is labelled on the diagram.

What is the angle ?

  1.  
Show Answers Only

Show Worked Solution
 

 

CORE, FUR1 2017 VCAA 19-20 MC

Shirley would like to purchase a new home. She will establish a loan for $225 000 with interest charged at the rate of 3.6% per annum, compounding monthly.

Each month, Shirley will pay only the interest charged for that month.

Part 1

After three years, the amount that Shirley will owe is

  1.    $73 362
  2.  $170 752
  3.  $225 000
  4.  $239 605
  5.  $245 865

 
Part 2

Let be the value of Shirley’s loan, in dollars, after months.

A recurrence relation that models the value of is

Show Answers Only

Show Worked Solution


 


 


 

Algebra, STD2 A4 SM-Bank 3

Temperature can be measured in degrees Celsius () or degrees Fahrenheit ().

The two temperature scales are related by the equation  .

  1. Calculate the temperature in degrees Fahrenheit when it is  −20 degrees Celsius.  (1 mark)

  2. The following two graphs are drawn on the axes below:
     
             and  
     

         

    Explain what happens at the point where the two graphs intersect.  (1 mark)

Show Answers Only

  2.  

Show Worked Solution
i.  
   

 

ii.   

CORE, FUR1 2017 VCAA 1-3 MC

The boxplot below shows the distribution of the forearm circumference, in centimetres, of 252 people.
 

Part 1

The percentage of these 252 people with a forearm circumference of less than 30 cm is closest to

 

Part 2

The five-number summary for the forearm circumference of these 252 people is closest to

 

Part 3

The table below shows the forearm circumference, in centimetres, of a sample of 10 people selected from this group of 252 people.
 

 
The mean, , and the standard deviation, , of the forearm circumference for this sample of people are closest to

Show Answers Only

Show Worked Solution

 

 

Measurement, STD2 M2 SM-Bank 01

Island A and island B are both on the equator. Island B is west of island A. The longitude of island A is 5°E and the angle at the centre of Earth (O), between A and B, is 30°.
 


 

  1. What is the longitude of island B?  (1 mark)
  2. What time is it on island B when it is 10 am on island A?  (1 mark)
Show Answers Only
Show Worked Solution
(i)   
   
   

 

 

(ii)  

 

Statistics, EXT1 S1 2017 HSC 11g

The probability that a particular type of seedling produces red flowers is  .

Eight of these seedlings are planted.

  1. Write an expression for the probability that exactly three of the eight seedlings produce red flowers.  (1 mark)

  2. Write an expression for the probability that none of the eight seedlings produces red flowers.  (1 mark)

  3. Write an expression for the probability that at least one of the eight seedlings produces red flowers.  (1 mark)

Show Answers Only
Show Worked Solution

i.  

 

ii.   

 

iii.   

Calculus, EXT1* C1 2017 HSC 15c

Two particles move along the -axis.

When  , particle is at the origin and moving with velocity 3.

For  , particle has acceleration given by  .

  1. Show that the velocity of particle is given by    (2 marks)

When  , particle is also at the origin.

For  , particle has velocity given by  .

  1. When do the two particles have the same velocity?  (2 marks)

  2. Show that the two particles do not meet for  .  (3 marks)

Show Answers Only
Show Worked Solution
i.  
 
   
   

 

 

ii. 

 

iii.  
   
   

 

♦ Mean mark (iii) 39%.

 

 

 

 

 

 

Calculus, EXT1* C1 2017 HSC 14c

Carbon-14 is a radioactive substance that decays over time. The amount of carbon-14 present in a kangaroo bone is given by

where and are constants, and is the number of years since the kangaroo died.

  1. Show that satisfies  .  (1 mark)

  2. After 5730 years, half of the original amount of carbon-14 is present.

     

    Show that the value of , correct to 2 significant figures, is – 0.00012.  (2 marks)

  3. The amount of carbon-14 now present in a kangaroo bone is 90% of the original amount.

     

    Find the number of years since the kangaroo died. Give your answer correct to 2 significant  figures.  (2 marks)

Show Answers Only
Show Worked Solution
i.  
   
   

 

ii. 

 
 

 

iii. 

 
 
 

Calculus, 2ADV C4 2017 HSC 14b

  1. Find the exact value of
     
  2. .  (1 mark)

  3. Using Simpson’s rule with one application, find an approximation to the integral
  4.  

     
  5. leaving your answer in terms of and .  (2 marks)
     

  6. Using parts (i) and (ii), show that
     
  7. .  (1 mark)

 

 

Show Answers Only
(i)  
(ii)  
(iii)  
Show Worked Solution
(i)  
   
   

 

(ii)  
                    
                     
                  
 
 
 

 

(iii)  

♦ Mean mark 49%.
 

Plane Geometry, EXT1 2017 HSC 3 MC

The points , , and lie on a circle and the tangents at and meet at , as shown in the diagram.The angles and are 65° and 110° respectively.

What is the value of  ?

A.     

B.     

C.     

D.     

Show Answers Only

Show Worked Solution
     

 

 

Calculus, 2ADV C4 2017 HSC 13d

The rate at which water flows into a tank is given by

,

where is the volume of water in the tank in litres and is the time in seconds.

Initially the tank is empty.

Find the exact amount of water in the tank after 10 seconds.  (3 marks)

Show Answers Only

Show Worked Solution
 

 

 

 

Calculus, 2ADV C3 2017 HSC 13b

Consider the curve  .

  1. Find the stationary points of the curve and determine their nature.  (4 marks)

  2. Sketch the curve, labelling the stationary points.  (2 marks)

  3. Hence, or otherwise, find the values of for which is positive.  (1 mark)

Show Answers Only

  1.  

  2.    
Show Worked Solution
i.  
 
 

 

 

 


 

 

ii.  

 

iii. 

 

 
 

Statistics, 2ADV 2017 HSC 12e

A spinner is marked with the numbers 1, 2, 3, 4 and 5. When it is spun, each of the five numbers is equally likely to occur.
 

 
The spinner is spun three times.

  1. What is the probability that an even number occurs on the first spin?  (1 mark)
  2. What is the probability that an even number occurs on at least one of the three spins?  (1 mark)
  3. What is the probability that an even number occurs on the first spin and odd numbers occur on the second and third spins?  (1 mark)
  4. What is the probability that an even number occurs on exactly one of the three spins?  (1 mark)
Show Answers Only
Show Worked Solution

i.  
 

ii. 


 

iii. 


 

iv. 

Linear Functions, 2UA 2017 HSC 12d

The points    and    lie on the line  .

The length of    is  .

The points    and    lie on the line  .

The points form a trapezium as shown.
 


 

  1. Find the perpendicular distance from point to the line  .  (1 mark)
  2. Calculate the area of the trapezium.  (2 marks)
Show Answers Only

(i)  

(ii)  ²

Show Worked Solution

(i)   

 
 
 

 

(ii) 

 
 

 

 
  ²

Trigonometry, 2ADV T1 2017 HSC 11e

In the diagram, is a sector of the circle with centre and radius 6 cm, where  .


 

  1.  Find the exact value of the area of the triangle .  (1 mark)

  2. Find the exact value of the area of the shaded segment.  (1 mark)

Show Answers Only
  1.  ²
  2. ²
Show Worked Solution
i.  
   
    ²

 

ii. 
   
    ²

Functions, 2ADV F1 2017 HSC 11a

Rationalise the denominator of  .  (2 marks)

Show Answers Only

Show Worked Solution

COMMENT: Rationalising binomial surds in the denominator is not required in 2ADV, although it is an algebraic skill we would recommend.

 
 

Statistics, STD2 S5 2017 HSC 29d

All the students in a class of 30 did a test.

The marks, out of 10, are shown in the dot plot.
 


 

  1. Find the median test mark.  (1 mark)

  2. The mean test mark is 5.4. The standard deviation of the test marks is 4.22.

     

    Using the dot plot, calculate the percentage of the marks which lie within one standard deviation of the mean.  (2 marks)

  3. A student states that for any data set, 68% of the scores should lie within one standard deviation of the mean. With reference to the dot plot, explain why the student’s statement is NOT relevant in this context.  (1 mark)

Show Answers Only

Show Worked Solution
♦ Mean mark 50%.
i.   
   
   

 

ii.   

♦♦ Mean mark 34%.

 

iii.   

♦♦♦ Mean mark 13%.

Algebra, 2UG 2017 HSC 28a

Temperature can be measured in degrees Celsius () or degrees Fahrenheit ().

The two temperature scales are related by the equation  .

  1. Calculate the temperature in degrees Fahrenheit when it is  −20 degrees Celsius.  (1 mark)
  2. Solve the following equations simultaneously, using either the substitution method or the elimination method.  (2 marks)

     

  3. The graphs of   and    are shown below.
  4.  


  5. What does the result from part (ii) mean in the context of the graph?  (1 mark)     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Show Answers Only

 

 

Show Worked Solution
(i)  
   

 

(ii)  
 

 

♦♦ Mean mark 31%.
MARKER’S COMMENT: An area that requires attention.

 

♦♦♦ Mean mark 20%.

 

(iii)  

Statistics, STD2 S1 2017 HSC 27a

Jamal surveyed eight households in his street. He asked them how many kilolitres (kL) of water they used in the last year. Here are the results.

  1. Calculate the mean of this set of data.  (1 mark)

  2. What is the standard deviation of this set of data, correct to one decimal place?  (1 mark)

Show Answers Only
Show Worked Solution
i.  
   
♦ Mean mark part (ii) 47%.
IMPORTANT: The population standard deviation is required here.

 

ii.  
   

Algebra, STD2 A2 2017 HSC 14 MC

Kate is comparing two different models of car. Car A uses fuel at the rate of 9 L/100 km. Car B uses 3.5 L/100 km.

Suppose Kate plans on driving 8000 km in the next year.

How much less fuel will she use driving car B instead of car A?

A.    

B.    

C.    

D.    

Show Answers Only

Show Worked Solution

Statistics, STD2 S4 2017 HSC 12 MC

Which of the data sets graphed below has the largest positive correlation coefficient value?
 

A.      B.     
C.      D.     
Show Answers Only

Show Worked Solution

Financial Maths, STD2 F1 2017 HSC 6 MC

Tom earns a weekly wage of $1025. He also receives an additional allowance of $87.50 per day when handling toxic substances.

What is Tom’s income in a fortnight in which he handles toxic substances on 5 separate days?

  1. $1112.50
  2. $1462.50
  3. $2225.00
  4. $2487.50
Show Answers Only

Show Worked Solution
 
 

 

 

 

Probability, STD2 S2 2017 HSC 5 MC

In a survey of 200 randomly selected Year 12 students it was found that 180 use social media.

Based on this survey, approximately how many of 75 000 Year 12 students would be expected to use social media?

A.     60 000

B.     67 500

C.     74 980

D.     75 000

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


 

CHEMISTRY, M4 2009 HSC 20

  1. Calculate the mass of ethanol that must be burnt to increase the temperature of 210 g of water by 65°C, if exactly half of the heat released by this combustion is lost to the surroundings.
  2. The heat of combustion of ethanol is 1367 kJ mol −1.  (3 marks)

  3. What are TWO ways to limit heat loss from the apparatus when performing a first-hand investigation to determine and compare heat of combustion of different liquid alkanols?  (1 mark)

Show Answers Only

a.    3.85 grams

b.    Answers could include two of the following:

→ Use of an insulated vessel (Styrofoam cup)

→ Place the vessel as close as safely possible to the Bunsen’s flame.

→ Use a lid for the beaker

Show Worked Solution

a.   

Since half of the heat is lost to environmental surroundings.


 

b.    Answers could include two of the following:

→ Use of an insulated vessel (Styrofoam cup)

→ Place the vessel as close as safely possible to the Bunsen’s flame.

→ Use a lid for the beaker