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Plane Geometry, 2UA 2018 HSC 12c

The diagram shows the square . The point is chosen on and the point is chosen on so that  .
 

  1. Prove that is congruent to .   (2 marks)

  2. The side length of the square is 14 cm and has length 4 cm. Find the area of  .   (2 marks)

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i.   

 

ii.  
   

 

Measurement, STD2 M6 2018 HSC 30c

The diagram shows two triangles.

Triangle is right-angled, with    and  .

In triangle    and  . The area of triangle    is 30 cm².
 

 
What is the value of , correct to one decimal place?  (3 marks)

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♦ Mean mark 39%.

 

 

 
 

Financial Maths, STD2 F1 2018 HSC 30b

Last year, Luke’s taxable income was and the tax payable on this income was . This year, Luke’s taxable income has increased by .

  1. Use the table to calculate the tax payable by Luke this year.  (2 marks)
     

  2. How much extra money will Luke have this year, after paying tax, as a result of the increase in his taxable income? Ignore the Medicare levy.  (2 marks)

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i.   

 

 

ii.   


 


 

 

Measurement, STD2 M1 2018 HSC 30a

A cylindrical water tank has a radius of 9 metres and a capacity of 1.26 megalitres.
 

What is the height of the water tank? Give your answer in metres, correct to two decimal places.  (3 marks)

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³³

♦ Mean mark 48%.

 
 

 

 
 

Measurement, STD2 M1 2018 HSC 27c

A shade shelter is to be constructed in the shape of half a cylinder with open ends. The diameter is 3.8 m and the length is 10 m.
 

 
The curved roof is to be made of plastic sheeting.

What area of plastic sheeting is required, to the nearest m²?  (2 marks)

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²²

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  ²²

Financial Maths, STD2 F4 2018 HSC 26h

A car is purchased for $23 900.

The value of the car is depreciated by 11.5% each year using the declining-balance method.

What is the value of the car after three years?  (2 marks)

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Probability, STD2 S2 2018 HSC 26a

Jeremy rolled a biased 6-sided die a number of times. He recorded the results in a table.
  

 

What is the relative frequency of rolling a 3?  (1 mark)

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♦ Mean mark 40%.

 
 

Probability, STD2 S2 2018 HSC 20 MC

During a year, the maximum temperature each day was recorded. The results are shown in the table.
  


  

From the days with a maximum temperature less than 25°C, one day is selected at random.

What is the probability, to the nearest percentage, that the selected day occurred during winter?

  1. 19%
  2. 25%
  3. 32%
  4. 77%
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Statistics, STD2 S1 2018 HSC 11 MC

A set of data is summarised in this frequency distribution table.
 

 
Which of the following is true about the data?

  1. Mode = 7, median = 5.5
  2. Mode = 7, median = 6
  3. Mode = 9, median = 5.5
  4. Mode = 9, median = 6
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Statistics, STD2 S1 2018 HSC 3 MC

A survey asked the following question.

'How many brothers do you have?'

How would the responses be classified?

  1. Categorical, ordinal
  2. Categorical, nominal
  3. Numerical, discrete
  4. Numerical, continuous
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Functions, EXT1 F2 2018 HSC 11a

Consider the polynomial  .

  1. Show that    is a zero of  .  (1 mark)

  2. Find the other zeros.  (2 marks)

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i.   

 

ii.   


 

 

 

Measurement, STD2 M1 2017 HSC 30e

A solid is made up of a sphere sitting partially inside a cone.

The sphere, centre , has a radius of 4 cm and sits 2 cm inside the cone. The solid has a total height of 15 cm. The solid and its cross-section are shown.
 


 

Using the formula    where  is the radius of the cone's circular base and is the perpendicular height of the cone, find the volume of the cone, correct to the nearest cm³?  (3 marks)

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Algebra, STD2 A4 2017 HSC 28e

A movie theatre has 200 seats. Each ticket currently costs $8.

The theatre owners are currently selling all 200 tickets for each session. They decide to increase the price of tickets to see if they can increase the income earned from each movie session.

It is assumed that for each one dollar increase in ticket price, there will be 10 fewer tickets sold.

A graph showing the relationship between an increase in ticket price and the income is shown below.
 


 

  1. What ticket price should be charged to maximise the income from a movie session?  (1 mark)

  2. What is the number of tickets sold when the income is maximised?  (1 mark)

  3. The cost to the theatre owners of running each session is $500 plus $2 per ticket sold.

     

    Calculate the profit earned by the theatre owners when the income earned from a session is maximised.  (2 marks)

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i.   

♦ Mean mark 50%.
 

 

ii.   

♦ Mean mark 45%.
 

 

 
 

 

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)

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

 

ii.  
   

Measurement, STD2 M6 2017 HSC 26d

A sewer pipe needs to be placed into the ground so that it has a 2° angle of depression. The length of the pipe is 15 000 mm.
 


 

How much deeper should one end of the pipe be compared to the other end? Answer to the nearest mm.  (2 marks)

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Measurement, STD2 M1 2017 HSC 25 MC

In the circle, centre , the area of the quadrant is 100 cm².
 


 

What is the arc length , correct to one decimal place?

  1. 8.9 cm
  2. 11.3 cm
  3. 17.7 cm
  4. 25.1 cm
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♦ Mean mark 44%.

 

 
 
 

 

Probability, STD2 S2 2017 HSC 15 MC

The faces on a twenty-sided die are labelled  $0.05, $0.10, $0.15, … , $1.00.

The die is rolled once.

What is the probability that the amount showing on the upper face is more than 50 cents but less than 80 cents?

A.     

B.     

C.     

D.     

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♦ Mean mark 50%.

 

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.     
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Financial Maths, STD2 F1 2017 HSC 11 MC

A new car was bought for $19 900 and one year later its value had depreciated to $16 300.

What is the approximate depreciation, expressed as a percentage of the purchase price?

  1. 18%
  2. 22%
  3. 78%
  4. 82%
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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
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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

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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
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Statistics, STD2 S1 2017 HSC 1 MC

The box-and-whisker plot for a set of data is shown.
 

What is the median of this set of data?

  1. 15
  2. 20
  3. 30
  4. 35
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Measurement, STD2 M1 2016 HSC 30c

A school playground consists of part of a circle, with centre , and a rectangle as shown in the diagram. The radius of the circle is 45 m, the width of the rectangle is 20 m and is 100°.
 

What is the area of the whole playground, correct to the nearest square metre?  (5 marks)

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²²

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²

 

  ²

 

²

 

²²

Measurement, STD2 M1 2016 HSC 28e

A company makes large marshmallows. They are in the shape of a cylinder with diameter 5 cm and height 3 cm, as shown in the diagram.

2ug-2016-hsc-q28_4

  1. Find the volume of one of these large marshmallows, correct to one decimal place.  (2 marks)

A cake is to be made by stacking 24 of these large marshmallows and filling the gaps between them with chocolate. The diagrams show the cake and its top view. The shading shows the gaps to be filled with chocolate.
 

2ug-2016-hsc-q28_5

  1. What volume of chocolate will be required? Give your answer correct to the nearest whole number.  (3 marks)

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i.   
   
   
    ³

 

ii.    2ug-2016-hsc-q28-answer1

♦ Mean mark part (ii) 35%.


 

 

Financial Maths, STD2 F1 2016 HSC 26f

Theo is completing his tax return. He has a gross salary of $82 521 and income from a rental property totalling $10 920. He is claiming $13 420 in allowable deductions.

  1. Determine Theo’s taxable income.  (1 mark)

  2. Using the tax table below, calculate Theo’s tax payable.  (2 marks)

  1. In addition to the above tax, Theo must also pay a Medicare levy of $1600.42
  2. Theo has already paid $20 525 as Pay As You Go (PAYG) tax.
  3. Should Theo receive a tax refund or will he owe more tax? Justify your answer with calculations.  (2 marks)

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i.   

 

ii.   

 

iii.   


 

 

Financial Maths, STD2 F1 2016 HSC 26e

Jenny earns a yearly salary of  $63 752. Her annual leave loading is 17.5% of four weeks pay.

Calculate her total pay for her four weeks of annual leave.  (3 marks)

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Probability, STD2 S2 2016 HSC 23 MC

A group of 485 people was surveyed. The people were asked whether or not they smoke. The results are recorded in the table.
 

A person is selected at random from the group.

What is the approximate probability that the person selected is a smoker OR is male?

  1. 33%
  2. 18%
  3. 68%
  4. 87%
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♦♦ Mean mark 34%.

Statistics, STD2 S1 2016 HSC 22 MC

The box-and-whisker plots show the results of a History test and a Geography test.
 

In History, 112 students completed the test. The number of students who scored above 30 marks was the same for the History test and the Geography test.

How many students completed the Geography test?

  1. 8
  2. 50
  3. 56
  4. 112
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Financial Maths, STD2 F1 2016 HSC 20 MC

Isabella works a 35-hour week and is paid at an hourly rate of $18. Any overtime hours worked are paid at time-and-a-half. In a particular week, she earned $1008.

How many hours in total did Isabella work in this week to earn this amount?

  1. 37.3
  2. 42
  3. 49
  4. 56
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Statistics, STD2 S1 2016 HSC 19 MC

A soccer referee wrote down the number of goals scored in 9 different games during the season.

The last number has been omitted. The range of the data is 10.

What is the five-number summary for this data set?

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♦ Mean mark 46%.

Algebra, STD2 A2 2016 HSC 14 MC

The graph shows a line which has an equation in the form  .
 

Which of the following statements is true?

  1. is positive and is negative
  2. is negative and is positive
  3. and are both positive
  4. and are both negative
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is the gradient and the line slopes to the right so is positive.

is the -intercept which is negative.

is positive and is negative.

Measurement, STD2 M1 2016 HSC 12 MC

A container is in the shape of a triangular prism which has a capacity of 12 litres. The area of the base is 240 cm².
 

What is the distance, , between the two triangular ends of the container?

  1. 5 cm
  2. 20 cm
  3. 25 cm
  4. 50 cm
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♦♦ Mean mark 35%.

 

 

Statistics, STD2 S1 2016 HSC 7 MC

Which set of data is classified as categorical and nominal?

  1. blue, green, yellow
  2. small, medium, large
  3. 5.2 cm, 6 cm, 7.21 cm
  4. 4 people, 5 people, 9 people 
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♦♦ Mean mark 26%.