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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%.

 

 

Measurement, STD2 M1 2015 HSC 12 MC

The length of a fish was measured to be 49 cm, correct to the nearest cm.

What is the percentage error in this measurement, correct to one significant figure?

  1. 0.01%
  2. 0.5%
  3. 1%
  4. 2%
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♦ Mean mark 41%.

 
   
   
   

 

Statistics, STD2 S1 2015 HSC 6 MC

The times, in minutes, that a large group of students spend on exercise per day are presented in the box‑and‑whisker plot.
 

What percentage of these students spend between 40 minutes and 60 minutes per day on exercise?

  1. 17%
  2. 20%
  3. 25%
  4. 50%
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Measurement, STD2 M1 2015 HSC 1 MC

What is  1 560 200 km written in standard form correct to two significant figures?

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♦♦ Mean mark 30%.
COMMENT: Incredibly, the first MC question in 2015 had the lowest mean mark of all MC questions in the exam!

 

Financial Maths, STD2 F1 2004 HSC 27b

David is paid at these rates:
  

 

His time sheet for last week is:
  

  1. Calculate David’s gross pay for last week.  (3 marks)

  2. David decides not to work on Saturdays. He wants to keep his weekly gross pay the same. How many extra hours at the weekday rate must he work?  (1 mark)

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i.   
 
 
 

 

 

 

 ii. 

 

Financial Maths, STD2 F1 2006 HSC 22 MC

This income tax table is used to calculate Evelyn’s tax payable.
 

Evelyn’s taxable income increases from $50 000 to $80 000.

What percentage of her increase will she pay in additional tax?

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Measurement, STD2 M1 2005 HSC 23b

A clay brick is made in the shape of a rectangular prism with dimensions as shown.
 

  1. Calculate the volume of the clay brick.  (1 mark)

Three identical cylindrical holes are made through the brick as shown. Each hole has a radius of 1.4 cm.  
 

  1. What is the volume of clay remaining in the brick after the holes have been made? (Give your answer to the nearest cubic centimetre.)  (3 marks)

  2. What percentage of clay is removed by making the holes through the brick? (Give your answer correct to one decimal place.)  (1 mark)

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i.   
   
   

 

ii. 

 

 

iii. 

Statistics, STD2 S1 2005 HSC 22 MC

Two groups of people were surveyed about their weekly wages. The results are shown in the box-and-whisker plots.
 

Which of the following statements is true for the people surveyed?

  1. The same percentage of people in each group earned more than $325 per week.
  2. Approximately 75% of people under 21 years earned less than $350 per week.
  3. Approximately 75% of people 21 years and older earned more than $350 per week.
  4. Approximately 50% of people in each group earned between $325 and $350 per week.
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Financial Maths, STD2 F1 2006 HSC 5 MC

A salesman earns $200 per week plus $40 commission for each item he sells.

How many items does he need to sell to earn a total of $2640 in two weeks?

  1. 33
  2. 56
  3. 61
  4. 66
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Probability, STD2 S2 2005 HSC 23a

There are 100 tickets sold in a raffle. Justine sold all 100 tickets to five of her friends. The number of tickets she sold to each friend is shown in the table.
 

  1. Justine claims that each of her friends is equally likely to win first prize.

     

    Give a reason why Justine’s statement is NOT correct.   (1 mark)

  2. What is the probability that first prize is NOT won by Khalid or Herman?   (2 marks)

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i.   

 

ii. 


 

Probability, STD2 S2 2007 HSC 25c

In a stack of 10 DVDs, there are 5 rated PG, 3 rated G and 2 rated M.

  1. A DVD is selected at random. What is the probability that it is rated M?   (1 mark)

Grant chooses two DVDs at random from the stack. Copy or trace the tree diagram into your writing booklet.
 

  1. Complete the tree diagram by writing the correct probability on each branch.   (2 marks)

  2. Calculate the probability that Grant chooses two DVDs with the same rating.   (2 marks)

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  2.  
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i.   

 

 

ii.   

 

iii. 

Algebra, STD2 A1 2007 HSC 24b

The distance in kilometres () of an observer from the centre of a thunderstorm can be estimated by counting the number of seconds () between seeing the lightning and first hearing the thunder.

Use the formula    to estimate the number of seconds between seeing the lightning and hearing the thunder if the storm is 1.2 km away.   (1 mark)

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Financial Maths, STD2 F1 2007 HSC 3 MC

Joe is about to go on holidays for four weeks. His weekly salary is $280 and his holiday loading is 17.5% of four weeks pay.

What is Joe’s total pay for the four weeks holiday?

  1. $196
  2. $329
  3. $1169 
  4. $1316 
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Financial Maths, STD2 F1 2008 HSC 24a

Bob is employed as a salesman. He is offered two methods of calculating his income.

Bob’s research determines that the average sales total per employee per month is $15 670. 

  1. Based on his research, how much could Bob expect to earn in a year if he were to choose Method 1?   (2 marks)

  2. If Bob were to choose a method of payment based on the average sales figures, state which method he should choose in order to earn the greater income. Justify your answer with appropriate calculations.   (3 marks)

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i.   

 
 

 

ii. 

 
 
 

 

Statistics, STD2 S1 2008 HSC 10 MC

The marks for a Science test and a Mathematics test are presented in box-and-whisker plots.
 

 Which measure must be the same for both tests?

  1. Mean
  2. Range
  3. Median
  4. Interquartile range
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Financial Maths, STD2 F1 2008 HSC 7 MC

Luke’s normal rate of pay is $15 per hour. Last week he was paid for 12 hours, at time-and-a-half.

How many hours would Luke need to work this week, at double time, to earn the same amount?

  1. 4
  2. 6
  3. 8
  4. 9
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Measurement, STD2 M1 2014 HSC 27c

The base of a water tank is in the shape of a rectangle with a semicircle at each end, as shown.

The tank is 1400 mm long, 560 mm wide, and has a height of 810 mm.  
  

What is the capacity of the tank, to the nearest litre?   (4 marks) 

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♦ Mean mark 41%
STRATEGY: Adjusting measurements to metres makes the final conversion to litres simple.


 

 

 
 
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Probability, STD2 S2 2014 HSC 16 MC

In Mathsville, there are on average eight rainy days in October.

Which expression could be used to find a value for the probability that it will rain on two consecutive days in October in Mathsville?

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♦♦♦ Mean mark 16%.
Lowest mark of any MC question in 2014!

Financial Maths, STD2 F1 2014 HSC 13 MC

Jane sells jewellery. Her commission is based on a sliding scale of 6% on the first $2000 of her sales, 3.5% on the next $1000, and 2% thereafter.

What is Jane’s commission when her total sales are $5670? 

  1. $188.40
  2. $208.40
  3. $321.85
  4. $652.05
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Measurement, STD2 M1 2014 HSC 10 MC

The top of the Sydney Harbour Bridge is measured to be 138.4 m above sea level. 

What is the percentage error in this measurement?

  1. 0.036%
  2. 0.050%
  3. 0.072%
  4. 0.289%
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♦ Mean mark 48%

 
   
   

 

Statistics, STD2 S1 2010 HSC 27b

The graphs show the distribution of the ages of children in Numbertown in 2000 and 2010.
  

  1. In 2000 there were 1750 children aged 0–18 years.

     

    How many children were aged 12–18 years in 2000?   (1 mark)

  2. The number of children aged 12–18 years is the same in both 2000 and 2010.

     

    How many children aged 0–18 years are there in 2010?    (1 mark)

  3. Identify TWO changes in the distribution of ages between 2000 and 2010. In your answer, refer to measures of location or spread or the shape of the distributions.   (2 marks)

  4. What would be ONE possible implication for government planning, as a consequence of this change in the distribution of ages?   (1 mark)

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i.   

ii.   

iii. 

iv. 

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i.    

♦ Mean mark (i) 45%

 

♦♦ Mean mark (ii) 25%

ii.   


 

iii. 

♦ Mean mark (iii) 35%
MARKER’S COMMENT: A number of students incorrectly identified “positive” skew as “negative” skew here.

iv. 

♦ Mean mark (iv) 46%
MARKER’S COMMENT: Answers should reflect the 1 mark allocation.

Probability, STD2 S2 2013 HSC 30b

In a class there are 15 girls (G) and 7 boys (B). Two students are chosen at random to be class representatives.

  1. Complete the tree diagram below.    (2 marks)
     
     

  2. What is the probability that the two students chosen are of the same gender?    (2 marks)

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  1.  
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i.  

ii.   
   
   
   
   
♦ Mean mark (ii) 40%.

Measurement, STD2 M1 2013 HSC 27d

A rectangular wooden chopping board is advertised as being 17 cm by 25 cm, with each side measured to the nearest centimetre.

  1. Calculate the percentage error in the measurement of the longer side.   (1 mark)

  2. Between what lower and upper limits does the actual area of the top of the chopping board lie?     (2 marks)

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i.   

♦♦ Mean mark 23%
MARKER’S COMMENT: Be aware that measurements accurate to the nearest cm have an absolute error for calculation purposes of 0.5 cm.

 
   
   

 

ii.   

♦ Mean mark 35%
 

 

 

 

Probability, STD2 S2 2013 HSC 26c

The probability that Michael will score more than 100 points in a game of bowling is . 

  1. A commentator states that the probability that Michael will score less than 100 points in a game of bowling is  .

     

    Is the commentator correct? Give a reason for your answer.   (1 mark)

  2. Michael plays two games of bowling. What is the probability that he scores more than 100 points in the first game and then again in the second game?   (1 mark)

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♦♦♦ Mean mark 11%

i.  

 

♦ Mean mark 34%
ii.  
   

Algebra, STD2 A1 2010 HSC 24a

Fred tried to solve this equation and made a mistake in Line 2. 

Copy the equation in Line 1.

  1. Rewrite Line 2 correcting his mistake.   (1 mark)

  2. Continue your solution showing the correct working for Lines 3 and 4 to solve this equation for .   (1 mark)

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  1.  

  2.  

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i.   
 

 

ii.   
 

Probability, STD2 S2 2010 HSC 20 MC

Lou and Ali are on a fitness program for one month. The probability that Lou will finish the program successfully is 0.7 while the probability that Ali will finish successfully is 0.6. The probability tree shows this information

 

What is the probability that only one of them will be successful ?

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♦ Mean mark 48%.

Measurement, STD2 M1 2009 HSC 23c

The diagram shows the shape and dimensions of a terrace which is to be tiled.
 

  1. Find the area of the terrace.   (2 marks)

  2. Tiles are sold in boxes. Each box holds one square metre of tiles and costs $55. When buying the tiles, 10% more tiles are needed, due to cutting and wastage.

     

    Find the total cost of the boxes of tiles required for the terrace.   (2 marks)

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i.    ²

ii.   

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i.
 
 
  ²

 

ii.
    ²

 

 

 

Financial Maths, STD2 F1 2009 HSC 10 MC

Billy worked for 35 hours at the normal hourly rate of pay and for five hours at double time. He earned $561.60 in total for this work.

What was the normal hourly rate of pay?

  1. $7.02
  2. $12.48
  3. $14.04
  4. $16.05
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Probability, STD2 S2 2012 HSC 27e

A box contains 33 scarves made from two different fabrics. There are 14 scarves made from silk (S) and 19 made from wool (W).
Two girls each select, at random, a scarf to wear from the box.

  1. Complete the probability tree diagram below.   (2 marks) 
      
       

  2. Calculate the probability that the two scarves selected are made from silk.    (1 mark)

  3. Calculate the probability that the two scarves selected are made from different fabrics.   (2 marks)

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  1.  
       
     
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i. 

♦ Mean mark (i) 43%.
ii. 
 
 

 

iii. 
 
 
 
♦ Mean mark (iii) 41%.
MARKER’S COMMENT: In better responses, students multiplied along the branches and then added these two results together

Measurement, STD2 M6 2012 HSC 27d

A disability ramp is to be constructed to replace steps, as shown in the diagram.

The angle of inclination for the ramp is to be 5°.   
  

Calculate the extra distance, , that the ramp will extend beyond the bottom step.

Give your answer to the nearest centimetre.   (3 marks)

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♦♦ Mean mark 35%
MARKER’S COMMENT:  The better responses used a diagram of a simplified version of the ramp as per the Worked Solution.
 
   
 
 

Measurement, STD2 M7 2012 HSC 27c

A map has a scale of  1 : 500 000.

  1. Two mountain peaks are 2 cm apart on the map.

     

    What is the actual distance between the two mountain peaks, in kilometres?  (1 mark)

  2. Two cities are 75 km apart. How far apart are the two cities on the map, in centimetres?   (1 mark)

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♦ Mean mark 37%
MARKER’S COMMENT: Better responses realised that 1 unit on the map represented 1 unit x 500,000 in real life.
i. 
 
 
 

 

 

♦ Mean mark 44%

ii.  

 

Statistics, STD2 S1 2011 HSC 7 MC

A set of data is displayed in this box-and-whisker plot.
 

Which of the following best describes this set of data?

  1. Symmetrical
  2. Positively skewed
  3. Negatively skewed
  4. Normally distributed
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♦ Mean mark 47%.

Financial Maths, STD2 F1 2010 HSC 5 MC

Minjy invests $2000 for 1 year and 5 months. The simple interest is calculated at a rate of 6% per annum.

What is the total value of the investment at the end of this period?

  1. $2170
  2. $2180
  3. $3003
  4. $3700
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Financial Maths, STD2 F1 2012 HSC 18 MC

Jo qualifies for both Rent Assistance and Youth Allowance and receives a fortnightly payment from the government. 

Rent Assistance is  $119.40  per fortnight. 

The maximum Youth Allowance is $402.70 per fortnight. It is reduced by 50 cents in the dollar for any income earned over $236 per fortnight.

Jo earns $300 per fortnight from a part-time job.

What is the total payment Jo receives each fortnight from the government?

  1. $370.70
  2. $372.10
  3. $458.60
  4. $490.10
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Probability, STD2 S2 2013 HSC 18 MC

Two unbiased dice, each with faces numbered  1, 2, 3, 4, 5, 6,  are rolled.

What is the probability of obtaining a sum of 6?

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♦♦ Mean mark 35%.

Financial Maths, STD2 F1 2013 HSC 13 MC

Polly borrowed $11 000.  She repaid the loan in full at the end of two years with a lump sum of  $12 000.

What annual simple interest rate was she charged?

  1. 4.17%
  2. 4.55%
  3. 8.33%
  4. 9.09%
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Financial Maths, STD2 F1 2013 HSC 11 MC

An enterprise agreement has the following annual salary arrangements:
 

George's employer pays 6% more than the enterprise agreement. He is on Step 3 and receives an allowance for Leader 2.

What is George's gross monthly pay?

  1. $4375.00
  2. $4412.50
  3. $4600.00
  4. $4637.50
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♦ Mean mark 46%
 

 

 

 

Financial Maths, STD2 F1 2013 HSC 9 MC

Lynne invests $1000 for a term of 15 months. Simple interest is paid on the investment at a rate of 3.75% per annum.

How much will Lynne's investment be worth at the end of the term?

  1. $1046.88
  2. $1047.09
  3. $1296.88
  4. $1468.75
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Financial Maths, STD2 F1 2013 HSC 3 MC

Luke's normal rate of pay is  $24.80  per hour. In one week he worked 14 hours at the normal rate, 4 hours at time-and-a-half, and 3 .5 hours at double time. He was also paid a wet weather allowance of  $50  for the week.

What was his pay for the week?

  1. $583.20
  2. $620.40
  3. $669.60
  4. $719.60
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