Algebra, STD2 A1 2016 HSC 5 MC
Which expression is equivalent to `2(3x-4) + 2`?
- `6x-2`
- `6x-4`
- `6x-6`
- `6x-10`
Measurement, STD2 M1 2016 HSC 1 MC
What is 208.345 correct to two significant figures?
- 208
- 210
- 208.34
- 208.35
Probability, STD2 S2 2015 HSC 16 MC
The probability of winning a game is `7/10`.
Which expression represents the probability of winning two consecutive games?
- `7/10 xx 6/9`
- `7/10 xx 6/10`
- `7/10 xx 7/9`
- `7/10 xx 7/10`
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?
- 0.01%
- 0.5%
- 1%
- 2%
Statistics, STD2 S1 2015 HSC 6 MC
Algebra, STD2 A1 2015 HSC 2 MC
Which of the following is `4x + 3y-x-5y` in its simplest form?
- `3x - 2y`
- `3x + 8y`
- `5x - 2y`
- `5x + 8y`
Measurement, STD2 M1 2015 HSC 1 MC
What is 1 560 200 km written in standard form correct to two significant figures?
- `1.56 × 10^4 \ text(km)`
- `1.6 × 10^5 \ text(km)`
- `1.56 × 10^6 \ text(km)`
- `1.6 × 10^6 \ text(km)`
Financial Maths, STD2 F1 2004 HSC 27b
David is paid at these rates:
His time sheet for last week is:
- Calculate David’s gross pay for last week. (3 marks)
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- 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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Financial Maths, STD2 F1 2006 HSC 22 MC
Measurement, STD2 M1 2005 HSC 23b
A clay brick is made in the shape of a rectangular prism with dimensions as shown.
- Calculate the volume of the clay brick. (1 mark)
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Three identical cylindrical holes are made through the brick as shown. Each hole has a radius of 1.4 cm.
- 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)
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- 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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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?
- The same percentage of people in each group earned more than $325 per week.
- Approximately 75% of people under 21 years earned less than $350 per week.
- Approximately 75% of people 21 years and older earned more than $350 per week.
- Approximately 50% of people in each group earned between $325 and $350 per week.
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?
- 33
- 56
- 61
- 66
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.
- 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)
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- What is the probability that first prize is NOT won by Khalid or Herman? (2 marks)
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Algebra, STD2 A1 2005 HSC 2 MC
What is the value of `(a-b)/4`, if `a = 240` and `b = 56`?
- `4`
- `46`
- `226`
- `736`
Probability, STD2 S2 2007 HSC 25c
In a stack of 10 DVDs, there are 5 rated PG, 3 rated G and 2 rated M.
- A DVD is selected at random. What is the probability that it is rated M? (1 mark)
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Grant chooses two DVDs at random from the stack. Copy or trace the tree diagram into your writing booklet.
- Complete the tree diagram by writing the correct probability on each branch. (2 marks)
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- Calculate the probability that Grant chooses two DVDs with the same rating. (2 marks)
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Algebra, STD2 A1 2007 HSC 24b
The distance in kilometres (`D`) of an observer from the centre of a thunderstorm can be estimated by counting the number of seconds (`t`) between seeing the lightning and first hearing the thunder.
Use the formula `D = t/3` 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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Measurement, STD2 M7 2007 HSC 4 MC
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?
- $196
- $329
- $1169
- $1316
Financial Maths, STD2 F1 2008 HSC 24a
Bob is employed as a salesman. He is offered two methods of calculating his income.
\begin{array} {|l|}
\hline
\rule{0pt}{2.5ex}\text{Method 1: Commission only of 13% on all sales}\rule[-1ex]{0pt}{0pt} \\
\hline
\rule{0pt}{2.5ex}\text{Method 2: \$350 per week plus a commission of 4.5% on all sales}\rule[-1ex]{0pt}{0pt} \\
\hline
\end{array}
Bob’s research determines that the average sales total per employee per month is $15 670.
- Based on his research, how much could Bob expect to earn in a year if he were to choose Method 1? (2 marks)
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- 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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Statistics, STD2 S1 2008 HSC 10 MC
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?
- 4
- 6
- 8
- 9
Algebra, STD2 A4 2008 HSC 4 MC
Measurement, STD2 M1 2008 HSC 2 MC
Measurement, STD2 M1 2014 HSC 27c
Algebra, STD2 A1 2014 HSC 26c
Solve the equation `(5x + 1)/3-4 = 5-7x`. (3 marks)
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?
- `8/31 xx 7/30`
- `8/31 xx 7/31`
- `8/31 xx 8/30`
- `8/31 xx 8/31`
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?
- $188.40
- $208.40
- $321.85
- $652.05
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?
- 0.036%
- 0.050%
- 0.072%
- 0.289%
Statistics, STD2 S1 2010 HSC 27b
The graphs show the distribution of the ages of children in Numbertown in 2000 and 2010.
- In 2000 there were 1750 children aged 0–18 years.
How many children were aged 12–18 years in 2000? (1 mark)
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- 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)
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- 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)
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- 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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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.
Probability, STD2 S2 2011 HSC 15 MC
An unbiased coin is tossed 10 times.
A tail is obtained on each of the first 9 tosses.
What is the probability that a tail is obtained on the 10th toss?
- `1/2^10`
- `1/2`
- `1/10`
- `9/10`
Algebra, STD2 A1 2009 HSC 25a
Simplify `5-2(x + 7)`. (2 marks)
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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.
- Calculate the percentage error in the measurement of the longer side. (1 mark)
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- Between what lower and upper limits does the actual area of the top of the chopping board lie? (2 marks)
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Probability, STD2 S2 2013 HSC 26c
The probability that Michael will score more than 100 points in a game of bowling is `31/40`.
- A commentator states that the probability that Michael will score less than 100 points in a game of bowling is `9/40`.
Is the commentator correct? Give a reason for your answer. (1 mark)
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- 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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Algebra, STD2 A1 2010 HSC 24a
Fred tried to solve this equation and made a mistake in Line 2.
\begin{array}{rl}
4(y+2)-3(y+1)= -3\ & \ \ \ \text{Line 1} \\
4y+8-3y+3= -3\ &\ \ \ \text{Line 2} \\
y+11 =-3\ &\ \ \ \text{Line 3} \\
y =-14& \ \ \ \text{Line 3}
\end{array}
Copy the equation in Line 1.
- Rewrite Line 2 correcting his mistake. (1 mark)
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- Continue your solution showing the correct working for Lines 3 and 4 to solve this equation for `y`. (1 mark)
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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 ?
- `0.18`
- `0.28`
- `0.42`
- `0.46`
Measurement, STD2 M1 2009 HSC 23c
The diagram shows the shape and dimensions of a terrace which is to be tiled.
- Find the area of the terrace. (2 marks)
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- 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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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?
- $7.02
- $12.48
- $14.04
- $16.05
Measurement, STD2 M6 2009 HSC 4 MC
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.
- Complete the probability tree diagram below. (2 marks)
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- Calculate the probability that the two scarves selected are made from silk. (1 mark)
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- Calculate the probability that the two scarves selected are made from different fabrics. (2 marks)
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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, `d`, that the ramp will extend beyond the bottom step.
Give your answer to the nearest centimetre. (3 marks)
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Measurement, STD2 M7 2012 HSC 27c
A map has a scale of 1 : 500 000.
- Two mountain peaks are 2 cm apart on the map.
What is the actual distance between the two mountain peaks, in kilometres? (1 mark)
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- Two cities are 75 km apart. How far apart are the two cities on the map, in centimetres? (1 mark)
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Statistics, STD2 S1 2011 HSC 7 MC
Algebra, STD2 A4 2011 HSC 6 MC
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?
- $2170
- $2180
- $3003
- $3700
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?
- $370.70
- $372.10
- $458.60
- $490.10
Measurement, STD2 M1 2012 HSC 6 MC
Measurement, STD2 M6 2012 HSC 4 MC
Measurement, STD2 M1 2013 HSC 19 MC
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?
- `1/6`
- `1/12`
- `5/12`
- `5/36`
Measurement, STD2 M1 2013 HSC 17 MC
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?
- 4.17%
- 4.55%
- 8.33%
- 9.09%
Financial Maths, STD2 F1 2013 HSC 11 MC
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?
- $1046.88
- $1047.09
- $1296.88
- $1468.75
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?
- $583.20
- $620.40
- $669.60
- $719.60
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