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
Measurement, STD2 M6 2008 HSC 5 MC
Algebra, 2UG 2008 HSC 1 MC
Which expression is equivalent to `12k^3 ÷ 4k`?
- `3k^2 `
- `3k^3`
- `8k^2`
- `8k^3`
Algebra, STD2 A4 2008 HSC 4 MC
Measurement, STD2 M1 2008 HSC 2 MC
Plane Geometry, 2UA 2008 HSC 4a
Linear Functions, 2UA 2008 HSC 2b
Let `M` be the midpoint of `(-1, 4)` and `(5, 8)`.
Find the equation of the line through `M` with gradient `-1/2`. (2 marks)
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Functions, 2ADV F1 2008 HSC 1e
Expand and simplify `(sqrt3-1)(2 sqrt3 + 5)`. (2 marks)
Functions, 2ADV F1 2008 HSC 1c
Simplify `2/n-1/(n+1)`. (2 marks)
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Functions, EXT1 F2 2014 HSC 9 MC
The remainder when the polynomial `P(x) = x^4-8x^3-7x^2 + 3` is divided by `x^2 + x` is `ax + 3`.
What is the value of `a`?
- `-14`
- `-11`
- `-2`
- `5`
Plane Geometry, EXT1 2014 HSC 1 MC
Functions, EXT1 F2 2009 HSC 2a
The polynomial `p(x) = x^3-ax + b` has a remainder of `2` when divided by `(x-1)` and a remainder of `5` when divided by `(x + 2)`.
Find the values of `a` and `b`. (3 marks)
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Functions, 2ADV F1 2014 HSC 5 MC
Which equation represents the line perpendicular to `2x-3y = 8`, passing through the point `(2, 0)`?
- `3x + 2y = 4`
- `3x + 2y = 6`
- `3x-2y = -4`
- `3x-2y = 6`
L&E, 2ADV E1 2014 HSC 3 MC
What is the solution to the equation `log_2(x-1) = 8`?
- `4`
- `17`
- `65`
- `257`
Algebra, STD2 A4 2014 HSC 29a
The cost of hiring an open space for a music festival is $120 000. The cost will be shared equally by the people attending the festival, so that `C` (in dollars) is the cost per person when `n` people attend the festival.
- Complete the table below by filling in the THREE missing values. (1 mark)
\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Number of people} (n) \rule[-1ex]{0pt}{0pt} & \ 500\ & \ 1000 \ & 1500 \ & 2000 \ & 2500\ & 3000 \ \\
\hline
\rule{0pt}{2.5ex}\text{Cost per person} (C)\rule[-1ex]{0pt}{0pt} & & & & 60 & 48\ & 40 \ \\
\hline
\end{array} - Using the values from the table, draw the graph showing the relationship between `n` and `C`. (2 marks)
- What equation represents the relationship between `n` and `C`? (1 mark)
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- Give ONE limitation of this equation in relation to this context. (1 mark)
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- Is it possible for the cost per person to be $94? Support your answer with appropriate calculations. (1 mark)
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Measurement, STD2 M1 2014 HSC 27c
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)
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Algebra, STD2 A1 2014 HSC 26c
Solve the equation `(5x + 1)/3-4 = 5-7x`. (3 marks)
Measurement, STD2 M1 2014 HSC 25 MC
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
Algebra, 2UG 2014 HSC 11 MC
Simplify `6w^4 xx 1/3 w^2`.
- `2w^6`
- `2w^8`
- `18w^6`
- `18w^8`
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%
Financial Maths, STD2 F4 2014 HSC 9 MC
A car is bought for $19 990. It will depreciate at 18% per annum.
Using the declining balance method, what will be the salvage value of the car after 3 years, to the nearest dollar?
- $8968
- $9195
- $11 022
- $16 392
Probability, STD2 S2 2014 HSC 8 MC
Algebra, STD2 A2 2014 HSC 7 MC
Algebra, STD2 A4 2014 HSC 3 MC
Functions, EXT1 F2 2013 HSC 1 MC
The polynomial `P(x) = x^3-4x^2-6x + k` has a factor `x-2`.
What is the value of `k`?
- `2`
- `12`
- `20`
- `36`
Functions, EXT1 F2 2010 HSC 2c
Let `P(x) = (x + 1)(x-3) Q(x) + ax + b`,
where `Q(x)` is a polynomial and `a` and `b` are real numbers.
The polynomial `P(x)` has a factor of `x-3`.
When `P(x)` is divided by `x + 1` the remainder is `8`.
- Find the values of `a` and `b`. (2 marks)
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- Find the remainder when `P(x)` is divided by `(x + 1)(x-3)`. (1 mark)
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Functions, EXT1 F1 2010 HSC 1d
Solve `3/(x+2) < 4`. (3 marks)
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Functions, EXT1 F2 2011 HSC 2a
Let `P(x) = x^3-ax^2 + x` be a polynomial, where `a` is a real number.
When `P(x)` is divided by `x-3` the remainder is `12`.
Find the remainder when `P(x)` is divided by `x + 1`. (3 marks)
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Plane Geometry, EXT1 2012 HSC 10 MC
Functions, EXT1 F2 2012 HSC 8 MC
When the polynomial `P(x)` is divided by `(x + 1)(x-3)`, the remainder is `2x + 7`.
What is the remainder when `P(x)` is divided by `x-3`?
- `1`
- `7`
- `9`
- `13`
Functions, EXT1 F1 2011 HSC 1c
Solve `(4-x)/x <1`. (3 marks)
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Functions, EXT1* F1 2009 HSC 3c
Shade the region in the plane defined by `y >= 0` and `y <= 4-x^2`. (2 marks)
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Functions, 2ADV F1 2009 HSC 1a
Sketch the graph of `y-2x = 3`, showing the intercepts on both axes. (2 marks)
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Functions, 2ADV F1 2010 HSC 1g
Let `f(x) = sqrt(x-8)`. What is the domain of `f(x)`? (1 mark)
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Functions, 2ADV F1 2010 HSC 1c
Write down the equation of the circle with centre `(-1, 2)` and radius 5. (1 mark)
Functions, 2ADV F1 2010 HSC 1a
Solve `x^2 = 4x`. (2 marks)
Plane Geometry, 2UA 2011 HSC 6a
The diagram shows a regular pentagon `ABCDE`. Sides `ED` and `BC` are produced to meet at `P`.
- Find the size of `/_CDE`. (1 mark)
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- Hence, show that `Delta EPC` is isosceles. (2 marks)
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Functions, EXT1* F1 2012 HSC 8 MC
Functions, EXT1* F1 2013 HSC 11g
Sketch the region defined by `(x-2)^2 + ( y-3)^2 >= 4`. (3 marks)
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Functions, 2ADV F1 2013 HSC 3 MC
Which inequality defines the domain of the function `f(x) = 1/sqrt(x+3)` ?
- `x > -3`
- `x >= -3`
- `x < -3`
- `x <= -3`
Functions, 2ADV F1 2013 HSC 1 MC
What are the solutions of `2x^2-5x-1 = 0`?
- `x = (-5 +-sqrt17)/4`
- `x = (5 +-sqrt17)/4`
- `x = (-5 +-sqrt33)/4`
- `x = (5 +-sqrt33)/4`
Algebra, STD2 A4 2011 HSC 28a
The air pressure, `P`, in a bubble varies inversely with the volume, `V`, of the bubble.
- Write an equation relating `P`, `V` and `a`, where `a` is a constant. (1 mark)
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- It is known that `P = 3` when `V = 2`.
By finding the value of the constant, `a`, find the value of `P` when `V = 4`. (2 marks)
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- Sketch a graph to show how `P` varies for different values of `V`.
Use the horizontal axis to represent volume and the vertical axis to represent air pressure. (2 marks)
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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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Algebra, 2UG 2010 HSC 27a
Fully simplify `(4x^2)/(3y) -: (xy)/5`. (3 marks)
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Measurement, STD2 M6 2010 HSC 26d
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 A4 2009 HSC 28c
The height above the ground, in metres, of a person’s eyes varies directly with the square of the distance, in kilometres, that the person can see to the horizon.
A person whose eyes are 1.6 m above the ground can see 4.5 km out to sea.
How high above the ground, in metres, would a person’s eyes need to be to see an island that is 15 km out to sea? Give your answer correct to one decimal place. (3 marks)
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Statistics, STD2 S4 2009 HSC 28b
The height and mass of a child are measured and recorded over its first two years.
\begin{array} {|l|c|c|}
\hline \rule{0pt}{2.5ex} \text{Height (cm), } H \rule[-1ex]{0pt}{0pt} & \text{45} & \text{50} & \text{55} & \text{60} & \text{65} & \text{70} & \text{75} & \text{80} \\
\hline \rule{0pt}{2.5ex} \text{Mass (kg), } M \rule[-1ex]{0pt}{0pt} & \text{2.3} & \text{3.8} & \text{4.7} & \text{6.2} & \text{7.1} & \text{7.8} & \text{8.8} & \text{10.2} \\
\hline
\end{array}
This information is displayed in a scatter graph.
- Describe the correlation between the height and mass of this child, as shown in the graph. (1 mark)
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- A line of best fit has been drawn on the graph.
Find the equation of this line. (2 marks)
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Probability, STD2 S2 2009 HSC 27c
In each of three raffles, 100 tickets are sold and one prize is awarded.
Mary buys two tickets in one raffle. Jane buys one ticket in each of the other two raffles.
Determine who has the better chance of winning at least one prize. Justify your response using probability calculations. (4 marks)
Algebra, STD2 A1 2009 HSC 25a
Simplify `5-2(x + 7)`. (2 marks)
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Algebra, STD2 A1 2013 HSC 29a
Sarah tried to solve this equation and made a mistake in Line 2.
`(W+4)/3-(2W-1)/5` | `=1` | `text(... Line 1)` |
`5W+ 20-6W-3` | `=15` | `text(... Line 2)` |
`17-W` | `=15` | `text(... Line 3)` |
`W` | `=2` | `text(... Line 4)` |
Copy the equation in Line 1 and continue your solution to solve this equation for `W`.
Show all lines of working. (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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Measurement, STD2 M6 2010 HSC 24d
The base of a lighthouse, `D`, is at the top of a cliff 168 metres above sea level. The angle of depression from `D` to a boat at `C` is 28°. The boat heads towards the base of the cliff, `A`, and stops at `B`. The distance `AB` is 126 metres.
- What is the angle of depression from `D` to `B`, correct to the nearest degree? (3 marks)
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- How far did the boat travel from `C` to `B`, correct to the nearest metre? (2 marks)
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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`