Which of the following could represent the graph of `y = -x^2 + 1`?
Functions, 2ADV F1 2020 HSC 1 MC
Which inequality gives the domain of `y = sqrt(2x-3)`?
- `x < 3/2`
- `x > 3/2`
- `x <= 3/2`
- `x >= 3/2`
Statistics, STD1 S3 2019 HSC 27
A set of bivariate data is collected by measuring the height and arm span of eight children. The graph shows a scatterplot of these measurements.
- On the graph, draw a line of best fit by eye. (1 mark)
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- Robert is a child from the class who was absent when the measurements were taken. He has an arm span of 147 cm. Using your line of best fit from part (a), estimate Robert’s height. (1 mark)
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Probability, STD1 S2 2019 HSC 24
The faces on a biased six-sided die are labelled 1, 2, 3, 4, 5 and 6. The die was rolled twenty times. The relative frequency of rolling a 6 was 30% and the relative frequency of rolling a 2 was 15%. The number 3 was the only other number rolled in the twenty rolls.
How many times was the number 3 rolled in the twenty rolls of the die? (3 marks)
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Measurement, STD1 M1 2019 HSC 15
Networks, STD1 N1 2019 HSC 1 MC
Functions, EXT1 F2 2019 HSC 11d
Find the polynomial `Q(x)` that satisfies `x^3 + 2x^2-3x-7 = (x-2) Q(x) + 3`. (2 marks)
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Financial Maths, STD2 F4 2019 HSC 37
A new car is bought for $24 950. Each year the value of the car is depreciated by the same percentage.
The table shows the value of the car, based on the declining-balance method of depreciation, for the first three years.
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{End of year}\rule[-1ex]{0pt}{0pt} & \textit{Value}\\
\hline
\rule{0pt}{2.5ex}1\rule[-1ex]{0pt}{0pt} & \$21\ 457.00 \\
\hline
\rule{0pt}{2.5ex}2\rule[-1ex]{0pt}{0pt} & \$18\ 453.02 \\
\hline
\rule{0pt}{2.5ex}3\rule[-1ex]{0pt}{0pt} & \$15\ 869.60 \\
\hline
\end{array}
What is the value of the car at the end of 10 years? (3 marks)
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Algebra, STD2 A2 2019 HSC 34
The relationship between British pounds `(p)` and Australian dollars `(d)` on a particular day is shown in the graph.
- Write the direct variation equation relating British pounds to Australian dollars in the form `p = md`. Leave `m` as a fraction. (1 mark)
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- The relationship between Japanese yen `(y)` and Australian dollars `(d)` on the same day is given by the equation `y = 76d`.
Convert 93 100 Japanese yen to British pounds. (2 marks)
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Algebra, STD2 A4 2019 HSC 33
The time taken for a car to travel between two towns at a constant speed varies inversely with its speed.
It takes 1.5 hours for the car to travel between the two towns at a constant speed of 80 km/h.
- Calculate the distance between the two towns. (1 mark)
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- By first plotting four points, draw the curve that shows the time taken to travel between the two towns at different constant speeds. (3 marks)
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Probability, STD2 S2 2019 HSC 25
A bowl of fruit contains 17 apples of which 9 are red and 8 are green.
Dennis takes one apple at random and eats it. Margaret also takes an apple at random and eats it.
By drawing a probability tree diagram, or otherwise, find the probability that Dennis and Margaret eat apples of the same colour. (3 marks)
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Algebra, STD2 A2 2019 HSC 14 MC
Last Saturday, Luke had 165 followers on social media. Rhys had 537 followers. On average, Luke gains another 3 followers per day and Rhys loses 2 followers per day.
If `x` represents the number of days since last Saturday and `y` represents the number of followers, which pair of equations model this situation?
A. | `text(Luke:)\ \ y = 165x + 3`
`text(Rhys:)\ \ y = 537x - 2` |
B. | `text(Luke:)\ \ y = 165 + 3x`
`text(Rhys:)\ \ y = 537 - 2x` |
C. | `text(Luke:)\ \ y = 3x + 165`
`text(Rhys:)\ \ y = 2x - 537` |
D. | `text(Luke:)\ \ y = 3 + 165x`
`text(Rhys:)\ \ y = 2 - 537x` |
Financial Maths, STD2 F4 2019 HSC 13 MC
Measurement, STD2 M6 2019 HSC 12 MC
An owl is 7 metres above ground level, in a tree. The owl sees a mouse on the ground at an angle of depression of 32°.
How far must the owl fly in a straight line to catch the mouse, assuming the mouse does not move?
- 3.7 m
- 5.9 m
- 8.3 m
- 13.2 m
Algebra, STD2 A1 2019 HSC 11 MC
Which of the following correctly expresses `y` as the subject of the formula `3x-4y-1 = 0`
- `y = 3/4 x-1`
- `y = 3/4 x + 1`
- `y = (3x-1)/4`
- `y = (3x + 1)/4`
Financial Maths, STD2 F1 2019 HSC 9 MC
What is the interest earned, in dollars, if $800 is invested for `x` months at a simple interest rate of 3% per annum?
- `2x`
- `24x`
- `200x`
- `2400x`
Measurement, STD2 M1 2019 HSC 8 MC
A person's weight is measured as 79.3 kg.
What is the absolute error of this measurement?
- 10 grams
- 50 grams
- 100 grams
- 500 grams
Financial Maths, STD2 F1 2019 HSC 7 MC
Julia earns $28 per hour. Her hourly pay rate increases by 2%.
How much will she earn for a 4-hour shift with this increase?
- $2.24
- $28.56
- $112
- $114.24
Measurement, STD2 M6 2019 HSC 4 MC
Which compass bearing is the same as a true bearing of 110°?
- `text(S20°E)`
- `text(S20°W)`
- `text(S70°E)`
- `text(S70°W)`
Financial Maths, STD2 F4 2019 HSC 3 MC
Chris opens a bank account and deposits $1000 into it. Interest is paid at 3.5% per annum, compounding annually.
Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of two years?
- $1070.00
- $1071.23
- $1822.50
- $2070.00
Measurement, STD2 M6 2019 HSC 22
Probability, STD2 S2 2019 HSC 20
Measurement, STD2 M1 2019 HSC 16
L&E, 2ADV E1 2019 HSC 5 MC
Which of the following is equal to `(log_2 9)/(log_2 3)`?
- `2`
- `3`
- `log_2 3`
- `log_2 6`
L&E, 2ADV E1 2019 HSC 3 MC
What is the value of `p` so that `(a^2a^(-3))/sqrt a = a^p`?
- `-3`
- `-3/2`
- `-1/2`
- `12`
Functions, 2ADV F1 2019 HSC 2 MC
What values of `x` satisfy `4-3x <= 12`?
- `x <= -16/3`
- `x >= -16/3`
- `x <= -8/3`
- `x >= -8/3`
Statistics, STD2 S1 SM-Bank 1 MC
A survey asked the following question for students born in Australia:
"Which State or Territory were you born in?"
How would the responses be classified?
- Categorical, ordinal
- Categorical, nominal
- Numerical, discrete
- Numerical, continuous
Measurement, STD2 M1 2008 HSC 21 MC
A sphere and a closed cylinder have the same radius.
The height of the cylinder is four times the radius.
What is the ratio of the volume of the cylinder to the volume of the sphere?
- `2 : 1`
- `3 : 1`
- `4 : 1`
- `8 : 1`
Plane Geometry, 2UA 2018 HSC 13b
In `Delta ABC`, sides `AB` and `AC` have length 3, and `BC` has length 2. The point `D` is chosen on `AB` so that `DC` has length 2.
- Prove that `Delta ABC` and `Delta CBD` are similar. (2 marks)
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- Find the length `AD`. (2 marks)
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Plane Geometry, 2UA 2018 HSC 12c
The diagram shows the square `ABCD`. The point `E` is chosen on `BC` and the point `F` is chosen on `CD` so that `EC = FC`.
- Prove that `Delta ADF` is congruent to `Delta ABE`. (2 marks)
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- The side length of the square is 14 cm and `EC` has length 4 cm. Find the area of `AECF`. (2 marks)
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Measurement, STD2 M6 2018 HSC 30c
The diagram shows two triangles.
Triangle `ABC` is right-angled, with `AB = 13 text(cm)` and `/_ABC = 62°`.
In triangle `ACD, \ AD = x\ text(cm)` and `/_DAC = 40°`. The area of triangle `ACD` is 30 cm².
What is the value of `x`, correct to one decimal place? (3 marks)
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Financial Maths, STD2 F1 2018 HSC 30b
Last year, Luke’s taxable income was `$87\ 000` and the tax payable on this income was `$19\ 822`. This year, Luke’s taxable income has increased by `$16\ 800`.
- Use the table to calculate the tax payable by Luke this year. (2 marks)
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- 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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Measurement, STD2 M1 2018 HSC 30a
Algebra, STD2 A1 2018 HSC 28b
Solve the equation `(2x)/5 + 1 = (3x + 1)/2`, leaving your answer as a fraction. (3 marks)
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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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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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Functions, 2ADV F1 2018 HSC 3 MC
What is the `x`-intercept of the line `x + 3y + 6 = 0`?
- `(-6, 0)`
- `(6, 0)`
- `(0, -2)`
- `(0, 2)`
Linear Functions, 2UA 2018 HSC 2 MC
Probability, STD2 S2 2018 HSC 20 MC
Measurement, STD2 M1 2018 HSC 18 MC
The length of a window is measured as 2.4 m.
Which calculation will give the percentage error for this measurement?
- `0.05/2.4 xx 100`
- `0.05/100 xx 2.4`
- `0.5/2.4 xx 100`
- `0.5/100 xx 2.4`
Measurement, STD2 M1 2018 HSC 13 MC
Measurement, STD2 M6 2018 HSC 12 MC
Statistics, STD2 S1 2018 HSC 11 MC
Probability, STD2 S2 2018 HSC 9 MC
An experiment has three distinct outcomes, A, B and C. Outcome A occurs 50% of the time. Outcome B occurs 23% of the time.
What is the expected number of times outcome C would occur if the experiment is conducted 500 times?
- 115
- 135
- 250
- 365
Algebra, STD2 A4 2018 HSC 4 MC
Which graph best represents the equation `y = x^2-2`?
A. | B. | ||
C. | D. |
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?
- Categorical, ordinal
- Categorical, nominal
- Numerical, discrete
- Numerical, continuous
Plane Geometry, EXT1 2018 HSC 11d
Functions, EXT1 F2 2018 HSC 11a
Consider the polynomial `P(x) = x^3-2x^2-5x + 6`.
- Show that `x = 1` is a zero of `P(x)`. (1 mark)
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- Find the other zeros. (2 marks)
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Measurement, STD2 M1 2017 HSC 30e
A solid is made up of a sphere sitting partially inside a cone.
The sphere, centre `O`, 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 `V=1/3 pi r^2h` where `r` is the radius of the cone's circular base and `h` is the perpendicular height of the cone, find the volume of the cone, correct to the nearest cm³? (3 marks)
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Plane Geometry, 2UA 2017 HSC 15a
The triangle `ABC` is isosceles with `AB = AC` and the size of `/_BAC` is `x^@`.
Points `D` and `E` are chosen so that `Delta ABC, Delta ACD` and `Delta ADE` are congruent, as shown in the diagram.
Find the value of `x` for which `AB` is parallel to `ED`, giving reasons. (3 marks)
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Functions, EXT1 F2 2017 HSC 1 MC
Which polynomial is a factor of `x^3-5x^2 + 11x-10`?
- `x-2`
- `x + 2`
- `11x-10`
- `x^2-5x + 11`
Functions, 2ADV F1 2017 HSC 11h
Find the domain of the function `f(x) = sqrt (3-x)`. (2 marks)
Functions, EXT1* F1 2017 HSC 8 MC
The region enclosed by `y = 4 - x,\ \ y = x` and `y = 2x + 1` is shaded in the diagram below.
Which of the following defines the shaded region?
(A) | `y <= 2x + 1, qquad` | `y <= 4-x, qquad` | `y >= x` |
(B) | `y >= 2x + 1, qquad` | `y <= 4-x, qquad` | `y >= x` |
(C) | `y <= 2x + 1, qquad` | `y >= 4-x, qquad` | `y >= x` |
(D) | `y >= 2x + 1, qquad` | `y >= 4-x, qquad` | `y >= x` |
Functions, 2ADV F1 2017 HSC 2 MC
Which expression is equal to `3x^2-x-2`?
- `(3x-1) (x + 2)`
- `(3x + 1) (x-2)`
- `(3x-2) (x + 1)`
- `(3x + 2) (x-1)`
Functions, 2ADV F1 2017 HSC 1 MC
What is the gradient of the line `2x + 3y + 4 = 0`?
- `-2/3`
- `2/3`
- `-3/2`
- `3/2`
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.
- What ticket price should be charged to maximise the income from a movie session? (1 mark)
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- What is the number of tickets sold when the income is maximised? (1 mark)
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- 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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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.
`220, 105, 101, 450, 37, 338, 151, 205`
- Calculate the mean of this set of data. (1 mark)
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- What is the standard deviation of this set of data, correct to one decimal place? (1 mark)
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Measurement, STD2 M6 2017 HSC 26d
Measurement, STD2 M1 2017 HSC 25 MC
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