EXAMCOPY Algebra, STD2 A2 2022 HSC 16
Tom is 25 years old, and likes to keep fit by exercising.
- Use this formula to find his maximum heart rate (bpm).
- Maximum heart rate = 220 – age in years
- Tom's maximum heart rate is ........................... bpm. (1 mark)
- Tom will get the most benefit from this exercise if his heart rate is between 50% and 85% of his maximum heart rate.
- Between what two heart rates should Tom be aiming for to get the most benefit from his exercise? (2 marks)
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EXAMCOPY Algebra, STD2 A4 2022 HSC 22
The formula `C=100 n+b` is used to calculate the cost of producing laptops, where `C` is the cost in dollars, `n` is the number of laptops produced and `b` is the fixed cost in dollars.
- Find the cost when 1943 laptops are produced and the fixed cost is $20 180. (1 mark)
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- Some laptops have some extra features added. The formula to calculate the production cost for these is
- `C=100 n+a n+20\ 180`
- where `a` is the additional cost in dollars per laptop produced.
- Find the number of laptops produced if the additional cost is $26 per laptop and the total production cost is $97 040. (2 marks)
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v1 Algebra, STD2 A1 2005 HSC 2 MC
What is the value of \(\dfrac{x-y}{6}\), if \(x=184\) and \(y=46\)?
- \(6\)
- \(23\)
- \(176\)
- \(552\)
v1 Algebra, STD2 A1 2006 HSC 2 MC
If \(V=\dfrac{4}{3}\pi r^3\), what is the value of \(V\) when \(r = 5\), correct to two decimal places?
- \(20.94\)
- \(53.05\)
- \(104.72\)
- \(523.60\)
v1 Algebra, STD2 A1 2016 HSC 2 MC
Which of the following equations has \(x=7\) as the solution?
- \(x-7=14\)
- \(7-x=14\)
- \(2x=14\)
- \(\dfrac{x}{2}=14\)
v1 Algebra, STD2 A1 SM-Bank 2
If \(A=P(1 + r)^n\), find \(A\) given \(P=$500\), \(r=0.09\) and \(n=5\) (give your answer to the nearest cent). (2 marks)
v1 Algebra, STD2 A1 SM-Bank 3
Find the value of \(b\) given \(\dfrac{b}{9}-5=3\). (1 mark)
v1 Algebra, STD2 A1 SM-Bank 13
If \(\dfrac{x-8}{9}=2\), find \(x\). (1 mark)
v1 Algebra, STD2 A1 2017 HSC 7 MC
It is given that \(I=\dfrac{3}{2}MR^2\).
What is the value of \(I\) when \(M =19.12\) and \(R = 1.02\), correct to two decimal places?
- \(13.26\)
- \(29.84\)
- \(119.35\)
- \(570.52\)
PHYSICS, M6 2019 VCE 1 MC
Magnetic and gravitational forces have a variety of properties.
Which of the following best describes the attraction/repulsion properties of magnetic and gravitational forces?
Magnetic forces | Gravitational forces | |
A. | either attract or repel | only attract |
B. | only repel | neither attract nor repel |
C. | only attract | only attract |
D. | either attract or repel | either attract or repel |
Probability, MET2 2022 VCAA 3
Mika is flipping a coin. The unbiased coin has a probability of \(\dfrac{1}{2}\) of landing on heads and \(\dfrac{1}{2}\) of landing on tails.
Let \(X\) be the binomial random variable representing the number of times that the coin lands on heads.
Mika flips the coin five times.
- i. Find \(\text{Pr}(X=5)\). (1 mark)
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ii. Find \(\text{Pr}(X \geq 2).\) (1 mark)
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- iii. Find \(\text{Pr}(X \geq 2 | X<5)\), correct to three decimal places. (2 marks)
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- iv. Find the expected value and the standard deviation for \(X\). (2 marks)
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The height reached by each of Mika's coin flips is given by a continuous random variable, \(H\), with the probability density function
\(f(h)=\begin{cases} ah^2+bh+c &\ \ 1.5\leq h\leq 3 \\ \\ 0 &\ \ \text{elsewhere} \\ \end{cases}\)
where \(h\) is the vertical height reached by the coin flip, in metres, between the coin and the floor, and \(a, b\) and \(c\) are real constants.
- i. State the value of the definite integral \(\displaystyle\int_{1.5}^3 f(h)\,dh\). (1 mark)
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- ii. Given that \(\text{Pr}(H \leq 2)=0.35\) and \(\text{Pr}(H \geq 2.5)=0.25\), find the values of \(a, b\) and \(c\). (3 marks)
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- iii. The ceiling of Mika's room is 3 m above the floor. The minimum distance between the coin and the ceiling is a continuous random variable, \(D\), with probability density function \(g\).
- The function \(g\) is a transformation of the function \(f\) given by \(g(d)=f(rd+s)\), where \(d\) is the minimum distance between the coin and the ceiling, and \(r\) and \(s\) are real constants.
- Find the values of \(r\) and \(s\). (1 mark)
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- Mika's sister Bella also has a coin. On each flip, Bella's coin has a probability of \(p\) of landing on heads and \((1-p)\) of landing on tails, where \(p\) is a constant value between 0 and 1 .
- Bella flips her coin 25 times in order to estimate \(p\).
- Let \(\hat{P}\) be the random variable representing the proportion of times that Bella's coin lands on heads in her sample.
-
- Is the random variable \(\hat{P}\) discrete or continuous? Justify your answer. (1 mark)
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- If \(\hat{p}=0.4\), find an approximate 95% confidence interval for \(p\), correct to three decimal places. (1 mark)
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- Bella knows that she can decrease the width of a 95% confidence interval by using a larger sample of coin flips.
- If \(\hat{p}=0.4\), how many coin flips would be required to halve the width of the confidence interval found in part c.ii.? (1 mark)
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- Is the random variable \(\hat{P}\) discrete or continuous? Justify your answer. (1 mark)
Calculus, MET2 2022 VCAA 2
On a remote island, there are only two species of animals: foxes and rabbits. The foxes are the predators and the rabbits are their prey.
The populations of foxes and rabbits increase and decrease in a periodic pattern, with the period of both populations being the same, as shown in the graph below, for all `t \geq 0`, where time `t` is measured in weeks.
One point of minimum fox population, (20, 700), and one point of maximum fox population, (100, 2500), are also shown on the graph.
The graph has been drawn to scale.
The population of rabbits can be modelled by the rule `r(t)=1700 \sin \left(\frac{\pi t}{80}\right)+2500`.
- i. State the initial population of rabbits. (1 mark)
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- ii. State the minimum and maximum population of rabbits. (1 mark)
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- iii. State the number of weeks between maximum populations of rabbits. (1 mark)
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The population of foxes can be modelled by the rule `f(t)=a \sin (b(t-60))+1600`.
- Show that `a=900` and `b=\frac{\pi}{80}`. (2 marks)
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- Find the maximum combined population of foxes and rabbits. Give your answer correct to the nearest whole number. (1 mark)
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- What is the number of weeks between the periods when the combined population of foxes and rabbits is a maximum? (1 mark)
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The population of foxes is better modelled by the transformation of `y=\sin (t)` under `Q` given by
- Find the average population during the first 300 weeks for the combined population of foxes and rabbits, where the population of foxes is modelled by the transformation of `y=\sin(t)` under the transformation `Q`. Give your answer correct to the nearest whole number. (4 marks)
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Over a longer period of time, it is found that the increase and decrease in the population of rabbits gets smaller and smaller.
The population of rabbits over a longer period of time can be modelled by the rule
- Find the average rate of change between the first two times when the population of rabbits is at a maximum. Give your answer correct to one decimal place. (2 marks)
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- Find the time, where `t>40`, in weeks, when the rate of change of the rabbit population is at its greatest positive value. Give your answer correct to the nearest whole number. (2 marks)
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- Over time, the rabbit population approaches a particular value.
- State this value. (1 mark)
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Calculus, MET2 2022 VCAA 1
The diagram below shows part of the graph of `y=f(x)`, where `f(x)=\frac{x^2}{12}`.
- State the equation of the axis of symmetry of the graph of `f`. (1 mark)
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- State the derivative of `f` with respect to `x`. (1 mark)
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The tangent to `f` at point `M` has gradient `-2` .
- Find the equation of the tangent to `f` at point `M`. (2 marks)
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The diagram below shows part of the graph of `y=f(x)`, the tangent to `f` at point `M` and the line perpendicular to the tangent at point `M`.
- i. Find the equation of the line perpendicular to the tangent passing through point `M`. (1 mark)
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- ii. The line perpendicular to the tangent at point `M` also cuts `f` at point `N`, as shown in the diagram above.
- Find the area enclosed by this line and the curve `y=f(x)`. (2 marks)
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- Another parabola is defined by the rule `g(x)=\frac{x^2}{4 a^2}`, where `a>0`.
- A tangent to `g` and the line perpendicular to the tangent at `x=-b`, where `b>0`, are shown below.
- Find the value of `b`, in terms of `a`, such that the shaded area is a minimum. (4 marks)
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Graphs, MET2 2022 VCAA 1 MC
The period of the function `f(x)=3 \ cos (2 x+\pi)` is
- `2 \pi`
- `\pi`
- `\frac{2\pi}{3}`
- `2`
- `3`
Calculus, MET2 2023 VCAA 3
Consider the function \(g:R \to R, g(x)=2^x+5\).
- State the value of \(\lim\limits_{x\to -\infty} g(x)\). (1 mark)
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- The derivative, \(g'(x)\), can be expressed in the form \(g'(x)=k\times 2^x\).
- Find the real number \(k\). (1 mark)
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-
- Let \(a\) be a real number. Find, in terms of \(a\), the equation of the tangent to \(g\) at the point \(\big(a, g(a)\big)\). (1 mark)
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- Let \(a\) be a real number. Find, in terms of \(a\), the equation of the tangent to \(g\) at the point \(\big(a, g(a)\big)\). (1 mark)
-
- Hence, or otherwise, find the equation of the tangent to \(g\) that passes through the origin, correct to three decimal places. (2 marks)
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- Hence, or otherwise, find the equation of the tangent to \(g\) that passes through the origin, correct to three decimal places. (2 marks)
Let \(h:R\to R, h(x)=2^x-x^2\).
- Find the coordinates of the point of inflection for \(h\), correct to two decimal places. (1 mark)
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- Find the largest interval of \(x\) values for which \(h\) is strictly decreasing.
- Give your answer correct to two decimal places. (1 mark)
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- Apply Newton's method, with an initial estimate of \(x_0=0\), to find an approximate \(x\)-intercept of \(h\).
- Write the estimates \(x_1, x_2,\) and \(x_3\) in the table below, correct to three decimal places. (2 marks)
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \qquad x_0\qquad \ \rule[-1ex]{0pt}{0pt} & \qquad \qquad 0 \qquad\qquad \\
\hline
\rule{0pt}{2.5ex} x_1 \rule[-1ex]{0pt}{0pt} & \\
\hline
\rule{0pt}{2.5ex} x_2 \rule[-1ex]{0pt}{0pt} & \\
\hline
\rule{0pt}{2.5ex} x_3 \rule[-1ex]{0pt}{0pt} & \\
\hline
\end{array}
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- For the function \(h\), explain why a solution to the equation \(\log_e(2)\times (2^x)-2x=0\) should not be used as an initial estimate \(x_0\) in Newton's method. (1 mark)
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- There is a positive real number \(n\) for which the function \(f(x)=n^x-x^n\) has a local minimum on the \(x\)-axis.
- Find this value of \(n\). (2 marks)
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Calculus, MET2 2023 VCAA 1
Let \(f:R \rightarrow R, f(x)=x(x-2)(x+1)\). Part of the graph of \(f\) is shown below.
- State the coordinates of all axial intercepts of \(f\). (1 mark)
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- Find the coordinates of the stationary points of \(f\). (2 marks)
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-
- Let \(g:R\rightarrow R, g(x)=x-2\).
- Find the values of \(x\) for which \(f(x)=g(x)\). (1 mark)
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-
- Write down an expression using definite integrals that gives the area of the regions bound by \(f\) and \(g\). (2 marks)
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- Hence, find the total area of the regions bound by \(f\) and \(g\), correct to two decimal places. (1 mark)
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- Write down an expression using definite integrals that gives the area of the regions bound by \(f\) and \(g\). (2 marks)
- Let \(h:R\rightarrow R, h(x)=(x-a)(x-b)^2\), where \(h(x)=f(x)+k\) and \(a, b, k \in R\).
- Find the possible values of \(a\) and \(b\). (4 marks)
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Data Analysis, GEN2 2023 VCAA 2a
The following data shows the sizes of a sample of 20 oysters rated as small, medium or large.
\begin{array} {ccccc}
\text{small} & \text{small} & \text{large} & \text{medium} & \text{medium} \\
\text{medium} & \text{large} & \text{small} & \text{medium} & \text{medium}\\
\text{small} & \text{medium} & \text{small} & \text{small} & \text{medium}\\
\text{medium} & \text{medium} & \text{medium} & \text{small} & \text{large}
\end{array}
- Use the data above to complete the following frequency table. (1 mark)
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- Use the percentages in the table to construct a percentage segmented bar chart below. A key has been provided. (1 mark)
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Data Analysis, GEN1 2023 VCAA 1-2 MC
The dot plot below shows the times, in seconds, of 40 runners in the qualifying heats of their 800 m club championship.
Question 1
The median time, in seconds, of these runners is
- 135.5
- 136
- 136.5
- 137
- 137
Question 2
The shape of this distribution is best described as
- positively skewed with one or more possible outliers.
- positively skewed with no outliers.
- approximately symmetric with one or more possible outliers.
- approximately symmetric with no outliers.
- negatively skewed with one or more possible outliers.
ENGINEERING, TE 2023 HSC 3 MC
Why is pure copper preferred over a copper alloy in telecommunications applications?
- It has higher stiffness.
- It has better conductivity.
- It can be precipitation hardened.
- It has a better strength to weight ratio.
ENGINEERING, PPT 2023 HSC 24a
Roller coaster support structures can be made from either timber or steel. Compare the properties of the two materials in roller coaster support structures. (2 marks) --- 4 WORK AREA LINES (style=lined) ---
ENGINEERING, AE 2023 HSC 21b
You are part of a team of engineers working collaboratively on the design of a new aircraft. Explain the benefits of collaboration when completing the engineering report. (3 marks) --- 6 WORK AREA LINES (style=lined) ---
ENGINEERING, AE 2023 HSC 21a
How can computer graphics be utilised as a tool in aeronautical engineering? (2 marks) --- 4 WORK AREA LINES (style=lined) ---
PHYSICS, M2 2017 VCE 7 MC
A model car of mass 2.0 kg is propelled from rest by a rocket motor that applies a constant horizontal force of 4.0 N, as shown below. Assume that friction is negligible.
Which one of the following best gives the magnitude of the acceleration of the model car?
- \(0.50 \text{ m s} ^{-2}\)
- \(1.0 \text{ m s}^{-2}\)
- \(2.0 \text{ m s} ^{-2}\)
- \( 4.0\text{ m s} ^{-2}\)
PHYSICS, M4 2021 VCE 2 MC
The diagram below shows the electric field lines between four charged spheres: \(\text{P, Q, R}\) and \(\text{S}\). The magnitude of the charge on each sphere is the same.
Which of the following correctly identifies the type of charge (+ positive or – negative) that resides on each of the spheres \(\text{P, Q, R}\) and \(\text{S}\)?
\(\textbf{P}\) | \(\textbf{Q}\) | \(\textbf{R}\) | \(\textbf{S}\) | |
A. | \(\quad - \quad\) | \(\quad + \quad\) | \(\quad - \quad\) | \(\quad + \quad\) |
B. | \(\quad + \quad\) | \(\quad - \quad\) | \(\quad + \quad\) | \(\quad - \quad\) |
C. | \(\quad - \quad\) | \(\quad - \quad\) | \(\quad + \quad\) | \(\quad + \quad\) |
D. | \(\quad + \quad\) | \(\quad + \quad\) | \(\quad - \quad\) | \(\quad - \quad\) |
CHEMISTRY, M3 2012 HSC 3 MC
What effect does a catalyst have on a reaction?
- It increases the rate.
- It increases the yield.
- It increases the heat of reaction.
- It increases the activation energy.
CHEMISTRY, M3 2017 VCE 1 MC
A catalyst
- slows the rate of reaction.
- ensures that a reaction is exothermic.
- moves the chemical equilibrium of a reaction in the forward direction.
- provides an alternative pathway for the reaction with a lower activation energy.
CHEMISTRY, M2 2016 VCE 9a
Standard solutions of sodium hydroxide, \(\ce{NaOH}\), must be kept in airtight containers. This is because \(\ce{NaOH}\) is a strong base and absorbs acidic oxides, such as carbon dioxide, \(\ce{CO2}\), from the air and reacts with them. As a result, the concentration of \(\ce{NaOH}\) is changed to an unknown extent.
\(\ce{CO2}\) in the air reacts with water to form carbonic acid, \(\ce{H2CO3}\). This can react with \(\ce{NaOH}\) to form sodium carbonate, \(\ce{Na2CO3}\).
- Write a balanced overall equation for the reaction between \(\ce{CO2}\) gas and water to form \(\ce{H2CO3}\). (1 mark)
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- Write a balanced equation for the complete reaction between \(\ce{H2CO3}\) and \(\ce{NaOH}\) to form \(\ce{Na2CO3}\). (1 mark)
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PHYSICS, M2 2014 HSC 3 MC
A pendulum is used to determine the value of acceleration due to gravity. The length of the pendulum is varied, and the time taken for the same number of oscillations is recorded.
Which of the following could increase the reliability of the results?
- Changing the mass of the pendulum
- Identifying the independent and dependent variables
- Recording all measurements to at least four significant figures
- Repeating each measurement several times and recording the average
CHEMISTRY, M7 2023 HSC 1 MC
What is the safest method for disposing of a liquid hydrocarbon after an experiment?
- Pour it down the sink
- Place it in a garbage bin
- Burn it by igniting with a match
- Place it in a separate waste container
PHYSICS, M5 2023 HSC 1 MC
The gravitational field strength acting on a spacecraft decreases as its altitude increases.
This is due to a change in the
- mass of Earth.
- mass of the spacecraft.
- density of the atmosphere.
- distance of the spacecraft from Earth's centre.
Vectors, EXT2 V1 2023 HSC 11b
Find the angle between the vectors
\(\underset{\sim}{a}=\underset{\sim}{i}+2 \underset{\sim}{j}-3 \underset{\sim}{k}\)
\(\underset{\sim}{b}=-\underset{\sim}{i}+4 \underset{\sim}{j}+2 \underset{\sim}{k}\),
giving your answer to the nearest degree. (3 marks)
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Calculus, EXT1 C1 2023 HSC 1 MC
The temperature \(T(t)^{\circ} \text{C}\) of an object at time \(t\) seconds is modelled using Newton's Law of Cooling,
\(T(t)=15+4 e^{-3 t}\)
What is the initial temperature of the object?
- \(-3\)
- \(4\)
- \(15\)
- \(19\)
Complex Numbers, EXT2 N1 2023 HSC 1 MC
Which of the following is equal to \((a+i b)^3\)?
- \( (a^3-3 a b^2)+i (3 a^2 b+b^3) \)
- \( (a^3+3 a b^2)+i (3 a^2 b+b^3) \)
- \( (a^3-3 a b^2)+i (3 a^2 b-b^3) \)
- \( (a^3+3 a b^2)+i(3 a^2 b-b^3)\)
Financial Maths, 2ADV M1 2023 HSC 11
The first three terms of an arithmetic sequence are 3, 7 and 11 .
Find the 15th term. (2 marks)
Algebra, STD2 A4 2023 HSC 20
On another planet, a ball is launched vertically into the air from the ground. The height above the ground, `h` metres, can be modelled using the function `h=-6 t^2+24t`, where `t` is measured in seconds. The graph of the function is shown. --- 1 WORK AREA LINES (style=lined) --- --- 3 WORK AREA LINES (style=lined) ---
Measurement, STD2 M7 2023 HSC 16
The graph shows Peta's heart rate, in beats per minute, during the first 60 minutes of a marathon.
- What was Peta's heart rate 20 minutes after she started her marathon? (1 mark)
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- Peta started the marathon at 10 am. At what time would her heart rate first reach 140 beats/minute? (1 mark)
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BIOLOGY, M7 EQ-Bank 1 MC
All pathogens can be described as
- infectious.
- macroscopic.
- microscopic.
- viral.
BIOLOGY, M5 EQ-Bank 1 MC
A strawberry plant will send out over the ground runners which will take root and grow a new plant as shown.
This method of growing a new plant is an example of
- budding.
- binary fission.
- external fertilisation.
- asexual reproduction.
Vectors, EXT2 V1 EQ-Bank 3
If `underset ~a = 3 underset ~i-underset ~j` and `underset ~b = −2 underset ~i + 6 underset ~j + 2underset ~k`
- Calculate `underset ~a-1/2underset ~b` (2 marks)
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- Find `hat underset ~b` (2 marks)
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Vectors, EXT2 V1 EQ-Bank 2
Find the angle between the vectors `underset~r = ((3),(-2),(-1))` and `underset~s = ((2),(1),(1))`, giving the angle in degrees correct to 1 decimal place. (3 marks)
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Vectors, EXT2 V1 EQ-Bank 1
Prove that the vectors `4 underset ~i + 5 underset ~j - 2 underset ~k` and ` −5 underset ~i + 6 underset ~j + 5underset ~k`, are perpendicular. (2 marks)
BIOLOGY, M7 2014 HSC 22a
Explain how TWO specific personal hygiene practices reduce the risk of infection. (4 marks)
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BIOLOGY, M7 2014 HSC 22b
Drinking water contaminated with dissolved lead (a heavy metal) can cause a serious disease.
Classify this disease as either infectious or non-infectious. Justify your answer. (2 marks)
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BIOLOGY, M6 2014 HSC 1 MC
Exposure to radiation such as X-rays may change the sequence of bases in DNA.
What is this called?
- Mutation
- Translation
- Replication
- Transcription
ENGINEERING, PPT 2017 HSC 4 MC
Specifications for a Ø10 steel bar require it to have a tolerance of `pm`0.05 mm.
What is the permitted range of diameters for this bar?
- 9.90`-`10.00 mm
- 9.95`-`10.00 mm
- 9.95`-`10.05 mm
- 10.00`-`10.05 mm
ENGINEERING, PPT 2018 HSC 21a
The diagram shows a self-driving electric vehicle.
Innovations in global positioning systems (GPS) and sensor technologies are used in the operation of this vehicle.
Describe how both of these innovations are used in the control of the vehicle. (3 marks)
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BIOLOGY, M8 2017 HSC 2 MC
Which of the following body systems is involved in detecting and responding to environmental changes?
- Circulatory
- Digestive
- Excretory
- Nervous
BIOLOGY, M8 2017 HSC 1 MC
What is the name of the process that enables organisms to maintain a relatively stable internal environment?
- Osmosis
- Adaptation
- Homeostasis
- Active transport
CHEMISTRY, M8 2018 HSC 4 MC
Which of the following greatly enhanced scientific understanding of the effects of trace elements?
- Improved filtration techniques
- The development of atomic absorption spectroscopy
- The creation of new elements in particle accelerators
- The work of Le Chatelier in describing chemical equilibrium
CHEMISTRY, M6 2016 HSC 7 MC
Which indicator in the table would be best for distinguishing between lemon juice (pH = 2.3) and potato juice (pH = 5.8)?
ENGINEERING, AE 2022 HSC 17 MC
During routine maintenance, ultrasonic testing is performed on some aircraft components such as aircraft landing gear.
What is the reason for performing this test?
- It can be performed quickly.
- It reveals any surface defects.
- It reveals any hidden internal faults.
- It can be carried out using simple techniques.
PHYSICS, M5 2015 HSC 21
A projectile is fired horizontally from a platform.
Measurements of the distance travelled by the projectile from the base of the platform are made for a range of initial velocities.
- Graph the data on the grid provided and draw the line of best fit. (2 marks)
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- Calculate the height of the platform. (2 marks)
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PHYSICS, M5 2017 HSC 4 MC
An astronaut with a mass of 75 kg lands on Planet X where her weight is 630 N.
What is the acceleration due to gravity (in `text{m s}^(-2)`) on Planet X ?
- 0.12
- 8.4
- 9.8
- 735
Measurement, STD1 M4 2022 HSC 15
Tom is 25 years old, and likes to keep fit by exercising.
- Use this formula to find his maximum heart rate (bpm).
- Maximum heart rate = 220 – age in years
- Tom's maximum heart rate is .................... bpm. (1 mark)
- Tom will get the most benefit from this exercise if his heart rate is between 50% and 85% of his maximum heart rate.
- Between what two heart rates should Tom be aiming for to get the most benefit from his exercise? (2 marks)
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Algebra, STD1 A2 2022 HSC 12
The cost of hiring a campervan is $210 per day. There is also a charge of $0.35 per km travelled.
A family hired a campervan for 9 days and travelled 2700 km.
How much did the family pay in total? (2 marks)
Calculus, EXT2 C1 2022 HSC 14b
Let `J_(n)=int_(0)^(1)x^(n)e^(-x)\ dx`, where "n" is a non-negative integer.
- Show that `J_(0)=1-(1)/(e)`. (1 mark)
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- Show that `J_(n) <= (1)/(n+1)`. (2 marks)
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- Show that `J_(n)=nJ_(n-1)-(1)/(e)`. (2 marks)
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- Using parts (i) and (iii), show by mathematical induction, or otherwise, that for all `n >= 1`,
- `J_(n)=n!-(n!)/(e)sum_(r=0)^(n)(1)/(r!)` (2 marks)
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- Using parts (ii) and (iv) prove that `e=lim_(n rarr oo)sum_(r=0)^(n)(1)/(r!)`. (1 mark)
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BIOLOGY, M8 2019 HSC 1 MC
Which of the following is an example of a non-infectious disease?
- Polio caused by a virus
- Cholera caused by a bacterium
- Wheat rust caused by a fungus
- Haemophilia caused by a gene mutation
BIOLOGY, M7 2022 HSC 21a
Outline ONE way that a pathogen can pass from person to person. (2 marks)
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ENGINEERING, TE 2020 HSC 21a
Outline how ONE telecommunications engineering innovation has influenced traditional voice communication systems. (2 marks)
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