Aussie Maths & Science Teachers: Save your time with SmarterEd
The table shows the types of customer complaints received by an online business in a month.
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Lily wanted to estimate the number of fish in a lake.
She randomly captured 30 fish, then tagged and released them.
One week later she randomly captured 40 fish from the same lake. She found that 12 of these 40 fish were tagged.
What is the best estimate for the total number of fish in the lake?
Which of the following could be the graph of `y= –2 x+2`?
Which graph represents a negatively skewed distribution?
The diagram shows a model of electromagnetic waves.
Relate this model to predictions made by Maxwell. (4 marks)
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A step-up transformer is constructed using a solid iron core. The coils are made using copper wires of different thicknesses as shown.
The table shows electrical data for this transformer.
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In the apparatus shown, a backboard is connected by a rod to a shaft. The shaft is spun by an electric motor causing the backboard to rotate in the horizontal plane around the axis X `–` X′.
A cube is suspended by a string so that it touches the surface of the backboard.
When the angular velocity of the motor is great enough, the string is cut and the position of the cube does not change relative to the backboard.
Which statement correctly describes the forces after the string is cut?
Consider the following nuclear reaction.
\(\text{W} + \text{X} \rightarrow \text{Y} + \text{Z}\)
Information about W, X and Y is given in the table.
\begin{array}{|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{Species} & \textit{Mass defect} & \textit{Total binding energy} & \textit{Binding energy per nucleon}\\
\textit{} & \textit{(u)} \rule[-1ex]{0pt}{0pt}& \text{(MeV)} & \text{(MeV)}\\
\hline \rule{0pt}{2.5ex}\text{W} \rule[-1ex]{0pt}{0pt}& 0.00238817 & 2.224566 & 1.112283 \\
\hline \rule{0pt}{2.5ex}\text{X} \rule[-1ex]{0pt}{0pt}& 0.00910558 & 8.481798 & 2.827266 \\
\hline \rule{0pt}{2.5ex}\text{Y }\rule[-1ex]{0pt}{0pt}& 0.03037664 & 28.29566 & 7.073915 \\
\hline
\end{array}
Which of the following is a correct statement about energy in this reaction?
A straight current-carrying conductor, `QR`, is connected to a battery and a variable resistor. `QR` is enclosed in an evacuated chamber with a fluorescent screen at one end.
A cathode ray enters the chamber directly above `Q`, initially travelling parallel to `QR`. It passes through the chamber and strikes the fluorescent screen causing a bright spot.
Which direction will this spot move towards if the resistance is increased?
The diagram shows the trajectory of a particle with charge `q` and mass `m` when fired horizontally into a vacuum chamber, where it falls under the influence of gravity.
The horizontal distance, `d`, travelled by the particle is recorded.
The experiment is repeated with a uniform vertical electric field applied such that the particle travels the same horizontal distance, `d`, but strikes the upper surface of the chamber.
What is the magnitude of the electric field?
A satellite in circular orbit at a distance `r` from the centre of Earth has an orbital velocity `v`.
If the distance was increased to `2r`, what would be the satellite's orbital velocity?
A laser has a power output of 30 mW and emits light with a wavelength of 650 nm.
How many photons does this laser emit per second?
The table shows two types of quarks and their respective charges.
In a particular nuclear transformation, a particle having a quark composition `udd` is transformed into a particle having a quark composition `u ud`.
What is another product of this transformation?
Two satellites have the same mass. One (LEO) is in low-Earth orbit and the other (GEO) is in a geostationary orbit.
The total energy of a satellite is half its gravitational potential energy.
Which row of the table correctly identifies the satellite with the greater orbital period and the satellite with the greater total energy?
\begin{align*}
\begin{array}{l}
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt}& \\
\rule{0pt}{2.5ex}\textbf{A.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{B.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{C.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{D.}\rule[-1ex]{0pt}{0pt}\\
\end{array}
\begin{array}{|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{Greater orbital period}\rule[-1ex]{0pt}{0pt}& \textit{Greater total energy} \\
\hline
\rule{0pt}{2.5ex}\text{LEO}\rule[-1ex]{0pt}{0pt}&\text{LEO}\\
\hline
\rule{0pt}{2.5ex}\text{LEO}\rule[-1ex]{0pt}{0pt}& \text{GEO}\\
\hline
\rule{0pt}{2.5ex}\text{GEO}\rule[-1ex]{0pt}{0pt}& \text{LEO} \\
\hline
\rule{0pt}{2.5ex}\text{GEO}\rule[-1ex]{0pt}{0pt}& \text{GEO} \\
\hline
\end{array}
\end{align*}
A bar magnet is moved away from a stationary coil.
Which diagram correctly shows the direction of the induced current in the coil and the resulting magnetic polarity of the coil?
A rope connects a mass on a horizontal surface to a pulley attached to an electric motor as shown.
Explain the factors that limit the speed at which the mass can be pulled along the horizontal surface. Use mathematical models to support your answer. (7 marks)
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Explain, using an example, how a particle accelerator has provided evidence for the Standard Model of matter. (3 marks)
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A spacecraft is powered by a radioisotope generator. Pu-238 in the generator undergoes alpha decay, releasing energy. The decay is shown with the mass of each species in atomic mass units, `u`
\begin{array} {ccccc}
\ce{^{238}Pu} & \rightarrow & \ce{^{234}U} & + & \alpha \\
238.0495\ u & & 234.0409\ u & & 4.0026\ u \end{array}
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The graph shows the levels of three hormones, oestrogen, progesterone and human chorionic gonadotrophin (HCG), measured in the blood of a woman during her pregnancy.
Which statement can be inferred from the graph?
A quantity of silver nitrate is added to 250.0 mL of 0.100 mol L ¯1 potassium sulfate at 298 K in order to produce a precipitate. Silver nitrate has a molar mass of 169.9 g mol ¯1.
What mass of silver nitrate will cause precipitation to start?
The table lists the information from a proton NMR spectrum.
Which compound could have produced this spectrum?
A sample was contaminated with sodium phosphate. The sample was dissolved in water and added to an excess of acidified \(\ce{(NH_4)_2MoO_4}\) to produce a precipitate of \(\ce{(NH_4)_3PO_4.12MoO_3\ \ \ \ \ \ ($MM$ = 1877 g mol^{-1})} \).
If 24.21 g of dry \(\ce{(NH_4)_3PO_4.12MoO_3}\) was obtained, what was the mass of sodium phosphate in the original sample?
This titration curve is produced when an acid is titrated with a sodium hydroxide solution of the same concentration.
How many acidic protons does this acid possess?
What is the pH of the resultant solution after 20.0 mL of 0.20 mol `text{L}^{-1}\ text{HCl} (aq)` is mixed with 20.0 mL of 0.50 mol `text{L}^{-1}\ text{NaOH} (aq)`?
A sample of nickel was dissolved in nitric acid to produce a solution with a volume of 50.00 mL. 10.00 mL of this solution was then diluted to 250.0 mL. This solution was subjected to colorimetric analysis. A calibration curve for this analysis is given.
The solution gave an absorbance value of 0.30.
What was the mass of the sample of nickel?
A metal rod sits on a pair of parallel metal rails, 20 cm apart, that are connected by a copper wire. The rails are at 30° to the horizontal.
The apparatus is in a uniform magnetic field of 1 T which is upward, perpendicular to the table.
A force, `F`, is applied parallel to the rails to move the rod at a constant speed along the rails. The rod is moved a distance of 30 cm in 2.5 s.
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The following apparatus is used to investigate light interference using a double slit.
The distance, `y`, from the slits to the screen can be varied. The adjustment screws `(S)` vary the distance, `d`, between the slits. The wavelength of the laser light can be varied across the visible spectrum. The diffraction pattern shown is for a specific wavelength of light.
Explain TWO methods of keeping the distance between the maxima at `A` and `B` constant when the wavelength of the laser light is reduced. (4 marks)
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Identify an assumption of EACH model which determines the shape of its curve. (2 marks)
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On the same diagram, sketch a curve for a black body radiator at a temperature of 4000 K and explain the differences between the curves. (4 marks)
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a. The spectra of light produced by a gas discharge tube will consist of lines only at a few discrete wavelengths.
The spectra of light produced by an incandescent lamp will be a continuous spectrum.
b. Model `X` black bodies absorb and emit energy continuously.
Model `Y` assumes that black bodies absorb and emit energy in discrete quantities.
c.
Using `lambda_(max)=(b)/(T)\ \ =>\ \ lambda prop (1)/(T)`
Therefore, the 4000 K curve will have a peak wavelength greater than the 5000 K curve.
The area under the curve and the intensity at all wavelengths will be less for the 4000 K curve, as the total power output of a black body decreases as its temperature decreases.
a. Differences:
→ The spectra of light produced by a gas discharge tube will consist of lines only at a few discrete wavelengths.
→ The spectra of light produced by an incandescent lamp will be a continuous spectrum.
b. Assumptions of EACH model:
→ Model `X` black bodies absorb and emit energy continuously.
→ Model `Y` assumes that black bodies absorb and emit energy in discrete quantities.
c.
Using `lambda_(max)=(b)/(T)\ \ =>\ \ lambda prop (1)/(T)`
Therefore, the 4000 K curve will have a peak wavelength greater than the 5000 K curve.
The area under the curve and the intensity at all wavelengths will be less for the 4000 K curve, as the total power output of a black body decreases as its temperature decreases.
Describe the hydrogen atom in terms of the Standard Model of matter. (4 marks)
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A capsule travelling at 12 900 m s ¯1 enters Earth's atmosphere, causing it to rapidly slow down to 400 m s ¯1.
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The diagram shows a smooth, semi-circular, vertical wall with radius, `r`.
A ball is launched from the position shown with a velocity `u` towards north at an angle to the horizontal.
The ball follows a trajectory around the wall before landing on the ground, opposite its starting point. It does not reach the top of the wall.
Assume that there is no friction between the ball and the wall.
Which statement correctly describes the net force acting on the ball during its motion?
Two parallel wires, `X` and `Y`, each carry a current `I`.
The magnitude and direction of the force on wire `Y` are represented by the vector `F`.
The current in wire `Y` is then doubled and its direction is reversed. The current in wire `X` remains unchanged.
Which vector arrow represents the force on wire `X` after the change to the current in wire `Y`?
The graph shows the relationship between the frequency of light used to irradiate two different metals, and the maximum kinetic energy of photoelectrons emitted.
Suppose that light having a frequency of `8 × 10^(14)` Hz is used to irradiate both metals.
Compared to the photoelectrons emitted from metal `X`, photoelectrons emitted from metal `Y` will
An electron travelling in a straight line with an initial velocity, `u`, enters a region between two charged plates in which there is an electric field causing it to travel along the path as shown.
A magnetic field is then applied causing a second electron with the same initial velocity to pass through undeflected.
Which row of the table shows the directions of the electric and magnetic fields when the second electron enters the region between the plates?
\begin{align*}
\begin{array}{l}
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt}& \\
\rule{0pt}{2.5ex}\textbf{A.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{B.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{C.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{D.}\rule[-1ex]{0pt}{0pt}\\
\end{array}
\begin{array}{|l|c|}
\hline
\rule{0pt}{2.5ex}\quad \quad \textit{Electric Field}\quad \rule[-1ex]{0pt}{0pt}& \quad \textit{Magnetic Field} \quad \\
\hline
\rule{0pt}{2.5ex}\text{Towards top of page}\rule[-1ex]{0pt}{0pt}&\text{Into page}\\
\hline
\rule{0pt}{2.5ex}\text{Towards top of page}\rule[-1ex]{0pt}{0pt}& \text{Out of page}\\
\hline
\rule{0pt}{2.5ex}\text{Towards bottom of page}\rule[-1ex]{0pt}{0pt}& \text{Into page} \\
\hline
\rule{0pt}{2.5ex}\text{Towards bottom of page}\rule[-1ex]{0pt}{0pt}& \text{Out of page} \\
\hline
\end{array}
\end{align*}
The Hertzsprung-Russell diagram shows characteristics of stars in a globular cluster 100 light years in diameter and 27 000 light years from Earth.
The stars plotted on this Hertzsprung-Russell diagram have approximately the same
Two experiments are performed with identical light sources having a wavelength of 400 nm.
In experiment \(A\), the light is incident on a pair of narrow slits \(5.0 \times 10^{-5}\) m apart, producing a pattern on a screen located 3.0 m behind the slits.
In experiment \(B\), the light is incident on different metal samples inside an evacuated tube as shown. The kinetic energy of any emitted photoelectrons can be measured.
Some results from experiment \(B\) are shown.
\begin{array}{|l|l|c|}
\hline
\rule{0pt}{1.5ex}\textit{Metal sample}\rule[-0.5ex]{0pt}{0pt}& \textit{Work function} \ \text{(J)} & \textit{Photoelectrons observed?} \\
\hline
\rule{0pt}{2.5ex}\text{Nickel}\rule[-1ex]{0pt}{0pt}&8.25 \times 10^{-19}&\text{No}\\
\hline
\rule{0pt}{2.5ex}\text{Calcium}\rule[-1ex]{0pt}{0pt}& 4.60 \times 10^{-19}&\text{Yes}\\
\hline
\end{array}
How do the results from Experiment \(A\) and Experiment \(B\) support TWO different models of light? In your answer, include a quantitative analysis of each experiment. (9 marks)
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Two students perform an investigation with a piece of elastic laid out straight on a table. The elastic is fixed at one end and has three markings at regular intervals. The distances from each marking to the fixed end, `d_1, d_2` and `d_3`, are measured as shown.
A student pulls the elastic to extend it, and the new values of `d_1, d_2` and `d_3` are measured. The student observes that each value has doubled.
How well do the observations from this investigation model the evidence that led to Hubble's discovery of the expansion of the universe? Justify your answer. (5 marks)
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Two identical solenoids are mounted on carts as shown. Each solenoid is connected to a galvanometer, and the solenoid on cart 1 is also connected to an open switch and a battery. The total mass of cart 1 is twice that of cart 2.
Explain what would be observed when the switch on cart 1 is closed. In your answer, refer to the current in each galvanometer and the initial movement of the carts. (7 marks)
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Bohr, de Broglie and Schrödinger EACH proposed a model for the structure of the atom.
How does the nature of the electron proposed in each of the three models differ? (5 marks)
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A spaceship travels to a distant star at a constant speed, `v`. When it arrives, 15 years have passed on Earth but 9.4 years have passed for an astronaut on the spaceship.
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Rh-106 is a metallic, beta-emitting radioisotope with a half-life of 30 seconds.
A sample of Rh-106 and an electrode are placed inside an evacuated chamber. They are connected to a galvanometer and a variable DC power supply.
A student measures the current, `I`, when the power supply is set to zero. They then measure the stopping voltage, `V_s`. The stopping voltage is the minimum voltage needed to prevent current flowing.
A few minutes later, these measurements are repeated.
How do the TWO sets of measurements compare?
An evacuated chamber contains a pair of parallel plates connected to a power supply and a switch which is initially closed.
A positively charged mass (•) falls within the chamber, under the influence of gravity, from the position shown.
When the mass has fallen half the height of the chamber, the switch is opened.
Which of the following correctly shows the trajectory of the mass?
Two long, parallel conductors `X` and `Y` are connected to a light bulb and an AC power supply. The conductors are suspended horizontally from fixed points using sensitive spring balances. `X` is positioned directly below `Y`.
Which statement correctly compares the forces measured by the spring balances?
Unpolarised light is incident upon two consecutive polarisers as shown. The second polariser has a fixed transmission axis which cannot be rotated. `I_1` is the intensity of light after the first polariser, and `I_2` is the intensity of light after the second polariser.
How would `I_1` and `I_2` be affected if the transmission axis of the first polariser was rotated?
Which graph shows the magnitude of back emf induced in a DC motor rotating continuously at different angular velocities?
A mass, `M`, is positioned at an equal distance from two identical stars as shown.
The mass is then moved to position `X`.
Which graph best represents the gravitational potential energy, `U`, of the mass during this movement?
In a certain ideal transformer, the current in the secondary coil is four times as large as the current in the primary coil.
Which row of the table correctly identifies the type of transformer and the ratio of turns?
\begin{align*}
\begin{array}{l}
\rule{0pt}{0.5ex}\textit{} & \textit{} \\
\textit{}\rule[-0.5ex]{0pt}{0pt}& \textit{} \\
\rule{0pt}{2.5ex}\textbf{A.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{B.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{C.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{D.}\rule[-1ex]{0pt}{0pt}\\
\end{array}
\begin{array}{|l|c|}
\hline
\rule{0pt}{0.5ex} \quad \textit{Type of} & \textit{Ratio of turns in primary coil} \\
\textit{transformer}\rule[-0.5ex]{0pt}{0pt}& \textit{to turns in secondary coil} \\
\hline
\rule{0pt}{2.5ex}\text{Step up}\rule[-1ex]{0pt}{0pt}&4:1\\
\hline
\rule{0pt}{2.5ex}\text{Step up}\rule[-1ex]{0pt}{0pt}& 1:4\\
\hline
\rule{0pt}{2.5ex}\text{Step down}\rule[-1ex]{0pt}{0pt}& 4:1 \\
\hline
\rule{0pt}{2.5ex}\text{Step down}\rule[-1ex]{0pt}{0pt}& 1:4 \\
\hline
\end{array}
\end{align*}
The Sun has an energy output of `3.85 × 10^{28}\ `W.
By how much does the Sun's mass decrease each minute?
A positively charged particle is moving at velocity, `v`, in an electric field as shown.
What is the direction of the force acting on the particle due to the electric field?
A student used the following method to titrate an acetic acid solution of unknown concentration with a standardised solution of dilute sodium hydroxide.
Compared to the actual concentration of the acetic acid, the calculated concentration will be
Streptomycin is an antibiotic that kills bacteria by interfering with the function of their ribosomes.
The primary effect of the antibiotic is that it prevents the bacteria from producing
A mutation involving a DNA deletion is illustrated.
Which statement about the mutation is correct?
Glucose levels are maintained by the hormones insulin and glucagon.
Which statement best describes the changes in hormone levels of a healthy human soon after a high glucose meal?
Let `f: R to R, \ f(x)=x^{3}-x`.
Let `g_{a}: R to R` be the function representing the tangent to the graph of `f` at `x=a`, where `a in R`.
Let `(b, 0)` be the `x`-intercept of the graph of `g_{a}`.
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The coordinate `(b, 0)` is the horizontal axis intercept of `g_a`.
Let `g_b` be the function representing the tangent to the graph of `f` at `x=b`, as shown in the graph below.
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Let `p:R rarr R, \ p(x)=x^(3)+wx`, where `w in R`.
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A property of the graphs of `p` is that two distinct parallel tangents will always occur at `(t, p(t))` and `(-t,p(-t))` for all `t!=0`.
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The graph of the function `f(x)=2xe^((1-x^(2)))`, where `0 <= x <= 3`, is shown below.
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Two line segments connect the points `(0, f(0))` and `(3, f(3))` to a single point `Q(n, f(n))`, where `1 < n < 3`, as shown in the graph below.
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The Sunny Coast cricket clubroom is undergoing a major works project.
This project involves nine activities: `A` to `I`.
The table below shows the earliest start time (EST) and duration, in months, for each activity.
The immediate predecessor(s) is also shown.
The duration for activity `C` is missing.
The information in the table above can be used to complete a directed network.
This network will require a dummy activity.
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What is the minimum time, in months, that the project can be completed in? (1 mark)
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a. `B\ text{to the start of activity}\ C.`
b. `text{Sketch network diagram.}`
`text{Duration of Activity C = 2 months}`
c. `text{Critical path:}\ BCDGI`
`text{Activities with a float time are activities}`
`text{not on critical path.}`
`:. \ text{Four activities are:}\ \ A, E, F, H`
d. `text{Completion time of}\ BCDGI = 20\ text{months}`
`text{Reduce the completion of}\ B\ text{by 3 months to create}`
`text{a new minimum completion time of 17 months.}`
A transport company has detailed records of all its deliveries. The number of minutes a delivery is made before or after its schedule delivery time can be modelled as a normally distributed random variable, `T`, with a mean of zero and a standard deviation of four minutes. A graph of the probability distribution of `T` is shown below. --- 3 WORK AREA LINES (style=lined) --- --- 3 WORK AREA LINES (style=lined) --- --- 5 WORK AREA LINES (style=lined) --- A rival transport company claims that there is a 0.85 probability that each delivery it makes will arrive on time or earlier. Assume that whether each delivery is on time or earlier is independent of other deliveries. --- 3 WORK AREA LINES (style=lined) --- --- 3 WORK AREA LINES (style=lined) --- --- 3 WORK AREA LINES (style=lined) --- --- 5 WORK AREA LINES (style=lined) ---
Hence, or otherwise, find the minimum value of `n` such that there is at least a 0.95 probability that one or more deliveries will not arrive on time or earlier. (1 mark)
